From 5515f588e3e56399196d1570dc13f98f3c1aaa41 Mon Sep 17 00:00:00 2001
From: c9s <yoanlin93@gmail.com>
Date: Wed, 31 May 2023 19:35:44 +0800
Subject: [PATCH] all: add parameter index to the Last method

---
 pkg/bbgo/exit_lower_shadow_take_profit.go     |   2 +-
 pkg/bbgo/stop_ema.go                          |   2 +-
 pkg/bbgo/trend_ema.go                         |   4 +-
 pkg/datatype/floats/slice.go                  |   8 +-
 pkg/indicator/ad.go                           |  13 +-
 pkg/indicator/alma.go                         |  11 +-
 pkg/indicator/alma_test.go                    |   2 +-
 pkg/indicator/atr.go                          |   8 +-
 pkg/indicator/atr_test.go                     |   2 +-
 pkg/indicator/atrp.go                         |  10 +-
 pkg/indicator/boll.go                         |   8 +-
 pkg/indicator/boll_test.go                    |   4 +-
 pkg/indicator/cci.go                          |  20 +-
 pkg/indicator/cci_test.go                     |   2 +-
 pkg/indicator/cma.go                          |  23 +-
 pkg/indicator/dema.go                         |  17 +-
 pkg/indicator/dema_test.go                    |   2 +-
 pkg/indicator/dmi.go                          |  10 +-
 pkg/indicator/dmi_test.go                     |   6 +-
 pkg/indicator/drift.go                        |  20 +-
 pkg/indicator/emv.go                          |   5 +-
 pkg/indicator/emv_test.go                     |   4 +-
 pkg/indicator/ewma.go                         |  14 +-
 pkg/indicator/fisher.go                       |  10 +-
 pkg/indicator/float64updater.go               |  10 +-
 pkg/indicator/ghfilter.go                     |  14 +-
 pkg/indicator/ghfilter_test.go                |  10 +-
 pkg/indicator/gma.go                          |   9 +-
 pkg/indicator/gma_test.go                     |   4 +-
 pkg/indicator/hull.go                         |   9 +-
 pkg/indicator/hull_test.go                    |   2 +-
 pkg/indicator/interface.go                    |   2 +-
 pkg/indicator/kalmanfilter.go                 |  22 +-
 pkg/indicator/kalmanfilter_test.go            |  10 +-
 pkg/indicator/klingeroscillator.go            |  11 +-
 pkg/indicator/line.go                         |   6 +-
 pkg/indicator/linreg.go                       |  25 +-
 pkg/indicator/low.go                          |   2 +-
 pkg/indicator/macd.go                         |  23 +-
 pkg/indicator/macd_test.go                    |   2 +-
 pkg/indicator/obv.go                          |  18 +-
 pkg/indicator/pivot.go                        |   5 +-
 pkg/indicator/pivothigh.go                    |   6 +-
 pkg/indicator/pivotlow.go                     |   6 +-
 pkg/indicator/psar.go                         |  10 +-
 pkg/indicator/psar_test.go                    |   2 +-
 pkg/indicator/rma.go                          |  12 +-
 pkg/indicator/rsi.go                          |  15 +-
 pkg/indicator/sma.go                          |  15 +-
 pkg/indicator/sma_test.go                     |   4 +-
 pkg/indicator/ssf.go                          |  30 +-
 pkg/indicator/ssf_test.go                     |   2 +-
 pkg/indicator/stddev.go                       |  15 +-
 pkg/indicator/supertrend.go                   |  26 +-
 pkg/indicator/supertrendPivot.go              |  42 ++-
 pkg/indicator/tema.go                         |  22 +-
 pkg/indicator/tema_test.go                    |   2 +-
 pkg/indicator/till.go                         |  30 +-
 pkg/indicator/till_test.go                    |   2 +-
 pkg/indicator/tma.go                          |  19 +-
 pkg/indicator/tsi.go                          |  13 +-
 pkg/indicator/tsi_test.go                     |   2 +-
 pkg/indicator/utBotAlert.go                   |  24 +-
 pkg/indicator/v2_atr_test.go                  |   2 +-
 pkg/indicator/v2_ewma.go                      |   2 +-
 pkg/indicator/v2_rsi.go                       |   4 +-
 pkg/indicator/v2_tr_test.go                   |   2 +-
 pkg/indicator/vidya.go                        |  12 +-
 pkg/indicator/vidya_test.go                   |   6 +-
 pkg/indicator/volatility.go                   |  12 +-
 pkg/indicator/vwap.go                         |  18 +-
 pkg/indicator/vwma.go                         |  21 +-
 pkg/indicator/wdrift.go                       |  21 +-
 pkg/indicator/wwma.go                         |  18 +-
 pkg/indicator/zlema.go                        |  13 +-
 pkg/indicator/zlema_test.go                   |   2 +-
 pkg/risk/dynamicrisk/dynamic_exposure.go      |   6 +-
 pkg/risk/dynamicrisk/dynamic_spread.go        |  14 +-
 pkg/strategy/audacitymaker/orderflow.go       |   8 +-
 pkg/strategy/bollgrid/strategy.go             |   4 +-
 pkg/strategy/bollmaker/dynamic_spread.go      |  14 +-
 pkg/strategy/bollmaker/strategy.go            |  10 +-
 pkg/strategy/bollmaker/trend.go               |   2 +-
 pkg/strategy/drift/driftma.go                 |  10 +-
 pkg/strategy/drift/stoploss.go                |   2 +-
 pkg/strategy/drift/strategy.go                |  20 +-
 pkg/strategy/elliottwave/ewo.go               |   4 +-
 pkg/strategy/elliottwave/strategy.go          |   8 +-
 pkg/strategy/emastop/strategy.go              |   2 +-
 pkg/strategy/ewoDgtrd/heikinashi.go           |  12 +-
 pkg/strategy/ewoDgtrd/strategy.go             |  84 ++---
 pkg/strategy/factorzoo/factors/momentum.go    |  16 +-
 .../factorzoo/factors/price_mean_reversion.go |  10 +-
 .../factors/price_volume_divergence.go        |   8 +-
 pkg/strategy/factorzoo/factors/return_rate.go |  12 +-
 .../factorzoo/factors/volume_momentum.go      |  16 +-
 pkg/strategy/factorzoo/linear_regression.go   |  10 +-
 pkg/strategy/fixedmaker/strategy.go           |   2 +-
 pkg/strategy/flashcrash/strategy.go           |   2 +-
 pkg/strategy/fmaker/A18.go                    |   6 +-
 pkg/strategy/fmaker/A2.go                     |   6 +-
 pkg/strategy/fmaker/A3.go                     |   2 +-
 pkg/strategy/fmaker/A34.go                    |   4 +-
 pkg/strategy/fmaker/R.go                      |   2 +-
 pkg/strategy/fmaker/S0.go                     |   4 +-
 pkg/strategy/fmaker/S1.go                     |   2 +-
 pkg/strategy/fmaker/S2.go                     |   2 +-
 pkg/strategy/fmaker/S3.go                     |   2 +-
 pkg/strategy/fmaker/S4.go                     |   2 +-
 pkg/strategy/fmaker/S5.go                     |   4 +-
 pkg/strategy/fmaker/S6.go                     |  10 +-
 pkg/strategy/fmaker/S7.go                     |   6 +-
 pkg/strategy/fmaker/strategy.go               |   6 +-
 pkg/strategy/grid2/strategy.go                |   4 +-
 pkg/strategy/harmonic/shark.go                |   6 +-
 pkg/strategy/harmonic/strategy.go             |   6 +-
 pkg/strategy/irr/neg_return_rate.go           |  14 +-
 pkg/strategy/irr/strategy.go                  |   2 +-
 pkg/strategy/linregmaker/strategy.go          |  20 +-
 pkg/strategy/pivotshort/breaklow.go           |   8 +-
 pkg/strategy/pivotshort/failedbreakhigh.go    |  10 +-
 pkg/strategy/pivotshort/resistance.go         |   2 +-
 pkg/strategy/pricedrop/strategy.go            |   4 +-
 pkg/strategy/rsmaker/strategy.go              |   6 +-
 pkg/strategy/schedule/strategy.go             |   4 +-
 pkg/strategy/skeleton/strategy.go             |   2 +-
 pkg/strategy/supertrend/double_dema.go        |   4 +-
 pkg/strategy/supertrend/linreg.go             |  10 +-
 pkg/strategy/supertrend/strategy.go           |   6 +-
 pkg/strategy/support/strategy.go              |  12 +-
 pkg/strategy/swing/strategy.go                |   4 +-
 pkg/strategy/techsignal/strategy.go           |   2 +-
 pkg/strategy/trendtrader/trend.go             |  12 +-
 pkg/strategy/xmaker/strategy.go               |   4 +-
 pkg/types/filter.go                           |  10 +-
 pkg/types/indicator.go                        | 287 +++---------------
 pkg/types/indicator_test.go                   |  34 +--
 pkg/types/kline.go                            |   2 +-
 pkg/types/queue.go                            |  51 ++++
 pkg/types/series.go                           | 123 ++++++++
 pkg/types/seriesbase_imp.go                   |  10 +-
 pkg/types/sigmoid.go                          |  27 ++
 142 files changed, 845 insertions(+), 998 deletions(-)
 create mode 100644 pkg/types/queue.go
 create mode 100644 pkg/types/series.go
 create mode 100644 pkg/types/sigmoid.go

diff --git a/pkg/bbgo/exit_lower_shadow_take_profit.go b/pkg/bbgo/exit_lower_shadow_take_profit.go
index 1ffae6c36..32ac9928e 100644
--- a/pkg/bbgo/exit_lower_shadow_take_profit.go
+++ b/pkg/bbgo/exit_lower_shadow_take_profit.go
@@ -48,7 +48,7 @@ func (s *LowerShadowTakeProfit) Bind(session *ExchangeSession, orderExecutor *Ge
 		}
 
 		// skip close price higher than the ewma
-		if closePrice.Float64() > ewma.Last() {
+		if closePrice.Float64() > ewma.Last(0) {
 			return
 		}
 
diff --git a/pkg/bbgo/stop_ema.go b/pkg/bbgo/stop_ema.go
index 11c0472b6..f2ec45676 100644
--- a/pkg/bbgo/stop_ema.go
+++ b/pkg/bbgo/stop_ema.go
@@ -21,7 +21,7 @@ func (s *StopEMA) Bind(session *ExchangeSession, orderExecutor *GeneralOrderExec
 }
 
 func (s *StopEMA) Allowed(closePrice fixedpoint.Value) bool {
-	ema := fixedpoint.NewFromFloat(s.stopEWMA.Last())
+	ema := fixedpoint.NewFromFloat(s.stopEWMA.Last(0))
 	if ema.IsZero() {
 		logrus.Infof("stopEMA protection: value is zero, skip")
 		return false
diff --git a/pkg/bbgo/trend_ema.go b/pkg/bbgo/trend_ema.go
index c37e63aed..36242fead 100644
--- a/pkg/bbgo/trend_ema.go
+++ b/pkg/bbgo/trend_ema.go
@@ -29,12 +29,12 @@ func (s *TrendEMA) Bind(session *ExchangeSession, orderExecutor *GeneralOrderExe
 		}
 
 		s.last = s.ewma.Values[s.ewma.Length()-2]
-		s.current = s.ewma.Last()
+		s.current = s.ewma.Last(0)
 	})
 
 	session.MarketDataStream.OnKLineClosed(types.KLineWith(symbol, s.Interval, func(kline types.KLine) {
 		s.last = s.current
-		s.current = s.ewma.Last()
+		s.current = s.ewma.Last(0)
 	}))
 }
 
diff --git a/pkg/datatype/floats/slice.go b/pkg/datatype/floats/slice.go
index 84e1ff222..fe9314666 100644
--- a/pkg/datatype/floats/slice.go
+++ b/pkg/datatype/floats/slice.go
@@ -183,12 +183,12 @@ func (s Slice) Addr() *Slice {
 }
 
 // Last, Index, Length implements the types.Series interface
-func (s Slice) Last() float64 {
+func (s Slice) Last(i int) float64 {
 	length := len(s)
-	if length > 0 {
-		return s[length-1]
+	if i < 0 || length-1-i < 0 {
+		return 0.0
 	}
-	return 0.0
+	return s[length-1-i]
 }
 
 // Index fetches the element from the end of the slice
diff --git a/pkg/indicator/ad.go b/pkg/indicator/ad.go
index e94f8d246..463e304eb 100644
--- a/pkg/indicator/ad.go
+++ b/pkg/indicator/ad.go
@@ -35,15 +35,16 @@ func (inc *AD) Update(high, low, cloze, volume float64) {
 		moneyFlowVolume = ((2*cloze - high - low) / (high - low)) * volume
 	}
 
-	ad := inc.Last() + moneyFlowVolume
+	ad := inc.Last(0) + moneyFlowVolume
 	inc.Values.Push(ad)
 }
 
-func (inc *AD) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
+func (inc *AD) Last(i int) float64 {
+	length := len(inc.Values)
+	if length == 0 || length-i-1 < 0 {
+		return 0
 	}
-	return inc.Values[len(inc.Values)-1]
+	return inc.Values[length-i-1]
 }
 
 func (inc *AD) Index(i int) float64 {
@@ -68,7 +69,7 @@ func (inc *AD) CalculateAndUpdate(kLines []types.KLine) {
 		inc.Update(k.High.Float64(), k.Low.Float64(), k.Close.Float64(), k.Volume.Float64())
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = kLines[len(kLines)-1].EndTime.Time()
 }
 
diff --git a/pkg/indicator/alma.go b/pkg/indicator/alma.go
index f27de2b70..6837db766 100644
--- a/pkg/indicator/alma.go
+++ b/pkg/indicator/alma.go
@@ -20,6 +20,7 @@ import (
 //
 // @param offset: Gaussian applied to the combo line. 1->ema, 0->sma
 // @param sigma: the standard deviation applied to the combo line. This makes the combo line sharper
+//
 //go:generate callbackgen -type ALMA
 type ALMA struct {
 	types.SeriesBase
@@ -64,11 +65,11 @@ func (inc *ALMA) Update(value float64) {
 	}
 }
 
-func (inc *ALMA) Last() float64 {
-	if len(inc.Values) == 0 {
+func (inc *ALMA) Last(i int) float64 {
+	if i >= len(inc.Values) {
 		return 0
 	}
-	return inc.Values[len(inc.Values)-1]
+	return inc.Values[len(inc.Values)-i-1]
 }
 
 func (inc *ALMA) Index(i int) float64 {
@@ -88,12 +89,12 @@ func (inc *ALMA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.input == nil {
 		for _, k := range allKLines {
 			inc.Update(k.Close.Float64())
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 		return
 	}
 	inc.Update(allKLines[len(allKLines)-1].Close.Float64())
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *ALMA) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
diff --git a/pkg/indicator/alma_test.go b/pkg/indicator/alma_test.go
index a00d7113d..a21342f8a 100644
--- a/pkg/indicator/alma_test.go
+++ b/pkg/indicator/alma_test.go
@@ -53,7 +53,7 @@ func Test_ALMA(t *testing.T) {
 				Sigma:          6,
 			}
 			alma.CalculateAndUpdate(tt.kLines)
-			assert.InDelta(t, tt.want, alma.Last(), Delta)
+			assert.InDelta(t, tt.want, alma.Last(0), Delta)
 			assert.InDelta(t, tt.next, alma.Index(1), Delta)
 			assert.Equal(t, tt.all, alma.Length())
 		})
diff --git a/pkg/indicator/atr.go b/pkg/indicator/atr.go
index 0d5b264cb..335c36e2a 100644
--- a/pkg/indicator/atr.go
+++ b/pkg/indicator/atr.go
@@ -74,18 +74,18 @@ func (inc *ATR) Update(high, low, cloze float64) {
 
 	// apply rolling moving average
 	inc.RMA.Update(trueRange)
-	atr := inc.RMA.Last()
+	atr := inc.RMA.Last(0)
 	inc.PercentageVolatility.Push(atr / cloze)
 	if len(inc.PercentageVolatility) > MaxNumOfATR {
 		inc.PercentageVolatility = inc.PercentageVolatility[MaxNumOfATRTruncateSize-1:]
 	}
 }
 
-func (inc *ATR) Last() float64 {
+func (inc *ATR) Last(i int) float64 {
 	if inc.RMA == nil {
 		return 0
 	}
-	return inc.RMA.Last()
+	return inc.RMA.Last(i)
 }
 
 func (inc *ATR) Index(i int) float64 {
@@ -110,5 +110,5 @@ func (inc *ATR) PushK(k types.KLine) {
 
 	inc.Update(k.High.Float64(), k.Low.Float64(), k.Close.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
diff --git a/pkg/indicator/atr_test.go b/pkg/indicator/atr_test.go
index b5cb138e9..732dbae22 100644
--- a/pkg/indicator/atr_test.go
+++ b/pkg/indicator/atr_test.go
@@ -65,7 +65,7 @@ func Test_calculateATR(t *testing.T) {
 				atr.PushK(k)
 			}
 
-			got := atr.Last()
+			got := atr.Last(0)
 			diff := math.Trunc((got-tt.want)*100) / 100
 			if diff != 0 {
 				t.Errorf("calculateATR() = %v, want %v", got, tt.want)
diff --git a/pkg/indicator/atrp.go b/pkg/indicator/atrp.go
index 8d473942c..4e8558904 100644
--- a/pkg/indicator/atrp.go
+++ b/pkg/indicator/atrp.go
@@ -21,7 +21,7 @@ import (
 //
 // Calculation:
 //
-//     ATRP = (Average True Range / Close) * 100
+//	ATRP = (Average True Range / Close) * 100
 //
 //go:generate callbackgen -type ATRP
 type ATRP struct {
@@ -69,15 +69,15 @@ func (inc *ATRP) Update(high, low, cloze float64) {
 
 	// apply rolling moving average
 	inc.RMA.Update(trueRange)
-	atr := inc.RMA.Last()
+	atr := inc.RMA.Last(0)
 	inc.PercentageVolatility.Push(atr / cloze)
 }
 
-func (inc *ATRP) Last() float64 {
+func (inc *ATRP) Last(i int) float64 {
 	if inc.RMA == nil {
 		return 0
 	}
-	return inc.RMA.Last()
+	return inc.RMA.Last(i)
 }
 
 func (inc *ATRP) Index(i int) float64 {
@@ -109,7 +109,7 @@ func (inc *ATRP) CalculateAndUpdate(kLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = kLines[len(kLines)-1].EndTime.Time()
 }
 
diff --git a/pkg/indicator/boll.go b/pkg/indicator/boll.go
index 712481ffc..1a670608c 100644
--- a/pkg/indicator/boll.go
+++ b/pkg/indicator/boll.go
@@ -84,8 +84,8 @@ func (inc *BOLL) Update(value float64) {
 	inc.SMA.Update(value)
 	inc.StdDev.Update(value)
 
-	var sma = inc.SMA.Last()
-	var stdDev = inc.StdDev.Last()
+	var sma = inc.SMA.Last(0)
+	var stdDev = inc.StdDev.Last(0)
 	var band = inc.K * stdDev
 
 	var upBand = sma + band
@@ -105,7 +105,7 @@ func (inc *BOLL) PushK(k types.KLine) {
 	}
 	inc.Update(k.Close.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.SMA.Last(), inc.UpBand.Last(), inc.DownBand.Last())
+	inc.EmitUpdate(inc.SMA.Last(0), inc.UpBand.Last(0), inc.DownBand.Last(0))
 }
 
 func (inc *BOLL) LoadK(allKLines []types.KLine) {
@@ -113,7 +113,7 @@ func (inc *BOLL) LoadK(allKLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.SMA.Last(), inc.UpBand.Last(), inc.DownBand.Last())
+	inc.EmitUpdate(inc.SMA.Last(0), inc.UpBand.Last(0), inc.DownBand.Last(0))
 }
 
 func (inc *BOLL) CalculateAndUpdate(allKLines []types.KLine) {
diff --git a/pkg/indicator/boll_test.go b/pkg/indicator/boll_test.go
index 7bc8c574c..579ce2337 100644
--- a/pkg/indicator/boll_test.go
+++ b/pkg/indicator/boll_test.go
@@ -61,8 +61,8 @@ func TestBOLL(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			boll := BOLL{IntervalWindow: types.IntervalWindow{Window: tt.window}, K: tt.k}
 			boll.CalculateAndUpdate(tt.kLines)
-			assert.InDelta(t, tt.up, boll.UpBand.Last(), Delta)
-			assert.InDelta(t, tt.down, boll.DownBand.Last(), Delta)
+			assert.InDelta(t, tt.up, boll.UpBand.Last(0), Delta)
+			assert.InDelta(t, tt.down, boll.DownBand.Last(0), Delta)
 		})
 	}
 
diff --git a/pkg/indicator/cci.go b/pkg/indicator/cci.go
index 64d4427b2..dd24b46c3 100644
--- a/pkg/indicator/cci.go
+++ b/pkg/indicator/cci.go
@@ -43,7 +43,7 @@ func (inc *CCI) Update(value float64) {
 	}
 
 	inc.Input.Push(value)
-	tp := inc.TypicalPrice.Last() - inc.Input.Index(inc.Window) + value
+	tp := inc.TypicalPrice.Last(0) - inc.Input.Index(inc.Window) + value
 	inc.TypicalPrice.Push(tp)
 	if len(inc.Input) < inc.Window {
 		return
@@ -55,7 +55,7 @@ func (inc *CCI) Update(value float64) {
 	}
 	md := 0.
 	for i := 0; i < inc.Window; i++ {
-		diff := inc.Input.Index(i) - ma
+		diff := inc.Input.Last(i) - ma
 		md += diff * diff
 	}
 	md = math.Sqrt(md / float64(inc.Window))
@@ -68,18 +68,12 @@ func (inc *CCI) Update(value float64) {
 	}
 }
 
-func (inc *CCI) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *CCI) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *CCI) Index(i int) float64 {
-	if i >= len(inc.Values) {
-		return 0
-	}
-	return inc.Values[len(inc.Values)-1-i]
+	return inc.Last(i)
 }
 
 func (inc *CCI) Length() int {
@@ -96,12 +90,12 @@ func (inc *CCI) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.TypicalPrice.Length() == 0 {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/cci_test.go b/pkg/indicator/cci_test.go
index 4aeca6fca..8d93947ef 100644
--- a/pkg/indicator/cci_test.go
+++ b/pkg/indicator/cci_test.go
@@ -29,7 +29,7 @@ func Test_CCI(t *testing.T) {
 			cci.Update(value)
 		}
 
-		last := cci.Last()
+		last := cci.Last(0)
 		assert.InDelta(t, 93.250481, last, Delta)
 		assert.InDelta(t, 81.813449, cci.Index(1), Delta)
 		assert.Equal(t, 50-16+1, cci.Length())
diff --git a/pkg/indicator/cma.go b/pkg/indicator/cma.go
index 37dad3f8c..51043f805 100644
--- a/pkg/indicator/cma.go
+++ b/pkg/indicator/cma.go
@@ -7,12 +7,13 @@ import (
 
 // Refer: Cumulative Moving Average, Cumulative Average
 // Refer: https://en.wikipedia.org/wiki/Moving_average
+//
 //go:generate callbackgen -type CA
 type CA struct {
 	types.SeriesBase
-	Interval types.Interval
-	Values   floats.Slice
-	length   float64
+	Interval        types.Interval
+	Values          floats.Slice
+	length          float64
 	UpdateCallbacks []func(value float64)
 }
 
@@ -20,7 +21,7 @@ func (inc *CA) Update(x float64) {
 	if len(inc.Values) == 0 {
 		inc.SeriesBase.Series = inc
 	}
-	newVal := (inc.Values.Last()*inc.length + x) / (inc.length + 1.)
+	newVal := (inc.Values.Last(0)*inc.length + x) / (inc.length + 1.)
 	inc.length += 1
 	inc.Values.Push(newVal)
 	if len(inc.Values) > MaxNumOfEWMA {
@@ -29,18 +30,12 @@ func (inc *CA) Update(x float64) {
 	}
 }
 
-func (inc *CA) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *CA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *CA) Index(i int) float64 {
-	if i >= len(inc.Values) {
-		return 0
-	}
-	return inc.Values[len(inc.Values)-1-i]
+	return inc.Last(i)
 }
 
 func (inc *CA) Length() int {
@@ -56,7 +51,7 @@ func (inc *CA) PushK(k types.KLine) {
 func (inc *CA) CalculateAndUpdate(allKLines []types.KLine) {
 	for _, k := range allKLines {
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/dema.go b/pkg/indicator/dema.go
index 107923de5..6dbc97b59 100644
--- a/pkg/indicator/dema.go
+++ b/pkg/indicator/dema.go
@@ -51,22 +51,19 @@ func (inc *DEMA) Update(value float64) {
 	}
 
 	inc.a1.Update(value)
-	inc.a2.Update(inc.a1.Last())
-	inc.Values.Push(2*inc.a1.Last() - inc.a2.Last())
+	inc.a2.Update(inc.a1.Last(0))
+	inc.Values.Push(2*inc.a1.Last(0) - inc.a2.Last(0))
 	if len(inc.Values) > MaxNumOfEWMA {
 		inc.Values = inc.Values[MaxNumOfEWMATruncateSize-1:]
 	}
 }
 
-func (inc *DEMA) Last() float64 {
-	return inc.Values.Last()
+func (inc *DEMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *DEMA) Index(i int) float64 {
-	if len(inc.Values)-i-1 >= 0 {
-		return inc.Values[len(inc.Values)-1-i]
-	}
-	return 0
+	return inc.Last(i)
 }
 
 func (inc *DEMA) Length() int {
@@ -83,13 +80,13 @@ func (inc *DEMA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.a1 == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		// last k
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/dema_test.go b/pkg/indicator/dema_test.go
index 99da987b9..845399bbf 100644
--- a/pkg/indicator/dema_test.go
+++ b/pkg/indicator/dema_test.go
@@ -46,7 +46,7 @@ func Test_DEMA(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			dema := DEMA{IntervalWindow: types.IntervalWindow{Window: 16}}
 			dema.CalculateAndUpdate(tt.kLines)
-			last := dema.Last()
+			last := dema.Last(0)
 			assert.InDelta(t, tt.want, last, Delta)
 			assert.InDelta(t, tt.next, dema.Index(1), Delta)
 			assert.Equal(t, tt.all, dema.Length())
diff --git a/pkg/indicator/dmi.go b/pkg/indicator/dmi.go
index 853b9deb3..0bf270477 100644
--- a/pkg/indicator/dmi.go
+++ b/pkg/indicator/dmi.go
@@ -72,9 +72,9 @@ func (inc *DMI) Update(high, low, cloze float64) {
 	if inc.atr.Length() < inc.Window {
 		return
 	}
-	k := 100. / inc.atr.Last()
-	dmp := inc.DMP.Last()
-	dmn := inc.DMN.Last()
+	k := 100. / inc.atr.Last(0)
+	dmp := inc.DMP.Last(0)
+	dmn := inc.DMN.Last(0)
 	inc.DIPlus.Update(k * dmp)
 	inc.DIMinus.Update(k * dmn)
 	dx := 100. * math.Abs(dmp-dmn) / (dmp + dmn)
@@ -108,11 +108,11 @@ func (inc *DMI) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.ADX == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.DIPlus.Last(), inc.DIMinus.Last(), inc.ADX.Last())
+			inc.EmitUpdate(inc.DIPlus.Last(0), inc.DIMinus.Last(0), inc.ADX.Last(0))
 		}
 	} else {
 		inc.PushK(last)
-		inc.EmitUpdate(inc.DIPlus.Last(), inc.DIMinus.Last(), inc.ADX.Last())
+		inc.EmitUpdate(inc.DIPlus.Last(0), inc.DIMinus.Last(0), inc.ADX.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/dmi_test.go b/pkg/indicator/dmi_test.go
index d93e16440..dae952d52 100644
--- a/pkg/indicator/dmi_test.go
+++ b/pkg/indicator/dmi_test.go
@@ -78,9 +78,9 @@ func Test_DMI(t *testing.T) {
 				ADXSmoothing:   14,
 			}
 			dmi.CalculateAndUpdate(tt.klines)
-			assert.InDelta(t, dmi.GetDIPlus().Last(), tt.want.dip, Delta)
-			assert.InDelta(t, dmi.GetDIMinus().Last(), tt.want.dim, Delta)
-			assert.InDelta(t, dmi.GetADX().Last(), tt.want.adx, Delta)
+			assert.InDelta(t, dmi.GetDIPlus().Last(0), tt.want.dip, Delta)
+			assert.InDelta(t, dmi.GetDIMinus().Last(0), tt.want.dim, Delta)
+			assert.InDelta(t, dmi.GetADX().Last(0), tt.want.adx, Delta)
 		})
 	}
 
diff --git a/pkg/indicator/drift.go b/pkg/indicator/drift.go
index ac3df837a..eb1969720 100644
--- a/pkg/indicator/drift.go
+++ b/pkg/indicator/drift.go
@@ -51,7 +51,7 @@ func (inc *Drift) Update(value float64) {
 	inc.chng.Update(chng)
 	if inc.chng.Length() >= inc.Window {
 		stdev := types.Stdev(inc.chng, inc.Window)
-		drift := inc.MA.Last() - stdev*stdev*0.5
+		drift := inc.MA.Last(0) - stdev*stdev*0.5
 		inc.Values.Push(drift)
 	}
 }
@@ -74,7 +74,7 @@ func (inc *Drift) ZeroPoint() float64 {
 	} else {
 		return N2
 	}*/
-	return inc.LastValue * math.Exp(window*(0.5*stdev*stdev)+chng-inc.MA.Last()*window)
+	return inc.LastValue * math.Exp(window*(0.5*stdev*stdev)+chng-inc.MA.Last(0)*window)
 }
 
 func (inc *Drift) Clone() (out *Drift) {
@@ -96,17 +96,11 @@ func (inc *Drift) TestUpdate(value float64) *Drift {
 }
 
 func (inc *Drift) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
-func (inc *Drift) Last() float64 {
-	if inc.Values.Length() == 0 {
-		return 0
-	}
-	return inc.Values.Last()
+func (inc *Drift) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *Drift) Length() int {
@@ -126,12 +120,12 @@ func (inc *Drift) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.chng == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/emv.go b/pkg/indicator/emv.go
index a3a761a5a..a391a08e7 100644
--- a/pkg/indicator/emv.go
+++ b/pkg/indicator/emv.go
@@ -55,11 +55,12 @@ func (inc *EMV) Index(i int) float64 {
 	return inc.Values.Index(i)
 }
 
-func (inc *EMV) Last() float64 {
+func (inc *EMV) Last(i int) float64 {
 	if inc.Values == nil {
 		return 0
 	}
-	return inc.Values.Last()
+
+	return inc.Values.Last(i)
 }
 
 func (inc *EMV) Length() int {
diff --git a/pkg/indicator/emv_test.go b/pkg/indicator/emv_test.go
index 03b57a760..0be0b517d 100644
--- a/pkg/indicator/emv_test.go
+++ b/pkg/indicator/emv_test.go
@@ -16,7 +16,7 @@ func Test_EMV(t *testing.T) {
 	}
 	emv.Update(63.74, 62.63, 32178836)
 	emv.Update(64.51, 63.85, 36461672)
-	assert.InDelta(t, 1.8, emv.Values.rawValues.Last(), Delta)
+	assert.InDelta(t, 1.8, emv.Values.rawValues.Last(0), Delta)
 	emv.Update(64.57, 63.81, 51372680)
 	emv.Update(64.31, 62.62, 42476356)
 	emv.Update(63.43, 62.73, 29504176)
@@ -30,5 +30,5 @@ func Test_EMV(t *testing.T) {
 	emv.Update(65.25, 64.48, 37015388)
 	emv.Update(64.69, 63.65, 40672116)
 	emv.Update(64.26, 63.68, 35627200)
-	assert.InDelta(t, -0.03, emv.Last(), Delta)
+	assert.InDelta(t, -0.03, emv.Last(0), Delta)
 }
diff --git a/pkg/indicator/ewma.go b/pkg/indicator/ewma.go
index 533c27bd2..e05f30a3c 100644
--- a/pkg/indicator/ewma.go
+++ b/pkg/indicator/ewma.go
@@ -50,24 +50,20 @@ func (inc *EWMA) Update(value float64) {
 		inc.Values = inc.Values[MaxNumOfEWMATruncateSize-1:]
 	}
 
-	ema := (1-multiplier)*inc.Last() + multiplier*value
+	ema := (1-multiplier)*inc.Last(0) + multiplier*value
 	inc.Values.Push(ema)
 }
 
-func (inc *EWMA) Last() float64 {
+func (inc *EWMA) Last(i int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
 
-	return inc.Values[len(inc.Values)-1]
+	return inc.Values.Last(i)
 }
 
 func (inc *EWMA) Index(i int) float64 {
-	if i >= len(inc.Values) {
-		return 0
-	}
-
-	return inc.Values[len(inc.Values)-1-i]
+	return inc.Last(i)
 }
 
 func (inc *EWMA) Length() int {
@@ -81,7 +77,7 @@ func (inc *EWMA) PushK(k types.KLine) {
 
 	inc.Update(k.Close.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func CalculateKLinesEMA(allKLines []types.KLine, priceF KLineValueMapper, window int) float64 {
diff --git a/pkg/indicator/fisher.go b/pkg/indicator/fisher.go
index fcd492c95..98198fc04 100644
--- a/pkg/indicator/fisher.go
+++ b/pkg/indicator/fisher.go
@@ -16,6 +16,7 @@ import (
 // The Fisher Transform is calculated by taking the natural logarithm of the ratio of the security's current price to its moving average,
 // and then double-smoothing the result. This resulting line is called the Fisher Transform line, and can be plotted on the price chart
 // along with the security's price.
+//
 //go:generate callbackgen -type FisherTransform
 type FisherTransform struct {
 	types.SeriesBase
@@ -60,18 +61,15 @@ func (inc *FisherTransform) Update(value float64) {
 	}
 }
 
-func (inc *FisherTransform) Last() float64 {
+func (inc *FisherTransform) Last(i int) float64 {
 	if inc.Values == nil {
 		return 0.0
 	}
-	return inc.Values.Last()
+	return inc.Values.Last(i)
 }
 
 func (inc *FisherTransform) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *FisherTransform) Length() int {
diff --git a/pkg/indicator/float64updater.go b/pkg/indicator/float64updater.go
index 3c3746ffe..6f4e69ddb 100644
--- a/pkg/indicator/float64updater.go
+++ b/pkg/indicator/float64updater.go
@@ -23,16 +23,12 @@ func NewFloat64Series(v ...float64) Float64Series {
 	return s
 }
 
-func (f *Float64Series) Last() float64 {
-	return f.slice.Last()
+func (f *Float64Series) Last(i int) float64 {
+	return f.slice.Last(i)
 }
 
 func (f *Float64Series) Index(i int) float64 {
-	length := len(f.slice)
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-	return f.slice[length-i-1]
+	return f.slice.Last(i)
 }
 
 func (f *Float64Series) Length() int {
diff --git a/pkg/indicator/ghfilter.go b/pkg/indicator/ghfilter.go
index f5794d4d5..e5dea876f 100644
--- a/pkg/indicator/ghfilter.go
+++ b/pkg/indicator/ghfilter.go
@@ -1,9 +1,10 @@
 package indicator
 
 import (
+	"math"
+
 	"github.com/c9s/bbgo/pkg/datatype/floats"
 	"github.com/c9s/bbgo/pkg/types"
-	"math"
 )
 
 // Refer: https://jamesgoulding.com/Research_II/Ehlers/Ehlers%20(Optimal%20Tracking%20Filters).doc
@@ -39,16 +40,13 @@ func (inc *GHFilter) update(value, uncertainty float64) {
 	lambda := inc.a / inc.b
 	lambda2 := lambda * lambda
 	alpha := (-lambda2 + math.Sqrt(lambda2*lambda2+16*lambda2)) / 8
-	filtered := alpha*value + (1-alpha)*inc.Values.Last()
+	filtered := alpha*value + (1-alpha)*inc.Values.Last(0)
 	inc.Values.Push(filtered)
 	inc.lastMeasurement = value
 }
 
 func (inc *GHFilter) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *GHFilter) Length() int {
@@ -58,11 +56,11 @@ func (inc *GHFilter) Length() int {
 	return inc.Values.Length()
 }
 
-func (inc *GHFilter) Last() float64 {
+func (inc *GHFilter) Last(i int) float64 {
 	if inc.Values == nil {
 		return 0.0
 	}
-	return inc.Values.Last()
+	return inc.Values.Last(i)
 }
 
 // interfaces implementation check
diff --git a/pkg/indicator/ghfilter_test.go b/pkg/indicator/ghfilter_test.go
index ac7439933..849438859 100644
--- a/pkg/indicator/ghfilter_test.go
+++ b/pkg/indicator/ghfilter_test.go
@@ -6058,7 +6058,7 @@ func Test_GHFilter(t *testing.T) {
 			for _, k := range klines {
 				filter.PushK(k)
 			}
-			got := filter.Last()
+			got := filter.Last(0)
 			got = math.Trunc(got*100.0) / 100.0
 			if got != tt.want {
 				t.Errorf("GHFilter.Last() = %v, want %v", got, tt.want)
@@ -6125,10 +6125,10 @@ func Test_GHFilterEstimationAccurate(t *testing.T) {
 			for i, k := range klines {
 				// square error between last estimated state and current actual state
 				if i > 0 {
-					filterDiff2Sum += klineSquareError(filter.Last(), k)
-					ewmaDiff2Sum += klineSquareError(ewma.Last(), k)
-					filterCloseDiff2Sum += closeSquareError(filter.Last(), k)
-					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(), k)
+					filterDiff2Sum += klineSquareError(filter.Last(0), k)
+					ewmaDiff2Sum += klineSquareError(ewma.Last(0), k)
+					filterCloseDiff2Sum += closeSquareError(filter.Last(0), k)
+					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(0), k)
 				}
 
 				// update estimations
diff --git a/pkg/indicator/gma.go b/pkg/indicator/gma.go
index 8b8673300..1fe0abb52 100644
--- a/pkg/indicator/gma.go
+++ b/pkg/indicator/gma.go
@@ -22,18 +22,15 @@ type GMA struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *GMA) Last() float64 {
+func (inc *GMA) Last(i int) float64 {
 	if inc.SMA == nil {
 		return 0.0
 	}
-	return math.Exp(inc.SMA.Last())
+	return math.Exp(inc.SMA.Last(i))
 }
 
 func (inc *GMA) Index(i int) float64 {
-	if inc.SMA == nil {
-		return 0.0
-	}
-	return math.Exp(inc.SMA.Index(i))
+	return inc.Last(i)
 }
 
 func (inc *GMA) Length() int {
diff --git a/pkg/indicator/gma_test.go b/pkg/indicator/gma_test.go
index ab9740e09..0ad27f977 100644
--- a/pkg/indicator/gma_test.go
+++ b/pkg/indicator/gma_test.go
@@ -51,10 +51,10 @@ func Test_GMA(t *testing.T) {
 			for _, k := range tt.kLines {
 				gma.PushK(k)
 			}
-			assert.InDelta(t, tt.want, gma.Last(), Delta)
+			assert.InDelta(t, tt.want, gma.Last(0), Delta)
 			assert.InDelta(t, tt.next, gma.Index(1), Delta)
 			gma.Update(tt.update)
-			assert.InDelta(t, tt.updateResult, gma.Last(), Delta)
+			assert.InDelta(t, tt.updateResult, gma.Last(0), Delta)
 			assert.Equal(t, tt.all, gma.Length())
 		})
 	}
diff --git a/pkg/indicator/hull.go b/pkg/indicator/hull.go
index 214d2620d..7a432d39a 100644
--- a/pkg/indicator/hull.go
+++ b/pkg/indicator/hull.go
@@ -14,6 +14,7 @@ import (
 // the weighted moving average of the input data using a weighting factor of W, where W is the square root of the length of the moving average.
 // The result is then double-smoothed by taking the weighted moving average of this result using a weighting factor of W/2. This final average
 // forms the HMA line, which can be used to make predictions about future price movements.
+//
 //go:generate callbackgen -type HULL
 type HULL struct {
 	types.SeriesBase
@@ -36,14 +37,14 @@ func (inc *HULL) Update(value float64) {
 	}
 	inc.ma1.Update(value)
 	inc.ma2.Update(value)
-	inc.result.Update(2*inc.ma1.Last() - inc.ma2.Last())
+	inc.result.Update(2*inc.ma1.Last(0) - inc.ma2.Last(0))
 }
 
-func (inc *HULL) Last() float64 {
+func (inc *HULL) Last(i int) float64 {
 	if inc.result == nil {
 		return 0
 	}
-	return inc.result.Last()
+	return inc.result.Index(i)
 }
 
 func (inc *HULL) Index(i int) float64 {
@@ -66,5 +67,5 @@ func (inc *HULL) PushK(k types.KLine) {
 	}
 
 	inc.Update(k.Close.Float64())
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
diff --git a/pkg/indicator/hull_test.go b/pkg/indicator/hull_test.go
index 857c8d30d..e1c077a73 100644
--- a/pkg/indicator/hull_test.go
+++ b/pkg/indicator/hull_test.go
@@ -51,7 +51,7 @@ func Test_HULL(t *testing.T) {
 				hull.PushK(k)
 			}
 
-			last := hull.Last()
+			last := hull.Last(0)
 			assert.InDelta(t, tt.want, last, Delta)
 			assert.InDelta(t, tt.next, hull.Index(1), Delta)
 			assert.Equal(t, tt.all, hull.Length())
diff --git a/pkg/indicator/interface.go b/pkg/indicator/interface.go
index d784f5308..51307440b 100644
--- a/pkg/indicator/interface.go
+++ b/pkg/indicator/interface.go
@@ -25,7 +25,7 @@ type KLinePusher interface {
 // Simple is the simple indicator that only returns one float64 value
 type Simple interface {
 	KLinePusher
-	Last() float64
+	Last(int) float64
 	OnUpdate(f func(value float64))
 }
 
diff --git a/pkg/indicator/kalmanfilter.go b/pkg/indicator/kalmanfilter.go
index 5d8345729..0b9ce2b0a 100644
--- a/pkg/indicator/kalmanfilter.go
+++ b/pkg/indicator/kalmanfilter.go
@@ -1,9 +1,10 @@
 package indicator
 
 import (
+	"math"
+
 	"github.com/c9s/bbgo/pkg/datatype/floats"
 	"github.com/c9s/bbgo/pkg/types"
-	"math"
 )
 
 // Refer: https://www.kalmanfilter.net/kalman1d.html
@@ -25,7 +26,7 @@ type KalmanFilter struct {
 func (inc *KalmanFilter) Update(value float64) {
 	var measureMove = value
 	if inc.measurements != nil {
-		measureMove = value - inc.measurements.Last()
+		measureMove = value - inc.measurements.Last(0)
 	}
 	inc.update(value, math.Abs(measureMove))
 }
@@ -46,7 +47,7 @@ func (inc *KalmanFilter) update(value, amp float64) {
 	q := math.Sqrt(types.Mean(inc.amp2)) * float64(1+inc.AdditionalSmoothWindow)
 
 	// update
-	lastPredict := inc.Values.Last()
+	lastPredict := inc.Values.Last(0)
 	curState := value + (value - lastPredict)
 	estimated := lastPredict + inc.k*(curState-lastPredict)
 
@@ -57,24 +58,15 @@ func (inc *KalmanFilter) update(value, amp float64) {
 }
 
 func (inc *KalmanFilter) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *KalmanFilter) Length() int {
-	if inc.Values == nil {
-		return 0
-	}
 	return inc.Values.Length()
 }
 
-func (inc *KalmanFilter) Last() float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Last()
+func (inc *KalmanFilter) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 // interfaces implementation check
diff --git a/pkg/indicator/kalmanfilter_test.go b/pkg/indicator/kalmanfilter_test.go
index 250656047..c357748e4 100644
--- a/pkg/indicator/kalmanfilter_test.go
+++ b/pkg/indicator/kalmanfilter_test.go
@@ -6065,7 +6065,7 @@ func Test_KalmanFilter(t *testing.T) {
 			for _, k := range klines {
 				filter.PushK(k)
 			}
-			got := filter.Last()
+			got := filter.Last(0)
 			got = math.Trunc(got*100.0) / 100.0
 			if got != tt.want {
 				t.Errorf("KalmanFilter.Last() = %v, want %v", got, tt.want)
@@ -6160,10 +6160,10 @@ func Test_KalmanFilterEstimationAccurate(t *testing.T) {
 			for _, k := range klines {
 				// square error between last estimated state and current actual state
 				if ewma.Length() > 0 {
-					filterDiff2Sum += klineSquareError(filter.Last(), k)
-					ewmaDiff2Sum += klineSquareError(ewma.Last(), k)
-					filterCloseDiff2Sum += closeSquareError(filter.Last(), k)
-					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(), k)
+					filterDiff2Sum += klineSquareError(filter.Last(0), k)
+					ewmaDiff2Sum += klineSquareError(ewma.Last(0), k)
+					filterCloseDiff2Sum += closeSquareError(filter.Last(0), k)
+					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(0), k)
 					numEstimations++
 				}
 
diff --git a/pkg/indicator/klingeroscillator.go b/pkg/indicator/klingeroscillator.go
index 198a5d29d..0b5f70310 100644
--- a/pkg/indicator/klingeroscillator.go
+++ b/pkg/indicator/klingeroscillator.go
@@ -12,6 +12,7 @@ import (
 // The Klinger Oscillator is calculated by taking the difference between a 34-period and 55-period moving average.
 // Usually the indicator is using together with a 9-period or 13-period of moving average as the signal line.
 // This indicator is often used to identify potential turning points in the market, as well as to confirm the strength of a trend.
+//
 //go:generate callbackgen -type KlingerOscillator
 type KlingerOscillator struct {
 	types.SeriesBase
@@ -30,17 +31,11 @@ func (inc *KlingerOscillator) Length() int {
 	return inc.Fast.Length()
 }
 
-func (inc *KlingerOscillator) Last() float64 {
+func (inc *KlingerOscillator) Last(i int) float64 {
 	if inc.Fast == nil || inc.Slow == nil {
 		return 0
 	}
-	return inc.Fast.Last() - inc.Slow.Last()
-}
-func (inc *KlingerOscillator) Index(i int) float64 {
-	if inc.Fast == nil || inc.Slow == nil {
-		return 0
-	}
-	return inc.Fast.Index(i) - inc.Slow.Index(i)
+	return inc.Fast.Last(i) - inc.Slow.Last(i)
 }
 
 func (inc *KlingerOscillator) Update(high, low, cloze, volume float64) {
diff --git a/pkg/indicator/line.go b/pkg/indicator/line.go
index edb8276f1..e6227b30f 100644
--- a/pkg/indicator/line.go
+++ b/pkg/indicator/line.go
@@ -38,12 +38,12 @@ func (l *Line) Bind(updater KLineWindowUpdater) {
 	updater.OnKLineWindowUpdate(l.handleKLineWindowUpdate)
 }
 
-func (l *Line) Last() float64 {
-	return (l.end-l.start)/float64(l.startIndex-l.endIndex)*float64(l.endIndex) + l.end
+func (l *Line) Last(i int) float64 {
+	return (l.end-l.start)/float64(l.startIndex-l.endIndex)*float64(l.endIndex-i) + l.end
 }
 
 func (l *Line) Index(i int) float64 {
-	return (l.end-l.start)/float64(l.startIndex-l.endIndex)*float64(l.endIndex-i) + l.end
+	return l.Last(i)
 }
 
 func (l *Line) Length() int {
diff --git a/pkg/indicator/linreg.go b/pkg/indicator/linreg.go
index 3bb4606ed..f27e32c2a 100644
--- a/pkg/indicator/linreg.go
+++ b/pkg/indicator/linreg.go
@@ -1,9 +1,10 @@
 package indicator
 
 import (
-	"github.com/sirupsen/logrus"
 	"time"
 
+	"github.com/sirupsen/logrus"
+
 	"github.com/c9s/bbgo/pkg/datatype/floats"
 	"github.com/c9s/bbgo/pkg/types"
 )
@@ -11,6 +12,7 @@ import (
 var logLinReg = logrus.WithField("indicator", "LinReg")
 
 // LinReg is Linear Regression baseline
+//
 //go:generate callbackgen -type LinReg
 type LinReg struct {
 	types.SeriesBase
@@ -28,11 +30,8 @@ type LinReg struct {
 }
 
 // Last slope of linear regression baseline
-func (lr *LinReg) Last() float64 {
-	if lr.Values.Length() == 0 {
-		return 0.0
-	}
-	return lr.Values.Last()
+func (lr *LinReg) Last(i int) float64 {
+	return lr.Values.Last(i)
 }
 
 // LastRatio of slope to price
@@ -40,16 +39,12 @@ func (lr *LinReg) LastRatio() float64 {
 	if lr.ValueRatios.Length() == 0 {
 		return 0.0
 	}
-	return lr.ValueRatios.Last()
+	return lr.ValueRatios.Last(0)
 }
 
 // Index returns the slope of specified index
 func (lr *LinReg) Index(i int) float64 {
-	if i >= lr.Values.Length() {
-		return 0.0
-	}
-
-	return lr.Values.Index(i)
+	return lr.Values.Last(i)
 }
 
 // IndexRatio returns the slope ratio
@@ -58,7 +53,7 @@ func (lr *LinReg) IndexRatio(i int) float64 {
 		return 0.0
 	}
 
-	return lr.ValueRatios.Index(i)
+	return lr.ValueRatios.Last(i)
 }
 
 // Length of the slope values
@@ -99,9 +94,9 @@ func (lr *LinReg) Update(kline types.KLine) {
 	endPrice := average - slope*sumX/length + slope
 	startPrice := endPrice + slope*(length-1)
 	lr.Values.Push((endPrice - startPrice) / (length - 1))
-	lr.ValueRatios.Push(lr.Values.Last() / kline.GetClose().Float64())
+	lr.ValueRatios.Push(lr.Values.Last(0) / kline.GetClose().Float64())
 
-	logLinReg.Debugf("linear regression baseline slope: %f", lr.Last())
+	logLinReg.Debugf("linear regression baseline slope: %f", lr.Last(0))
 }
 
 func (lr *LinReg) BindK(target KLineClosedEmitter, symbol string, interval types.Interval) {
diff --git a/pkg/indicator/low.go b/pkg/indicator/low.go
index 77d0457ea..6f6d9468b 100644
--- a/pkg/indicator/low.go
+++ b/pkg/indicator/low.go
@@ -33,5 +33,5 @@ func (inc *Low) PushK(k types.KLine) {
 
 	inc.Update(k.Low.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
diff --git a/pkg/indicator/macd.go b/pkg/indicator/macd.go
index 19818c70e..2535e9681 100644
--- a/pkg/indicator/macd.go
+++ b/pkg/indicator/macd.go
@@ -59,14 +59,14 @@ func (inc *MACDLegacy) Update(x float64) {
 	inc.slowEWMA.Update(x)
 
 	// update MACD value, it's also the signal line
-	fast := inc.fastEWMA.Last()
-	slow := inc.slowEWMA.Last()
+	fast := inc.fastEWMA.Last(0)
+	slow := inc.slowEWMA.Last(0)
 	macd := fast - slow
 	inc.Values.Push(macd)
 
 	// update signal line
 	inc.signalLine.Update(macd)
-	signal := inc.signalLine.Last()
+	signal := inc.signalLine.Last(0)
 
 	// update histogram
 	histogram := macd - signal
@@ -75,7 +75,7 @@ func (inc *MACDLegacy) Update(x float64) {
 	inc.EmitUpdate(macd, signal, histogram)
 }
 
-func (inc *MACDLegacy) Last() float64 {
+func (inc *MACDLegacy) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -106,21 +106,12 @@ type MACDValues struct {
 	*MACDLegacy
 }
 
-func (inc *MACDValues) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-
-	return inc.Values[len(inc.Values)-1]
+func (inc *MACDValues) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *MACDValues) Index(i int) float64 {
-	length := len(inc.Values)
-	if length == 0 || length-1-i < 0 {
-		return 0.0
-	}
-
-	return inc.Values[length-1+i]
+	return inc.Values.Last(i)
 }
 
 func (inc *MACDValues) Length() int {
diff --git a/pkg/indicator/macd_test.go b/pkg/indicator/macd_test.go
index c9bede48a..eac9d54d9 100644
--- a/pkg/indicator/macd_test.go
+++ b/pkg/indicator/macd_test.go
@@ -45,7 +45,7 @@ func Test_calculateMACD(t *testing.T) {
 				macd.PushK(k)
 			}
 
-			got := macd.Last()
+			got := macd.Last(0)
 			diff := math.Trunc((got-tt.want)*100) / 100
 			if diff != 0 {
 				t.Errorf("calculateMACD() = %v, want %v", got, tt.want)
diff --git a/pkg/indicator/obv.go b/pkg/indicator/obv.go
index 4ca032445..f7b768ce3 100644
--- a/pkg/indicator/obv.go
+++ b/pkg/indicator/obv.go
@@ -40,24 +40,18 @@ func (inc *OBV) Update(price, volume float64) {
 	}
 
 	if volume < inc.PrePrice {
-		inc.Values.Push(inc.Last() - volume)
+		inc.Values.Push(inc.Last(0) - volume)
 	} else {
-		inc.Values.Push(inc.Last() + volume)
+		inc.Values.Push(inc.Last(0) + volume)
 	}
 }
 
-func (inc *OBV) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *OBV) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *OBV) Index(i int) float64 {
-	if len(inc.Values)-i <= 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-i-1]
+	return inc.Last(i)
 }
 
 var _ types.SeriesExtend = &OBV{}
@@ -75,7 +69,7 @@ func (inc *OBV) CalculateAndUpdate(kLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = kLines[len(kLines)-1].EndTime.Time()
 }
 
diff --git a/pkg/indicator/pivot.go b/pkg/indicator/pivot.go
index 8e027e410..c32db25cd 100644
--- a/pkg/indicator/pivot.go
+++ b/pkg/indicator/pivot.go
@@ -10,7 +10,6 @@ import (
 	"github.com/c9s/bbgo/pkg/types"
 )
 
-
 //go:generate callbackgen -type Pivot
 type Pivot struct {
 	types.IntervalWindow
@@ -105,12 +104,12 @@ func calculatePivot(klines []types.KLine, window int, valLow KLineValueMapper, v
 	}
 
 	pl := 0.
-	if lows.Min() == lows.Index(int(window/2.)-1) {
+	if lows.Min() == lows.Last(int(window/2.)-1) {
 		pl = lows.Min()
 	}
 
 	ph := 0.
-	if highs.Max() == highs.Index(int(window/2.)-1) {
+	if highs.Max() == highs.Last(int(window/2.)-1) {
 		ph = highs.Max()
 	}
 
diff --git a/pkg/indicator/pivothigh.go b/pkg/indicator/pivothigh.go
index 8414c826c..52fe7be0b 100644
--- a/pkg/indicator/pivothigh.go
+++ b/pkg/indicator/pivothigh.go
@@ -24,12 +24,12 @@ func (inc *PivotHigh) Length() int {
 	return inc.Values.Length()
 }
 
-func (inc *PivotHigh) Last() float64 {
+func (inc *PivotHigh) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
 
-	return inc.Values.Last()
+	return inc.Values.Last(0)
 }
 
 func (inc *PivotHigh) Update(value float64) {
@@ -60,5 +60,5 @@ func (inc *PivotHigh) PushK(k types.KLine) {
 
 	inc.Update(k.High.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
diff --git a/pkg/indicator/pivotlow.go b/pkg/indicator/pivotlow.go
index c195c488c..7bdbd58e6 100644
--- a/pkg/indicator/pivotlow.go
+++ b/pkg/indicator/pivotlow.go
@@ -24,12 +24,12 @@ func (inc *PivotLow) Length() int {
 	return inc.Values.Length()
 }
 
-func (inc *PivotLow) Last() float64 {
+func (inc *PivotLow) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
 
-	return inc.Values.Last()
+	return inc.Values.Last(0)
 }
 
 func (inc *PivotLow) Update(value float64) {
@@ -60,7 +60,7 @@ func (inc *PivotLow) PushK(k types.KLine) {
 
 	inc.Update(k.Low.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func calculatePivotHigh(highs floats.Slice, left, right int) (float64, bool) {
diff --git a/pkg/indicator/psar.go b/pkg/indicator/psar.go
index e39e3fb2c..5154c1b54 100644
--- a/pkg/indicator/psar.go
+++ b/pkg/indicator/psar.go
@@ -34,11 +34,11 @@ type PSAR struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *PSAR) Last() float64 {
+func (inc *PSAR) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
-	return inc.Values.Last()
+	return inc.Values.Last(0)
 }
 
 func (inc *PSAR) Length() int {
@@ -46,8 +46,8 @@ func (inc *PSAR) Length() int {
 }
 
 func (inc *PSAR) falling() bool {
-	up := inc.High.Last() - inc.High.Index(1)
-	dn := inc.Low.Index(1) - inc.Low.Last()
+	up := inc.High.Last(0) - inc.High.Index(1)
+	dn := inc.Low.Index(1) - inc.Low.Last(0)
 	return (dn > up) && (dn > 0)
 }
 
@@ -66,7 +66,7 @@ func (inc *PSAR) Update(high, low float64) {
 	inc.High.Update(high)
 	inc.Low.Update(low)
 	if !isFirst {
-		ppsar := inc.Values.Last()
+		ppsar := inc.Values.Last(0)
 		if inc.Falling { // falling formula
 			psar := ppsar - inc.AF*(ppsar-inc.EP)
 			h := inc.High.Shift(1).Highest(2)
diff --git a/pkg/indicator/psar_test.go b/pkg/indicator/psar_test.go
index 6914f7e54..a791a28cc 100644
--- a/pkg/indicator/psar_test.go
+++ b/pkg/indicator/psar_test.go
@@ -36,5 +36,5 @@ func Test_PSAR(t *testing.T) {
 	}
 	assert.Equal(t, psar.Length(), 29)
 	assert.Equal(t, psar.AF, 0.04)
-	assert.Equal(t, psar.Last(), 0.16)
+	assert.Equal(t, psar.Last(0), 0.16)
 }
diff --git a/pkg/indicator/rma.go b/pkg/indicator/rma.go
index 6785a54ec..a06ad18af 100644
--- a/pkg/indicator/rma.go
+++ b/pkg/indicator/rma.go
@@ -78,16 +78,12 @@ func (inc *RMA) Update(x float64) {
 	}
 }
 
-func (inc *RMA) Last() float64 {
-	return inc.Values.Last()
+func (inc *RMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *RMA) Index(i int) float64 {
-	length := len(inc.Values)
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-	return inc.Values[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *RMA) Length() int {
@@ -116,7 +112,7 @@ func (inc *RMA) CalculateAndUpdate(kLines []types.KLine) {
 		inc.PushK(last)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *RMA) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
diff --git a/pkg/indicator/rsi.go b/pkg/indicator/rsi.go
index 8689abbdf..acae219c3 100644
--- a/pkg/indicator/rsi.go
+++ b/pkg/indicator/rsi.go
@@ -65,19 +65,12 @@ func (inc *RSI) Update(price float64) {
 	inc.PreviousAvgLoss = avgLoss
 }
 
-func (inc *RSI) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *RSI) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *RSI) Index(i int) float64 {
-	length := len(inc.Values)
-	if length <= 0 || length-i-1 < 0 {
-		return 0.0
-	}
-	return inc.Values[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *RSI) Length() int {
@@ -99,7 +92,7 @@ func (inc *RSI) CalculateAndUpdate(kLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = kLines[len(kLines)-1].EndTime.Time()
 }
 
diff --git a/pkg/indicator/sma.go b/pkg/indicator/sma.go
index 508a0ce7e..cc3bb1bc7 100644
--- a/pkg/indicator/sma.go
+++ b/pkg/indicator/sma.go
@@ -22,19 +22,12 @@ type SMA struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *SMA) Last() float64 {
-	if inc.Values.Length() == 0 {
-		return 0.0
-	}
-	return inc.Values.Last()
+func (inc *SMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *SMA) Index(i int) float64 {
-	if i >= inc.Values.Length() {
-		return 0.0
-	}
-
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *SMA) Length() int {
@@ -81,7 +74,7 @@ func (inc *SMA) PushK(k types.KLine) {
 
 	inc.Update(k.Close.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Values.Last())
+	inc.EmitUpdate(inc.Values.Last(0))
 }
 
 func (inc *SMA) LoadK(allKLines []types.KLine) {
diff --git a/pkg/indicator/sma_test.go b/pkg/indicator/sma_test.go
index a6ecc1324..c577af215 100644
--- a/pkg/indicator/sma_test.go
+++ b/pkg/indicator/sma_test.go
@@ -58,10 +58,10 @@ func Test_SMA(t *testing.T) {
 				sma.PushK(k)
 			}
 
-			assert.InDelta(t, tt.want, sma.Last(), Delta)
+			assert.InDelta(t, tt.want, sma.Last(0), Delta)
 			assert.InDelta(t, tt.next, sma.Index(1), Delta)
 			sma.Update(tt.update)
-			assert.InDelta(t, tt.updateResult, sma.Last(), Delta)
+			assert.InDelta(t, tt.updateResult, sma.Last(0), Delta)
 			assert.Equal(t, tt.all, sma.Length())
 		})
 	}
diff --git a/pkg/indicator/ssf.go b/pkg/indicator/ssf.go
index 9458e16e8..3a0f71bb3 100644
--- a/pkg/indicator/ssf.go
+++ b/pkg/indicator/ssf.go
@@ -50,9 +50,9 @@ func (inc *SSF) Update(value float64) {
 		}
 
 		result := inc.c1*value +
-			inc.c2*inc.Values.Index(0) +
-			inc.c3*inc.Values.Index(1) +
-			inc.c4*inc.Values.Index(2)
+			inc.c2*inc.Values.Last(0) +
+			inc.c3*inc.Values.Last(1) +
+			inc.c4*inc.Values.Last(2)
 		inc.Values.Push(result)
 	} else { // poles == 2
 		if inc.Values == nil {
@@ -65,17 +65,18 @@ func (inc *SSF) Update(value float64) {
 			inc.Values = floats.Slice{}
 		}
 		result := inc.c1*value +
-			inc.c2*inc.Values.Index(0) +
-			inc.c3*inc.Values.Index(1)
+			inc.c2*inc.Values.Last(0) +
+			inc.c3*inc.Values.Last(1)
 		inc.Values.Push(result)
 	}
 }
 
+func (inc *SSF) Last(i int) float64 {
+	return inc.Values.Last(i)
+}
+
 func (inc *SSF) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *SSF) Length() int {
@@ -85,13 +86,6 @@ func (inc *SSF) Length() int {
 	return inc.Values.Length()
 }
 
-func (inc *SSF) Last() float64 {
-	if inc.Values == nil {
-		return 0.0
-	}
-	return inc.Values.Last()
-}
-
 var _ types.SeriesExtend = &SSF{}
 
 func (inc *SSF) PushK(k types.KLine) {
@@ -102,12 +96,12 @@ func (inc *SSF) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.Values != nil {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 		return
 	}
 	for _, k := range allKLines {
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/ssf_test.go b/pkg/indicator/ssf_test.go
index 253d72220..49f10c30f 100644
--- a/pkg/indicator/ssf_test.go
+++ b/pkg/indicator/ssf_test.go
@@ -63,7 +63,7 @@ func Test_SSF(t *testing.T) {
 				Poles:          tt.poles,
 			}
 			ssf.CalculateAndUpdate(tt.kLines)
-			assert.InDelta(t, tt.want, ssf.Last(), Delta)
+			assert.InDelta(t, tt.want, ssf.Last(0), Delta)
 			assert.InDelta(t, tt.next, ssf.Index(1), Delta)
 			assert.Equal(t, tt.all, ssf.Length())
 		})
diff --git a/pkg/indicator/stddev.go b/pkg/indicator/stddev.go
index a63aa89ef..7e06c448c 100644
--- a/pkg/indicator/stddev.go
+++ b/pkg/indicator/stddev.go
@@ -21,19 +21,12 @@ type StdDev struct {
 	updateCallbacks []func(value float64)
 }
 
-func (inc *StdDev) Last() float64 {
-	if inc.Values.Length() == 0 {
-		return 0.0
-	}
-	return inc.Values.Last()
+func (inc *StdDev) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *StdDev) Index(i int) float64 {
-	if i >= inc.Values.Length() {
-		return 0.0
-	}
-
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *StdDev) Length() int {
@@ -76,7 +69,7 @@ func (inc *StdDev) CalculateAndUpdate(allKLines []types.KLine) {
 		inc.PushK(last)
 	}
 
-	inc.EmitUpdate(inc.Values.Last())
+	inc.EmitUpdate(inc.Values.Last(0))
 }
 
 func (inc *StdDev) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
diff --git a/pkg/indicator/supertrend.go b/pkg/indicator/supertrend.go
index 4ab050dea..bd891dd44 100644
--- a/pkg/indicator/supertrend.go
+++ b/pkg/indicator/supertrend.go
@@ -50,16 +50,12 @@ type Supertrend struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *Supertrend) Last() float64 {
-	return inc.trendPrices.Last()
+func (inc *Supertrend) Last(i int) float64 {
+	return inc.trendPrices.Last(i)
 }
 
 func (inc *Supertrend) Index(i int) float64 {
-	length := inc.Length()
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-	return inc.trendPrices[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *Supertrend) Length() int {
@@ -94,13 +90,13 @@ func (inc *Supertrend) Update(highPrice, lowPrice, closePrice float64) {
 	src := (highPrice + lowPrice) / 2
 
 	// Update uptrend
-	inc.uptrendPrice = src - inc.AverageTrueRange.Last()*inc.ATRMultiplier
+	inc.uptrendPrice = src - inc.AverageTrueRange.Last(0)*inc.ATRMultiplier
 	if inc.previousClosePrice > inc.previousUptrendPrice {
 		inc.uptrendPrice = math.Max(inc.uptrendPrice, inc.previousUptrendPrice)
 	}
 
 	// Update downtrend
-	inc.downtrendPrice = src + inc.AverageTrueRange.Last()*inc.ATRMultiplier
+	inc.downtrendPrice = src + inc.AverageTrueRange.Last(0)*inc.ATRMultiplier
 	if inc.previousClosePrice < inc.previousDowntrendPrice {
 		inc.downtrendPrice = math.Min(inc.downtrendPrice, inc.previousDowntrendPrice)
 	}
@@ -115,7 +111,7 @@ func (inc *Supertrend) Update(highPrice, lowPrice, closePrice float64) {
 	}
 
 	// Update signal
-	if inc.AverageTrueRange.Last() <= 0 {
+	if inc.AverageTrueRange.Last(0) <= 0 {
 		inc.tradeSignal = types.DirectionNone
 	} else if inc.trend == types.DirectionUp && inc.previousTrend == types.DirectionDown {
 		inc.tradeSignal = types.DirectionUp
@@ -138,7 +134,7 @@ func (inc *Supertrend) Update(highPrice, lowPrice, closePrice float64) {
 
 	logst.Debugf("Update supertrend result: closePrice: %v, uptrendPrice: %v, downtrendPrice: %v, trend: %v,"+
 		" tradeSignal: %v, AverageTrueRange.Last(): %v", inc.closePrice, inc.uptrendPrice, inc.downtrendPrice,
-		inc.trend, inc.tradeSignal, inc.AverageTrueRange.Last())
+		inc.trend, inc.tradeSignal, inc.AverageTrueRange.Last(0))
 }
 
 func (inc *Supertrend) GetSignal() types.Direction {
@@ -152,12 +148,12 @@ func (inc *Supertrend) Direction() types.Direction {
 
 // LastSupertrendSupport return the current supertrend support
 func (inc *Supertrend) LastSupertrendSupport() float64 {
-	return inc.supportLine.Last()
+	return inc.supportLine.Last(0)
 }
 
 // LastSupertrendResistance return the current supertrend resistance
 func (inc *Supertrend) LastSupertrendResistance() float64 {
-	return inc.resistanceLine.Last()
+	return inc.resistanceLine.Last(0)
 }
 
 var _ types.SeriesExtend = &Supertrend{}
@@ -169,7 +165,7 @@ func (inc *Supertrend) PushK(k types.KLine) {
 
 	inc.Update(k.GetHigh().Float64(), k.GetLow().Float64(), k.GetClose().Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 
 }
 
@@ -192,7 +188,7 @@ func (inc *Supertrend) CalculateAndUpdate(kLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = kLines[len(kLines)-1].EndTime.Time()
 }
 
diff --git a/pkg/indicator/supertrendPivot.go b/pkg/indicator/supertrendPivot.go
index 14b62925d..85b68ac92 100644
--- a/pkg/indicator/supertrendPivot.go
+++ b/pkg/indicator/supertrendPivot.go
@@ -50,16 +50,12 @@ type PivotSupertrend struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *PivotSupertrend) Last() float64 {
-	return inc.trendPrices.Last()
+func (inc *PivotSupertrend) Last(i int) float64 {
+	return inc.trendPrices.Last(i)
 }
 
 func (inc *PivotSupertrend) Index(i int) float64 {
-	length := inc.Length()
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-	return inc.trendPrices[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *PivotSupertrend) Length() int {
@@ -80,8 +76,8 @@ func (inc *PivotSupertrend) Update(highPrice, lowPrice, closePrice float64) {
 		inc.trend = types.DirectionUp
 	}
 
-	inc.previousPivotLow = inc.PivotLow.Last()
-	inc.previousPivotHigh = inc.PivotHigh.Last()
+	inc.previousPivotLow = inc.PivotLow.Last(0)
+	inc.previousPivotHigh = inc.PivotHigh.Last(0)
 
 	// Update High / Low pivots
 	inc.PivotLow.Update(lowPrice)
@@ -101,9 +97,9 @@ func (inc *PivotSupertrend) Update(highPrice, lowPrice, closePrice float64) {
 	// Initialize lastPp as soon as pivots are made
 	if inc.lastPp == 0 || math.IsNaN(inc.lastPp) {
 		if inc.PivotHigh.Length() > 0 {
-			inc.lastPp = inc.PivotHigh.Last()
+			inc.lastPp = inc.PivotHigh.Last(0)
 		} else if inc.PivotLow.Length() > 0 {
-			inc.lastPp = inc.PivotLow.Last()
+			inc.lastPp = inc.PivotLow.Last(0)
 		} else {
 			inc.lastPp = math.NaN()
 			return
@@ -111,28 +107,28 @@ func (inc *PivotSupertrend) Update(highPrice, lowPrice, closePrice float64) {
 	}
 
 	// Set lastPp to the latest pivotPoint (only changed when new pivot is found)
-	if inc.PivotHigh.Last() != inc.previousPivotHigh {
-		inc.lastPp = inc.PivotHigh.Last()
-	} else if inc.PivotLow.Last() != inc.previousPivotLow {
-		inc.lastPp = inc.PivotLow.Last()
+	if inc.PivotHigh.Last(0) != inc.previousPivotHigh {
+		inc.lastPp = inc.PivotHigh.Last(0)
+	} else if inc.PivotLow.Last(0) != inc.previousPivotLow {
+		inc.lastPp = inc.PivotLow.Last(0)
 	}
 
 	// calculate the Center line using pivot points
 	if inc.src == 0 || math.IsNaN(inc.src) {
 		inc.src = inc.lastPp
 	} else {
-		//weighted calculation
+		// weighted calculation
 		inc.src = (inc.src*2 + inc.lastPp) / 3
 	}
 
 	// Update uptrend
-	inc.uptrendPrice = inc.src - inc.AverageTrueRange.Last()*inc.ATRMultiplier
+	inc.uptrendPrice = inc.src - inc.AverageTrueRange.Last(0)*inc.ATRMultiplier
 	if inc.previousClosePrice > inc.previousUptrendPrice {
 		inc.uptrendPrice = math.Max(inc.uptrendPrice, inc.previousUptrendPrice)
 	}
 
 	// Update downtrend
-	inc.downtrendPrice = inc.src + inc.AverageTrueRange.Last()*inc.ATRMultiplier
+	inc.downtrendPrice = inc.src + inc.AverageTrueRange.Last(0)*inc.ATRMultiplier
 	if inc.previousClosePrice < inc.previousDowntrendPrice {
 		inc.downtrendPrice = math.Min(inc.downtrendPrice, inc.previousDowntrendPrice)
 	}
@@ -147,7 +143,7 @@ func (inc *PivotSupertrend) Update(highPrice, lowPrice, closePrice float64) {
 	}
 
 	// Update signal
-	if inc.AverageTrueRange.Last() <= 0 {
+	if inc.AverageTrueRange.Last(0) <= 0 {
 		inc.tradeSignal = types.DirectionNone
 	} else if inc.trend == types.DirectionUp && inc.previousTrend == types.DirectionDown {
 		inc.tradeSignal = types.DirectionUp
@@ -170,7 +166,7 @@ func (inc *PivotSupertrend) Update(highPrice, lowPrice, closePrice float64) {
 
 	logpst.Debugf("Update pivot point supertrend result: closePrice: %v, uptrendPrice: %v, downtrendPrice: %v, trend: %v,"+
 		" tradeSignal: %v, AverageTrueRange.Last(): %v", inc.closePrice, inc.uptrendPrice, inc.downtrendPrice,
-		inc.trend, inc.tradeSignal, inc.AverageTrueRange.Last())
+		inc.trend, inc.tradeSignal, inc.AverageTrueRange.Last(0))
 }
 
 // GetSignal returns signal (Down, None or Up)
@@ -185,12 +181,12 @@ func (inc *PivotSupertrend) Direction() types.Direction {
 
 // LastSupertrendSupport return the current supertrend support value
 func (inc *PivotSupertrend) LastSupertrendSupport() float64 {
-	return inc.supportLine.Last()
+	return inc.supportLine.Last(0)
 }
 
 // LastSupertrendResistance return the current supertrend resistance value
 func (inc *PivotSupertrend) LastSupertrendResistance() float64 {
-	return inc.resistanceLine.Last()
+	return inc.resistanceLine.Last(0)
 }
 
 var _ types.SeriesExtend = &PivotSupertrend{}
@@ -202,7 +198,7 @@ func (inc *PivotSupertrend) PushK(k types.KLine) {
 
 	inc.Update(k.GetHigh().Float64(), k.GetLow().Float64(), k.GetClose().Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *PivotSupertrend) BindK(target KLineClosedEmitter, symbol string, interval types.Interval) {
diff --git a/pkg/indicator/tema.go b/pkg/indicator/tema.go
index a3a702409..f22a4c93a 100644
--- a/pkg/indicator/tema.go
+++ b/pkg/indicator/tema.go
@@ -36,26 +36,20 @@ func (inc *TEMA) Update(value float64) {
 		inc.A3 = &EWMA{IntervalWindow: inc.IntervalWindow}
 	}
 	inc.A1.Update(value)
-	a1 := inc.A1.Last()
+	a1 := inc.A1.Last(0)
 	inc.A2.Update(a1)
-	a2 := inc.A2.Last()
+	a2 := inc.A2.Last(0)
 	inc.A3.Update(a2)
-	a3 := inc.A3.Last()
+	a3 := inc.A3.Last(0)
 	inc.Values.Push(3*a1 - 3*a2 + a3)
 }
 
-func (inc *TEMA) Last() float64 {
-	if len(inc.Values) > 0 {
-		return inc.Values[len(inc.Values)-1]
-	}
-	return 0.0
+func (inc *TEMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *TEMA) Index(i int) float64 {
-	if i >= len(inc.Values) {
-		return 0
-	}
-	return inc.Values[len(inc.Values)-i-1]
+	return inc.Last(i)
 }
 
 func (inc *TEMA) Length() int {
@@ -72,12 +66,12 @@ func (inc *TEMA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.A1 == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/tema_test.go b/pkg/indicator/tema_test.go
index b50c72ca7..3012f5539 100644
--- a/pkg/indicator/tema_test.go
+++ b/pkg/indicator/tema_test.go
@@ -47,7 +47,7 @@ func Test_TEMA(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			tema := TEMA{IntervalWindow: types.IntervalWindow{Window: 16}}
 			tema.CalculateAndUpdate(tt.kLines)
-			last := tema.Last()
+			last := tema.Last(0)
 			assert.InDelta(t, tt.want, last, Delta)
 			assert.InDelta(t, tt.next, tema.Index(1), Delta)
 			assert.Equal(t, tt.all, tema.Length())
diff --git a/pkg/indicator/till.go b/pkg/indicator/till.go
index c7fca34dc..828175dca 100644
--- a/pkg/indicator/till.go
+++ b/pkg/indicator/till.go
@@ -57,28 +57,18 @@ func (inc *TILL) Update(value float64) {
 	}
 
 	inc.e1.Update(value)
-	inc.e2.Update(inc.e1.Last())
-	inc.e3.Update(inc.e2.Last())
-	inc.e4.Update(inc.e3.Last())
-	inc.e5.Update(inc.e4.Last())
-	inc.e6.Update(inc.e5.Last())
+	inc.e2.Update(inc.e1.Last(0))
+	inc.e3.Update(inc.e2.Last(0))
+	inc.e4.Update(inc.e3.Last(0))
+	inc.e5.Update(inc.e4.Last(0))
+	inc.e6.Update(inc.e5.Last(0))
 }
 
-func (inc *TILL) Last() float64 {
-	if inc.e1 == nil || inc.e1.Length() == 0 {
-		return 0
-	}
-	e3 := inc.e3.Last()
-	e4 := inc.e4.Last()
-	e5 := inc.e5.Last()
-	e6 := inc.e6.Last()
-	return inc.c1*e6 + inc.c2*e5 + inc.c3*e4 + inc.c4*e3
-}
-
-func (inc *TILL) Index(i int) float64 {
+func (inc *TILL) Last(i int) float64 {
 	if inc.e1 == nil || inc.e1.Length() <= i {
 		return 0
 	}
+
 	e3 := inc.e3.Index(i)
 	e4 := inc.e4.Index(i)
 	e5 := inc.e5.Index(i)
@@ -86,6 +76,10 @@ func (inc *TILL) Index(i int) float64 {
 	return inc.c1*e6 + inc.c2*e5 + inc.c3*e4 + inc.c4*e3
 }
 
+func (inc *TILL) Index(i int) float64 {
+	return inc.Last(i)
+}
+
 func (inc *TILL) Length() int {
 	if inc.e1 == nil {
 		return 0
@@ -101,7 +95,7 @@ func (inc *TILL) PushK(k types.KLine) {
 	}
 
 	inc.Update(k.Close.Float64())
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *TILL) LoadK(allKLines []types.KLine) {
diff --git a/pkg/indicator/till_test.go b/pkg/indicator/till_test.go
index 1b03017b8..e78e6620a 100644
--- a/pkg/indicator/till_test.go
+++ b/pkg/indicator/till_test.go
@@ -57,7 +57,7 @@ func Test_TILL(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			till := TILL{IntervalWindow: types.IntervalWindow{Window: 16}}
 			till.CalculateAndUpdate(tt.kLines)
-			last := till.Last()
+			last := till.Last(0)
 			assert.InDelta(t, tt.want, last, Delta)
 			assert.InDelta(t, tt.next, till.Index(1), Delta)
 			assert.Equal(t, tt.all, till.Length())
diff --git a/pkg/indicator/tma.go b/pkg/indicator/tma.go
index 97c5997d5..fd1c416db 100644
--- a/pkg/indicator/tma.go
+++ b/pkg/indicator/tma.go
@@ -6,6 +6,7 @@ import (
 
 // Refer: Triangular Moving Average
 // Refer URL: https://ja.wikipedia.org/wiki/移動平均
+//
 //go:generate callbackgen -type TMA
 type TMA struct {
 	types.SeriesBase
@@ -24,21 +25,15 @@ func (inc *TMA) Update(value float64) {
 	}
 
 	inc.s1.Update(value)
-	inc.s2.Update(inc.s1.Last())
+	inc.s2.Update(inc.s1.Last(0))
 }
 
-func (inc *TMA) Last() float64 {
-	if inc.s2 == nil {
-		return 0
-	}
-	return inc.s2.Last()
+func (inc *TMA) Last(i int) float64 {
+	return inc.s2.Last(i)
 }
 
 func (inc *TMA) Index(i int) float64 {
-	if inc.s2 == nil {
-		return 0
-	}
-	return inc.s2.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *TMA) Length() int {
@@ -58,12 +53,12 @@ func (inc *TMA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.s1 == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/tsi.go b/pkg/indicator/tsi.go
index 4cdb6c750..fa4546aa7 100644
--- a/pkg/indicator/tsi.go
+++ b/pkg/indicator/tsi.go
@@ -9,6 +9,7 @@ import (
 
 // Refer: True Strength Index
 // Refer URL: https://www.investopedia.com/terms/t/tsi.asp
+//
 //go:generate callbackgen -type TSI
 type TSI struct {
 	types.SeriesBase
@@ -66,10 +67,10 @@ func (inc *TSI) Update(value float64) {
 	apc := math.Abs(pc)
 	inc.Apcs.Update(apc)
 
-	inc.Pcds.Update(inc.Pcs.Last())
-	inc.Apcds.Update(inc.Apcs.Last())
+	inc.Pcds.Update(inc.Pcs.Last(0))
+	inc.Apcds.Update(inc.Apcs.Last(0))
 
-	tsi := (inc.Pcds.Last() / inc.Apcds.Last()) * 100.
+	tsi := (inc.Pcds.Last(0) / inc.Apcds.Last(0)) * 100.
 	inc.Values.Push(tsi)
 	if inc.Values.Length() > MaxNumOfEWMA {
 		inc.Values = inc.Values[MaxNumOfEWMATruncateSize-1:]
@@ -80,12 +81,12 @@ func (inc *TSI) Length() int {
 	return inc.Values.Length()
 }
 
-func (inc *TSI) Last() float64 {
-	return inc.Values.Last()
+func (inc *TSI) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *TSI) Index(i int) float64 {
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *TSI) PushK(k types.KLine) {
diff --git a/pkg/indicator/tsi_test.go b/pkg/indicator/tsi_test.go
index dc7c9c3cb..872cfbca0 100644
--- a/pkg/indicator/tsi_test.go
+++ b/pkg/indicator/tsi_test.go
@@ -32,5 +32,5 @@ func Test_TSI(t *testing.T) {
 	}
 	assert.Equal(t, tsi.Length(), 29)
 	Delta := 1.5e-2
-	assert.InDelta(t, tsi.Last(), 22.89, Delta)
+	assert.InDelta(t, tsi.Last(0), 22.89, Delta)
 }
diff --git a/pkg/indicator/utBotAlert.go b/pkg/indicator/utBotAlert.go
index 9d974ca42..4a9c5cda4 100644
--- a/pkg/indicator/utBotAlert.go
+++ b/pkg/indicator/utBotAlert.go
@@ -70,20 +70,20 @@ func (inc *UtBotAlert) Update(highPrice, lowPrice, closePrice float64) {
 	// Update ATR
 	inc.AverageTrueRange.Update(highPrice, lowPrice, closePrice)
 
-	nLoss := inc.AverageTrueRange.Last() * inc.KeyValue
+	nLoss := inc.AverageTrueRange.Last(0) * inc.KeyValue
 
 	// xATRTrailingStop
 	if inc.xATRTrailingStop.Length() == 0 {
 		// For first run
 		inc.xATRTrailingStop.Update(0)
 
-	} else if closePrice > inc.xATRTrailingStop.Index(1) && inc.previousClosePrice > inc.xATRTrailingStop.Index(1) {
-		inc.xATRTrailingStop.Update(math.Max(inc.xATRTrailingStop.Index(1), closePrice-nLoss))
+	} else if closePrice > inc.xATRTrailingStop.Last(1) && inc.previousClosePrice > inc.xATRTrailingStop.Last(1) {
+		inc.xATRTrailingStop.Update(math.Max(inc.xATRTrailingStop.Last(1), closePrice-nLoss))
 
-	} else if closePrice < inc.xATRTrailingStop.Index(1) && inc.previousClosePrice < inc.xATRTrailingStop.Index(1) {
-		inc.xATRTrailingStop.Update(math.Min(inc.xATRTrailingStop.Index(1), closePrice+nLoss))
+	} else if closePrice < inc.xATRTrailingStop.Last(1) && inc.previousClosePrice < inc.xATRTrailingStop.Last(1) {
+		inc.xATRTrailingStop.Update(math.Min(inc.xATRTrailingStop.Last(1), closePrice+nLoss))
 
-	} else if closePrice > inc.xATRTrailingStop.Index(1) {
+	} else if closePrice > inc.xATRTrailingStop.Last(1) {
 		inc.xATRTrailingStop.Update(closePrice - nLoss)
 
 	} else {
@@ -91,19 +91,19 @@ func (inc *UtBotAlert) Update(highPrice, lowPrice, closePrice float64) {
 	}
 
 	// pos
-	if inc.previousClosePrice < inc.xATRTrailingStop.Index(1) && closePrice > inc.xATRTrailingStop.Index(1) {
+	if inc.previousClosePrice < inc.xATRTrailingStop.Last(1) && closePrice > inc.xATRTrailingStop.Last(1) {
 		inc.pos = types.DirectionUp
-	} else if inc.previousClosePrice > inc.xATRTrailingStop.Index(1) && closePrice < inc.xATRTrailingStop.Index(1) {
+	} else if inc.previousClosePrice > inc.xATRTrailingStop.Last(1) && closePrice < inc.xATRTrailingStop.Last(1) {
 		inc.pos = types.DirectionDown
 	} else {
 		inc.pos = inc.previousPos
 	}
 
-	above := closePrice > inc.xATRTrailingStop.Last() && inc.previousClosePrice < inc.xATRTrailingStop.Index(1)
-	below := closePrice < inc.xATRTrailingStop.Last() && inc.previousClosePrice > inc.xATRTrailingStop.Index(1)
+	above := closePrice > inc.xATRTrailingStop.Last(0) && inc.previousClosePrice < inc.xATRTrailingStop.Last(1)
+	below := closePrice < inc.xATRTrailingStop.Last(0) && inc.previousClosePrice > inc.xATRTrailingStop.Last(1)
 
-	buy := closePrice > inc.xATRTrailingStop.Last() && above  // buy
-	sell := closePrice < inc.xATRTrailingStop.Last() && below // sell
+	buy := closePrice > inc.xATRTrailingStop.Last(0) && above  // buy
+	sell := closePrice < inc.xATRTrailingStop.Last(0) && below // sell
 
 	inc.buyValue.Push(buy)
 	inc.sellValue.Push(sell)
diff --git a/pkg/indicator/v2_atr_test.go b/pkg/indicator/v2_atr_test.go
index 1dd49501a..bacbc7861 100644
--- a/pkg/indicator/v2_atr_test.go
+++ b/pkg/indicator/v2_atr_test.go
@@ -71,7 +71,7 @@ func Test_ATR2(t *testing.T) {
 				stream.EmitKLineClosed(k)
 			}
 
-			got := atr.Last()
+			got := atr.Last(0)
 			diff := math.Trunc((got-tt.want)*100) / 100
 			if diff != 0 {
 				t.Errorf("ATR2() = %v, want %v", got, tt.want)
diff --git a/pkg/indicator/v2_ewma.go b/pkg/indicator/v2_ewma.go
index e452aaeda..afd0752ad 100644
--- a/pkg/indicator/v2_ewma.go
+++ b/pkg/indicator/v2_ewma.go
@@ -30,7 +30,7 @@ func (s *EWMAStream) calculateAndPush(v float64) {
 }
 
 func (s *EWMAStream) calculate(v float64) float64 {
-	last := s.slice.Last()
+	last := s.slice.Last(0)
 	m := s.multiplier
 	return (1.0-m)*last + m*v
 }
diff --git a/pkg/indicator/v2_rsi.go b/pkg/indicator/v2_rsi.go
index 16732f2bd..583e68baf 100644
--- a/pkg/indicator/v2_rsi.go
+++ b/pkg/indicator/v2_rsi.go
@@ -32,8 +32,8 @@ func (s *RSIStream) calculate(_ float64) float64 {
 	var sourceLen = s.source.Length()
 	var limit = min(s.window, sourceLen)
 	for i := 0; i < limit; i++ {
-		value := s.source.Index(i)
-		prev := s.source.Index(i + 1)
+		value := s.source.Last(i)
+		prev := s.source.Last(i + 1)
 		change := value - prev
 		if change >= 0 {
 			gainSum += change
diff --git a/pkg/indicator/v2_tr_test.go b/pkg/indicator/v2_tr_test.go
index 38195f55d..c6b46332a 100644
--- a/pkg/indicator/v2_tr_test.go
+++ b/pkg/indicator/v2_tr_test.go
@@ -72,7 +72,7 @@ func Test_TR_and_RMA(t *testing.T) {
 				stream.EmitKLineClosed(k)
 			}
 
-			got := rma.Last()
+			got := rma.Last(0)
 			diff := math.Trunc((got-tt.want)*100) / 100
 			if diff != 0 {
 				t.Errorf("RMA(TR()) = %v, want %v", got, tt.want)
diff --git a/pkg/indicator/vidya.go b/pkg/indicator/vidya.go
index 311e47f4f..5f21be1c0 100644
--- a/pkg/indicator/vidya.go
+++ b/pkg/indicator/vidya.go
@@ -58,18 +58,18 @@ func (inc *VIDYA) Update(value float64) {
 	change := types.Change(&inc.input)
 	CMO := math.Abs(types.Sum(change, inc.Window) / types.Sum(types.Abs(change), inc.Window))
 	alpha := 2. / float64(inc.Window+1)
-	inc.Values.Push(value*alpha*CMO + inc.Values.Last()*(1.-alpha*CMO))
+	inc.Values.Push(value*alpha*CMO + inc.Values.Last(0)*(1.-alpha*CMO))
 	if inc.Values.Length() > MaxNumOfEWMA {
 		inc.Values = inc.Values[MaxNumOfEWMATruncateSize-1:]
 	}
 }
 
-func (inc *VIDYA) Last() float64 {
-	return inc.Values.Last()
+func (inc *VIDYA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *VIDYA) Index(i int) float64 {
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
 func (inc *VIDYA) Length() int {
@@ -86,12 +86,12 @@ func (inc *VIDYA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.input.Length() == 0 {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/vidya_test.go b/pkg/indicator/vidya_test.go
index 8ac1df255..164173441 100644
--- a/pkg/indicator/vidya_test.go
+++ b/pkg/indicator/vidya_test.go
@@ -10,10 +10,10 @@ import (
 func Test_VIDYA(t *testing.T) {
 	vidya := &VIDYA{IntervalWindow: types.IntervalWindow{Window: 16}}
 	vidya.Update(1)
-	assert.Equal(t, vidya.Last(), 1.)
+	assert.Equal(t, vidya.Last(0), 1.)
 	vidya.Update(2)
 	newV := 2./17.*2. + 1.*(1.-2./17.)
-	assert.Equal(t, vidya.Last(), newV)
+	assert.Equal(t, vidya.Last(0), newV)
 	vidya.Update(1)
-	assert.Equal(t, vidya.Last(), vidya.Index(1))
+	assert.Equal(t, vidya.Last(0), vidya.Index(1))
 }
diff --git a/pkg/indicator/volatility.go b/pkg/indicator/volatility.go
index 6b3dcd7cb..3c5efce96 100644
--- a/pkg/indicator/volatility.go
+++ b/pkg/indicator/volatility.go
@@ -26,18 +26,12 @@ type Volatility struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *Volatility) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *Volatility) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *Volatility) Index(i int) float64 {
-	if len(inc.Values)-i <= 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-i-1]
+	return inc.Last(i)
 }
 
 func (inc *Volatility) Length() int {
diff --git a/pkg/indicator/vwap.go b/pkg/indicator/vwap.go
index 805def828..3f2e08085 100644
--- a/pkg/indicator/vwap.go
+++ b/pkg/indicator/vwap.go
@@ -56,20 +56,12 @@ func (inc *VWAP) Update(price, volume float64) {
 	inc.Values.Push(vwap)
 }
 
-func (inc *VWAP) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *VWAP) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *VWAP) Index(i int) float64 {
-	length := len(inc.Values)
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-
-	return inc.Values[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *VWAP) Length() int {
@@ -91,7 +83,7 @@ func (inc *VWAP) CalculateAndUpdate(allKLines []types.KLine) {
 		inc.PushK(k)
 	}
 
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 	inc.EndTime = allKLines[len(allKLines)-1].EndTime.Time()
 }
 
@@ -112,5 +104,5 @@ func calculateVWAP(klines []types.KLine, priceF KLineValueMapper, window int) fl
 	for _, k := range klines {
 		vwap.Update(priceF(k), k.Volume.Float64())
 	}
-	return vwap.Last()
+	return vwap.Last(0)
 }
diff --git a/pkg/indicator/vwma.go b/pkg/indicator/vwma.go
index a8a328e20..ed383531b 100644
--- a/pkg/indicator/vwma.go
+++ b/pkg/indicator/vwma.go
@@ -14,7 +14,7 @@ import (
 //	VWMA = SMA(pv, window) / SMA(volumes, window)
 //
 // Volume Weighted Moving Average
-//- https://www.motivewave.com/studies/volume_weighted_moving_average.htm
+// - https://www.motivewave.com/studies/volume_weighted_moving_average.htm
 //
 // The Volume Weighted Moving Average (VWMA) is a technical analysis indicator that is used to smooth price data and reduce the lag
 // associated with traditional moving averages. It is calculated by taking the weighted moving average of the input data, with the
@@ -36,19 +36,12 @@ type VWMA struct {
 	updateCallbacks []func(value float64)
 }
 
-func (inc *VWMA) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0.0
-	}
-	return inc.Values[len(inc.Values)-1]
+func (inc *VWMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *VWMA) Index(i int) float64 {
-	length := len(inc.Values)
-	if length == 0 || length-i-1 < 0 {
-		return 0
-	}
-	return inc.Values[length-i-1]
+	return inc.Last(i)
 }
 
 func (inc *VWMA) Length() int {
@@ -70,8 +63,8 @@ func (inc *VWMA) Update(price, volume float64) {
 	inc.PriceVolumeSMA.Update(price * volume)
 	inc.VolumeSMA.Update(volume)
 
-	pv := inc.PriceVolumeSMA.Last()
-	v := inc.VolumeSMA.Last()
+	pv := inc.PriceVolumeSMA.Last(0)
+	v := inc.VolumeSMA.Last(0)
 	vwma := pv / v
 	inc.Values.Push(vwma)
 }
@@ -104,7 +97,7 @@ func (inc *VWMA) CalculateAndUpdate(allKLines []types.KLine) {
 	}
 
 	inc.EndTime = last.EndTime.Time()
-	inc.EmitUpdate(inc.Values.Last())
+	inc.EmitUpdate(inc.Values.Last(0))
 }
 
 func (inc *VWMA) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
diff --git a/pkg/indicator/wdrift.go b/pkg/indicator/wdrift.go
index 61060a747..d9b6675a0 100644
--- a/pkg/indicator/wdrift.go
+++ b/pkg/indicator/wdrift.go
@@ -10,6 +10,7 @@ import (
 // Refer: https://tradingview.com/script/aDymGrFx-Drift-Study-Inspired-by-Monte-Carlo-Simulations-with-BM-KL/
 // Brownian Motion's drift factor
 // could be used in Monte Carlo Simulations
+//
 //go:generate callbackgen -type WeightedDrift
 type WeightedDrift struct {
 	types.SeriesBase
@@ -54,7 +55,7 @@ func (inc *WeightedDrift) Update(value float64, weight float64) {
 	}
 	if inc.chng.Length() >= inc.Window {
 		stdev := types.Stdev(inc.chng, inc.Window)
-		drift := inc.MA.Last() - stdev*stdev*0.5
+		drift := inc.MA.Last(0) - stdev*stdev*0.5
 		inc.Values.Push(drift)
 	}
 }
@@ -77,7 +78,7 @@ func (inc *WeightedDrift) ZeroPoint() float64 {
 	} else {
 		return N2
 	}*/
-	return inc.LastValue * math.Exp(window*(0.5*stdev*stdev)+chng-inc.MA.Last()*window)
+	return inc.LastValue * math.Exp(window*(0.5*stdev*stdev)+chng-inc.MA.Last(0)*window)
 }
 
 func (inc *WeightedDrift) Clone() (out *WeightedDrift) {
@@ -100,17 +101,11 @@ func (inc *WeightedDrift) TestUpdate(value float64, weight float64) *WeightedDri
 }
 
 func (inc *WeightedDrift) Index(i int) float64 {
-	if inc.Values == nil {
-		return 0
-	}
-	return inc.Values.Index(i)
+	return inc.Last(i)
 }
 
-func (inc *WeightedDrift) Last() float64 {
-	if inc.Values.Length() == 0 {
-		return 0
-	}
-	return inc.Values.Last()
+func (inc *WeightedDrift) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *WeightedDrift) Length() int {
@@ -130,12 +125,12 @@ func (inc *WeightedDrift) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.chng == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/wwma.go b/pkg/indicator/wwma.go
index 0dbc67ca1..f8fe954aa 100644
--- a/pkg/indicator/wwma.go
+++ b/pkg/indicator/wwma.go
@@ -33,25 +33,17 @@ func (inc *WWMA) Update(value float64) {
 		inc.Values = inc.Values[MaxNumOfWWMATruncateSize-1:]
 	}
 
-	last := inc.Last()
+	last := inc.Last(0)
 	wma := last + (value-last)/float64(inc.Window)
 	inc.Values.Push(wma)
 }
 
-func (inc *WWMA) Last() float64 {
-	if len(inc.Values) == 0 {
-		return 0
-	}
-
-	return inc.Values[len(inc.Values)-1]
+func (inc *WWMA) Last(i int) float64 {
+	return inc.Values.Last(i)
 }
 
 func (inc *WWMA) Index(i int) float64 {
-	if i >= len(inc.Values) {
-		return 0
-	}
-
-	return inc.Values[len(inc.Values)-1-i]
+	return inc.Last(i)
 }
 
 func (inc *WWMA) Length() int {
@@ -76,7 +68,7 @@ func (inc *WWMA) CalculateAndUpdate(allKLines []types.KLine) {
 		if doable {
 			inc.PushK(k)
 			inc.LastOpenTime = k.StartTime.Time()
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	}
 }
diff --git a/pkg/indicator/zlema.go b/pkg/indicator/zlema.go
index 5c7279f61..182cf29eb 100644
--- a/pkg/indicator/zlema.go
+++ b/pkg/indicator/zlema.go
@@ -27,17 +27,14 @@ type ZLEMA struct {
 }
 
 func (inc *ZLEMA) Index(i int) float64 {
-	if inc.zlema == nil {
-		return 0
-	}
-	return inc.zlema.Index(i)
+	return inc.Last(i)
 }
 
-func (inc *ZLEMA) Last() float64 {
+func (inc *ZLEMA) Last(i int) float64 {
 	if inc.zlema == nil {
 		return 0
 	}
-	return inc.zlema.Last()
+	return inc.zlema.Last(i)
 }
 
 func (inc *ZLEMA) Length() int {
@@ -74,12 +71,12 @@ func (inc *ZLEMA) CalculateAndUpdate(allKLines []types.KLine) {
 	if inc.zlema == nil {
 		for _, k := range allKLines {
 			inc.PushK(k)
-			inc.EmitUpdate(inc.Last())
+			inc.EmitUpdate(inc.Last(0))
 		}
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
diff --git a/pkg/indicator/zlema_test.go b/pkg/indicator/zlema_test.go
index 4560f4276..6f2ff3194 100644
--- a/pkg/indicator/zlema_test.go
+++ b/pkg/indicator/zlema_test.go
@@ -46,7 +46,7 @@ func Test_ZLEMA(t *testing.T) {
 		t.Run(tt.name, func(t *testing.T) {
 			zlema := ZLEMA{IntervalWindow: types.IntervalWindow{Window: 16}}
 			zlema.CalculateAndUpdate(tt.kLines)
-			last := zlema.Last()
+			last := zlema.Last(0)
 			assert.InDelta(t, tt.want, last, Delta)
 			assert.InDelta(t, tt.next, zlema.Index(1), Delta)
 			assert.Equal(t, tt.all, zlema.Length())
diff --git a/pkg/risk/dynamicrisk/dynamic_exposure.go b/pkg/risk/dynamicrisk/dynamic_exposure.go
index 71eb12155..415a287a3 100644
--- a/pkg/risk/dynamicrisk/dynamic_exposure.go
+++ b/pkg/risk/dynamicrisk/dynamic_exposure.go
@@ -59,9 +59,9 @@ func (d *DynamicExposureBollBand) initialize(symbol string, session *bbgo.Exchan
 
 // getMaxExposure returns the max exposure
 func (d *DynamicExposureBollBand) getMaxExposure(price float64, trend types.Direction) (fixedpoint.Value, error) {
-	downBand := d.dynamicExposureBollBand.DownBand.Last()
-	upBand := d.dynamicExposureBollBand.UpBand.Last()
-	sma := d.dynamicExposureBollBand.SMA.Last()
+	downBand := d.dynamicExposureBollBand.DownBand.Last(0)
+	upBand := d.dynamicExposureBollBand.UpBand.Last(0)
+	sma := d.dynamicExposureBollBand.SMA.Last(0)
 	log.Infof("dynamicExposureBollBand bollinger band: up %f sma %f down %f", upBand, sma, downBand)
 
 	bandPercentage := 0.0
diff --git a/pkg/risk/dynamicrisk/dynamic_spread.go b/pkg/risk/dynamicrisk/dynamic_spread.go
index 2b5cbbeb8..f6fab9cb6 100644
--- a/pkg/risk/dynamicrisk/dynamic_spread.go
+++ b/pkg/risk/dynamicrisk/dynamic_spread.go
@@ -114,7 +114,7 @@ func (ds *DynamicAmpSpread) update(kline types.KLine) {
 
 func (ds *DynamicAmpSpread) getAskSpread() (askSpread float64, err error) {
 	if ds.AskSpreadScale != nil && ds.dynamicAskSpread.Length() >= ds.Window {
-		askSpread, err = ds.AskSpreadScale.Scale(ds.dynamicAskSpread.Last())
+		askSpread, err = ds.AskSpreadScale.Scale(ds.dynamicAskSpread.Last(0))
 		if err != nil {
 			log.WithError(err).Errorf("can not calculate dynamicAskSpread")
 			return 0, err
@@ -128,7 +128,7 @@ func (ds *DynamicAmpSpread) getAskSpread() (askSpread float64, err error) {
 
 func (ds *DynamicAmpSpread) getBidSpread() (bidSpread float64, err error) {
 	if ds.BidSpreadScale != nil && ds.dynamicBidSpread.Length() >= ds.Window {
-		bidSpread, err = ds.BidSpreadScale.Scale(ds.dynamicBidSpread.Last())
+		bidSpread, err = ds.BidSpreadScale.Scale(ds.dynamicBidSpread.Last(0))
 		if err != nil {
 			log.WithError(err).Errorf("can not calculate dynamicBidSpread")
 			return 0, err
@@ -224,12 +224,12 @@ func (ds *DynamicSpreadBollWidthRatio) getWeightedBBWidthRatio(positiveSigmoid b
 	//   - To ask spread, the higher neutral band get greater ratio
 	//   - To bid spread, the lower neutral band get greater ratio
 
-	defaultMid := ds.defaultBoll.SMA.Last()
-	defaultUpper := ds.defaultBoll.UpBand.Last()
-	defaultLower := ds.defaultBoll.DownBand.Last()
+	defaultMid := ds.defaultBoll.SMA.Last(0)
+	defaultUpper := ds.defaultBoll.UpBand.Last(0)
+	defaultLower := ds.defaultBoll.DownBand.Last(0)
 	defaultWidth := defaultUpper - defaultLower
-	neutralUpper := ds.neutralBoll.UpBand.Last()
-	neutralLower := ds.neutralBoll.DownBand.Last()
+	neutralUpper := ds.neutralBoll.UpBand.Last(0)
+	neutralLower := ds.neutralBoll.DownBand.Last(0)
 	factor := defaultWidth / ds.Sensitivity
 	var weightedUpper, weightedLower, weightedDivUpper, weightedDivLower float64
 	if positiveSigmoid {
diff --git a/pkg/strategy/audacitymaker/orderflow.go b/pkg/strategy/audacitymaker/orderflow.go
index b8b0d80c7..94de68880 100644
--- a/pkg/strategy/audacitymaker/orderflow.go
+++ b/pkg/strategy/audacitymaker/orderflow.go
@@ -92,7 +92,7 @@ func (s *PerTrade) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gener
 			// min-max scaling
 			ofsMax := orderFlowSize.Tail(100).Max()
 			ofsMin := orderFlowSize.Tail(100).Min()
-			ofsMinMax := (orderFlowSize.Last() - ofsMin) / (ofsMax - ofsMin)
+			ofsMinMax := (orderFlowSize.Last(0) - ofsMin) / (ofsMax - ofsMin)
 			// preserves temporal dependency via polar encoded angles
 			orderFlowSizeMinMax.Push(ofsMinMax)
 		}
@@ -102,7 +102,7 @@ func (s *PerTrade) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gener
 			// min-max scaling
 			ofnMax := orderFlowNumber.Tail(100).Max()
 			ofnMin := orderFlowNumber.Tail(100).Min()
-			ofnMinMax := (orderFlowNumber.Last() - ofnMin) / (ofnMax - ofnMin)
+			ofnMinMax := (orderFlowNumber.Last(0) - ofnMin) / (ofnMax - ofnMin)
 			// preserves temporal dependency via polar encoded angles
 			orderFlowNumberMinMax.Push(ofnMinMax)
 		}
@@ -167,9 +167,9 @@ func (s *PerTrade) placeTrade(ctx context.Context, side types.SideType, quantity
 
 func outlier(fs floats.Slice, multiplier float64) int {
 	stddev := stat.StdDev(fs, nil)
-	if fs.Last() > fs.Mean()+multiplier*stddev {
+	if fs.Last(0) > fs.Mean()+multiplier*stddev {
 		return 1
-	} else if fs.Last() < fs.Mean()-multiplier*stddev {
+	} else if fs.Last(0) < fs.Mean()-multiplier*stddev {
 		return -1
 	}
 	return 0
diff --git a/pkg/strategy/bollgrid/strategy.go b/pkg/strategy/bollgrid/strategy.go
index 61be95202..2474c7b9c 100644
--- a/pkg/strategy/bollgrid/strategy.go
+++ b/pkg/strategy/bollgrid/strategy.go
@@ -135,7 +135,7 @@ func (s *Strategy) generateGridBuyOrders(session *bbgo.ExchangeSession) ([]types
 	ema99 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 99})
 	ema25 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 25})
 	ema7 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 7})
-	if ema7.Last() > ema25.Last()*1.001 && ema25.Last() > ema99.Last()*1.0005 {
+	if ema7.Last(0) > ema25.Last(0)*1.001 && ema25.Last(0) > ema99.Last(0)*1.0005 {
 		log.Infof("all ema lines trend up, skip buy")
 		return nil, nil
 	}
@@ -202,7 +202,7 @@ func (s *Strategy) generateGridSellOrders(session *bbgo.ExchangeSession) ([]type
 	ema99 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 99})
 	ema25 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 25})
 	ema7 := s.StandardIndicatorSet.EWMA(types.IntervalWindow{Interval: s.Interval, Window: 7})
-	if ema7.Last() < ema25.Last()*(1-0.004) && ema25.Last() < ema99.Last()*(1-0.0005) {
+	if ema7.Last(0) < ema25.Last(0)*(1-0.004) && ema25.Last(0) < ema99.Last(0)*(1-0.0005) {
 		log.Infof("all ema lines trend down, skip sell")
 		return nil, nil
 	}
diff --git a/pkg/strategy/bollmaker/dynamic_spread.go b/pkg/strategy/bollmaker/dynamic_spread.go
index f7583d110..51785f3df 100644
--- a/pkg/strategy/bollmaker/dynamic_spread.go
+++ b/pkg/strategy/bollmaker/dynamic_spread.go
@@ -126,7 +126,7 @@ func (ds *DynamicSpreadAmpSettings) update(kline types.KLine) {
 
 func (ds *DynamicSpreadAmpSettings) getAskSpread() (askSpread float64, err error) {
 	if ds.AskSpreadScale != nil && ds.dynamicAskSpread.Length() >= ds.Window {
-		askSpread, err = ds.AskSpreadScale.Scale(ds.dynamicAskSpread.Last())
+		askSpread, err = ds.AskSpreadScale.Scale(ds.dynamicAskSpread.Last(0))
 		if err != nil {
 			log.WithError(err).Errorf("can not calculate dynamicAskSpread")
 			return 0, err
@@ -140,7 +140,7 @@ func (ds *DynamicSpreadAmpSettings) getAskSpread() (askSpread float64, err error
 
 func (ds *DynamicSpreadAmpSettings) getBidSpread() (bidSpread float64, err error) {
 	if ds.BidSpreadScale != nil && ds.dynamicBidSpread.Length() >= ds.Window {
-		bidSpread, err = ds.BidSpreadScale.Scale(ds.dynamicBidSpread.Last())
+		bidSpread, err = ds.BidSpreadScale.Scale(ds.dynamicBidSpread.Last(0))
 		if err != nil {
 			log.WithError(err).Errorf("can not calculate dynamicBidSpread")
 			return 0, err
@@ -224,12 +224,12 @@ func (ds *DynamicSpreadBollWidthRatioSettings) getWeightedBBWidthRatio(positiveS
 	//   - To ask spread, the higher neutral band get greater ratio
 	//   - To bid spread, the lower neutral band get greater ratio
 
-	defaultMid := ds.defaultBoll.SMA.Last()
-	defaultUpper := ds.defaultBoll.UpBand.Last()
-	defaultLower := ds.defaultBoll.DownBand.Last()
+	defaultMid := ds.defaultBoll.SMA.Last(0)
+	defaultUpper := ds.defaultBoll.UpBand.Last(0)
+	defaultLower := ds.defaultBoll.DownBand.Last(0)
 	defaultWidth := defaultUpper - defaultLower
-	neutralUpper := ds.neutralBoll.UpBand.Last()
-	neutralLower := ds.neutralBoll.DownBand.Last()
+	neutralUpper := ds.neutralBoll.UpBand.Last(0)
+	neutralLower := ds.neutralBoll.DownBand.Last(0)
 	factor := defaultWidth / ds.Sensitivity
 	var weightedUpper, weightedLower, weightedDivUpper, weightedDivLower float64
 	if positiveSigmoid {
diff --git a/pkg/strategy/bollmaker/strategy.go b/pkg/strategy/bollmaker/strategy.go
index 92b3fc4af..efd1742d2 100644
--- a/pkg/strategy/bollmaker/strategy.go
+++ b/pkg/strategy/bollmaker/strategy.go
@@ -278,9 +278,9 @@ func (s *Strategy) placeOrders(ctx context.Context, midPrice fixedpoint.Value, k
 	baseBalance, hasBaseBalance := balances[s.Market.BaseCurrency]
 	quoteBalance, hasQuoteBalance := balances[s.Market.QuoteCurrency]
 
-	downBand := s.defaultBoll.DownBand.Last()
-	upBand := s.defaultBoll.UpBand.Last()
-	sma := s.defaultBoll.SMA.Last()
+	downBand := s.defaultBoll.DownBand.Last(0)
+	upBand := s.defaultBoll.UpBand.Last(0)
+	sma := s.defaultBoll.SMA.Last(0)
 	log.Infof("%s bollinger band: up %f sma %f down %f", s.Symbol, upBand, sma, downBand)
 
 	bandPercentage := calculateBandPercentage(upBand, downBand, sma, midPrice.Float64())
@@ -351,7 +351,7 @@ func (s *Strategy) placeOrders(ctx context.Context, midPrice fixedpoint.Value, k
 	// WHEN: price breaks the upper band (price > window 2) == strongUpTrend
 	// THEN: we apply strongUpTrend skew
 	if s.TradeInBand {
-		if !inBetween(midPrice.Float64(), s.neutralBoll.DownBand.Last(), s.neutralBoll.UpBand.Last()) {
+		if !inBetween(midPrice.Float64(), s.neutralBoll.DownBand.Last(0), s.neutralBoll.UpBand.Last(0)) {
 			log.Infof("tradeInBand is set, skip placing orders when the price is outside of the band")
 			return
 		}
@@ -410,7 +410,7 @@ func (s *Strategy) placeOrders(ctx context.Context, midPrice fixedpoint.Value, k
 		canSell = false
 	}
 
-	if s.BuyBelowNeutralSMA && midPrice.Float64() > s.neutralBoll.SMA.Last() {
+	if s.BuyBelowNeutralSMA && midPrice.Float64() > s.neutralBoll.SMA.Last(0) {
 		canBuy = false
 	}
 
diff --git a/pkg/strategy/bollmaker/trend.go b/pkg/strategy/bollmaker/trend.go
index 33167967b..4c0cb7fcd 100644
--- a/pkg/strategy/bollmaker/trend.go
+++ b/pkg/strategy/bollmaker/trend.go
@@ -12,7 +12,7 @@ const (
 )
 
 func detectPriceTrend(inc *indicator.BOLL, price float64) PriceTrend {
-	if inBetween(price, inc.DownBand.Last(), inc.UpBand.Last()) {
+	if inBetween(price, inc.DownBand.Last(0), inc.UpBand.Last(0)) {
 		return NeutralTrend
 	}
 
diff --git a/pkg/strategy/drift/driftma.go b/pkg/strategy/drift/driftma.go
index 0ff0a9c70..ba0468cdc 100644
--- a/pkg/strategy/drift/driftma.go
+++ b/pkg/strategy/drift/driftma.go
@@ -17,19 +17,19 @@ func (s *DriftMA) Update(value, weight float64) {
 	if s.ma1.Length() == 0 {
 		return
 	}
-	s.drift.Update(s.ma1.Last(), weight)
+	s.drift.Update(s.ma1.Last(0), weight)
 	if s.drift.Length() == 0 {
 		return
 	}
-	s.ma2.Update(s.drift.Last())
+	s.ma2.Update(s.drift.Last(0))
 }
 
-func (s *DriftMA) Last() float64 {
-	return s.ma2.Last()
+func (s *DriftMA) Last(int) float64 {
+	return s.ma2.Last(0)
 }
 
 func (s *DriftMA) Index(i int) float64 {
-	return s.ma2.Index(i)
+	return s.ma2.Last(i)
 }
 
 func (s *DriftMA) Length() int {
diff --git a/pkg/strategy/drift/stoploss.go b/pkg/strategy/drift/stoploss.go
index bd78efa1d..56d985f08 100644
--- a/pkg/strategy/drift/stoploss.go
+++ b/pkg/strategy/drift/stoploss.go
@@ -9,7 +9,7 @@ func (s *Strategy) CheckStopLoss() bool {
 		}
 	}
 	if s.UseAtr {
-		atr := s.atr.Last()
+		atr := s.atr.Last(0)
 		if s.sellPrice > 0 && s.sellPrice+atr <= s.highestPrice ||
 			s.buyPrice > 0 && s.buyPrice-atr >= s.lowestPrice {
 			return true
diff --git a/pkg/strategy/drift/strategy.go b/pkg/strategy/drift/strategy.go
index 21f748e4c..cf9c53e8e 100644
--- a/pkg/strategy/drift/strategy.go
+++ b/pkg/strategy/drift/strategy.go
@@ -261,8 +261,8 @@ func (s *Strategy) initIndicators(store *bbgo.SerialMarketDataStore) error {
 		high := kline.High.Float64()
 		low := kline.Low.Float64()
 		s.ma.Update(source)
-		s.stdevHigh.Update(high - s.ma.Last())
-		s.stdevLow.Update(s.ma.Last() - low)
+		s.stdevHigh.Update(high - s.ma.Last(0))
+		s.stdevLow.Update(s.ma.Last(0) - low)
 		s.drift.Update(source, kline.Volume.Abs().Float64())
 		s.trendLine.Update(source)
 		s.atr.PushK(kline)
@@ -485,7 +485,7 @@ func (s *Strategy) klineHandlerMin(ctx context.Context, kline types.KLine, count
 		return
 	}
 	// for doing the trailing stoploss during backtesting
-	atr := s.atr.Last()
+	atr := s.atr.Last(0)
 	price := s.getLastPrice()
 	pricef := price.Float64()
 
@@ -538,7 +538,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 
 	s.drift.Update(sourcef, kline.Volume.Abs().Float64())
 	s.atr.PushK(kline)
-	atr := s.atr.Last()
+	atr := s.atr.Last(0)
 
 	price := kline.Close // s.getLastPrice()
 	pricef := price.Float64()
@@ -563,7 +563,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 		return
 	}
 
-	log.Infof("highdiff: %3.2f open: %8v, close: %8v, high: %8v, low: %8v, time: %v %v", s.stdevHigh.Last(), kline.Open, kline.Close, kline.High, kline.Low, kline.StartTime, kline.EndTime)
+	log.Infof("highdiff: %3.2f open: %8v, close: %8v, high: %8v, low: %8v, time: %v %v", s.stdevHigh.Last(0), kline.Open, kline.Close, kline.High, kline.Low, kline.StartTime, kline.EndTime)
 
 	s.positionLock.Lock()
 	if s.lowestPrice > 0 && lowf < s.lowestPrice {
@@ -596,7 +596,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 	shortCondition := drift[1] >= 0 && drift[0] <= 0 || (drift[1] >= drift[0] && drift[1] <= 0) || ddrift[1] >= 0 && ddrift[0] <= 0 || (ddrift[1] >= ddrift[0] && ddrift[1] <= 0)
 	longCondition := drift[1] <= 0 && drift[0] >= 0 || (drift[1] <= drift[0] && drift[1] >= 0) || ddrift[1] <= 0 && ddrift[0] >= 0 || (ddrift[1] <= ddrift[0] && ddrift[1] >= 0)
 	if shortCondition && longCondition {
-		if s.priceLines.Index(1) > s.priceLines.Last() {
+		if s.priceLines.Index(1) > s.priceLines.Last(0) {
 			longCondition = false
 		} else {
 			shortCondition = false
@@ -625,7 +625,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 	}
 
 	if longCondition {
-		source = source.Sub(fixedpoint.NewFromFloat(s.stdevLow.Last() * s.HighLowVarianceMultiplier))
+		source = source.Sub(fixedpoint.NewFromFloat(s.stdevLow.Last(0) * s.HighLowVarianceMultiplier))
 		if source.Compare(price) > 0 {
 			source = price
 		}
@@ -654,7 +654,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 			return
 		}
 
-		log.Infof("source in long %v %v %f", source, price, s.stdevLow.Last())
+		log.Infof("source in long %v %v %f", source, price, s.stdevLow.Last(0))
 
 		o, err := s.SubmitOrder(ctx, *submitOrder)
 		if err != nil {
@@ -675,12 +675,12 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine, counter
 		return
 	}
 	if shortCondition {
-		source = source.Add(fixedpoint.NewFromFloat(s.stdevHigh.Last() * s.HighLowVarianceMultiplier))
+		source = source.Add(fixedpoint.NewFromFloat(s.stdevHigh.Last(0) * s.HighLowVarianceMultiplier))
 		if source.Compare(price) < 0 {
 			source = price
 		}
 
-		log.Infof("source in short: %v %v %f", source, price, s.stdevLow.Last())
+		log.Infof("source in short: %v %v %f", source, price, s.stdevLow.Last(0))
 
 		opt := s.OpenPositionOptions
 		opt.Short = true
diff --git a/pkg/strategy/elliottwave/ewo.go b/pkg/strategy/elliottwave/ewo.go
index ff6b7cf2e..f86706b18 100644
--- a/pkg/strategy/elliottwave/ewo.go
+++ b/pkg/strategy/elliottwave/ewo.go
@@ -11,8 +11,8 @@ func (s *ElliottWave) Index(i int) float64 {
 	return s.maQuick.Index(i)/s.maSlow.Index(i) - 1.0
 }
 
-func (s *ElliottWave) Last() float64 {
-	return s.maQuick.Last()/s.maSlow.Last() - 1.0
+func (s *ElliottWave) Last(int) float64 {
+	return s.maQuick.Last(0)/s.maSlow.Last(0) - 1.0
 }
 
 func (s *ElliottWave) Length() int {
diff --git a/pkg/strategy/elliottwave/strategy.go b/pkg/strategy/elliottwave/strategy.go
index feabe13b5..c307f054c 100644
--- a/pkg/strategy/elliottwave/strategy.go
+++ b/pkg/strategy/elliottwave/strategy.go
@@ -199,12 +199,12 @@ func (s *Strategy) smartCancel(ctx context.Context, pricef float64) int {
 			if s.counter-s.orderPendingCounter[order.OrderID] >= s.PendingMinInterval {
 				toCancel = true
 			} else if order.Side == types.SideTypeBuy {
-				if order.Price.Float64()+s.atr.Last()*2 <= pricef {
+				if order.Price.Float64()+s.atr.Last(0)*2 <= pricef {
 					toCancel = true
 				}
 			} else if order.Side == types.SideTypeSell {
 				// 75% of the probability
-				if order.Price.Float64()-s.atr.Last()*2 >= pricef {
+				if order.Price.Float64()-s.atr.Last(0)*2 >= pricef {
 					toCancel = true
 				}
 			} else {
@@ -425,7 +425,7 @@ func (s *Strategy) klineHandlerMin(ctx context.Context, kline types.KLine) {
 	stoploss := s.Stoploss.Float64()
 	price := s.getLastPrice()
 	pricef := price.Float64()
-	atr := s.atr.Last()
+	atr := s.atr.Last(0)
 
 	numPending := s.smartCancel(ctx, pricef)
 	if numPending > 0 {
@@ -476,7 +476,7 @@ func (s *Strategy) klineHandler(ctx context.Context, kline types.KLine) {
 
 	s.smartCancel(ctx, pricef)
 
-	atr := s.atr.Last()
+	atr := s.atr.Last(0)
 	ewo := types.Array(s.ewo, 4)
 	if len(ewo) < 4 {
 		return
diff --git a/pkg/strategy/emastop/strategy.go b/pkg/strategy/emastop/strategy.go
index 2326f5f78..d87ff5d44 100644
--- a/pkg/strategy/emastop/strategy.go
+++ b/pkg/strategy/emastop/strategy.go
@@ -93,7 +93,7 @@ func (s *Strategy) clear(ctx context.Context, orderExecutor bbgo.OrderExecutor)
 
 func (s *Strategy) place(ctx context.Context, orderExecutor bbgo.OrderExecutor, session *bbgo.ExchangeSession, indicator types.Float64Indicator, closePrice fixedpoint.Value) {
 	closePriceF := closePrice.Float64()
-	movingAveragePriceF := indicator.Last()
+	movingAveragePriceF := indicator.Last(0)
 
 	// skip it if it's near zero because it's not loaded yet
 	if movingAveragePriceF < 0.0001 {
diff --git a/pkg/strategy/ewoDgtrd/heikinashi.go b/pkg/strategy/ewoDgtrd/heikinashi.go
index fca1934c0..345d8e512 100644
--- a/pkg/strategy/ewoDgtrd/heikinashi.go
+++ b/pkg/strategy/ewoDgtrd/heikinashi.go
@@ -27,11 +27,11 @@ func NewHeikinAshi(size int) *HeikinAshi {
 
 func (s *HeikinAshi) Print() string {
 	return fmt.Sprintf("Heikin c: %.3f, o: %.3f, h: %.3f, l: %.3f, v: %.3f",
-		s.Close.Last(),
-		s.Open.Last(),
-		s.High.Last(),
-		s.Low.Last(),
-		s.Volume.Last())
+		s.Close.Last(0),
+		s.Open.Last(0),
+		s.High.Last(0),
+		s.Low.Last(0),
+		s.Volume.Last(0))
 }
 
 func (inc *HeikinAshi) Update(kline types.KLine) {
@@ -40,7 +40,7 @@ func (inc *HeikinAshi) Update(kline types.KLine) {
 	high := kline.High.Float64()
 	low := kline.Low.Float64()
 	newClose := (open + high + low + cloze) / 4.
-	newOpen := (inc.Open.Last() + inc.Close.Last()) / 2.
+	newOpen := (inc.Open.Last(0) + inc.Close.Last(0)) / 2.
 	inc.Close.Update(newClose)
 	inc.Open.Update(newOpen)
 	inc.High.Update(math.Max(math.Max(high, newOpen), newClose))
diff --git a/pkg/strategy/ewoDgtrd/strategy.go b/pkg/strategy/ewoDgtrd/strategy.go
index e13b84b0e..50af7f4bf 100644
--- a/pkg/strategy/ewoDgtrd/strategy.go
+++ b/pkg/strategy/ewoDgtrd/strategy.go
@@ -139,7 +139,7 @@ func NewCCISTOCH(i types.Interval, filterHigh, filterLow float64) *CCISTOCH {
 
 func (inc *CCISTOCH) Update(cloze float64) {
 	inc.cci.Update(cloze)
-	inc.stoch.Update(inc.cci.Last(), inc.cci.Last(), inc.cci.Last())
+	inc.stoch.Update(inc.cci.Last(0), inc.cci.Last(0), inc.cci.Last(0))
 	inc.ma.Update(inc.stoch.LastD())
 }
 
@@ -180,19 +180,19 @@ type VWEMA struct {
 	V  types.UpdatableSeries
 }
 
-func (inc *VWEMA) Last() float64 {
-	return inc.PV.Last() / inc.V.Last()
+func (inc *VWEMA) Last(int) float64 {
+	return inc.PV.Last(0) / inc.V.Last(0)
 }
 
 func (inc *VWEMA) Index(i int) float64 {
 	if i >= inc.PV.Length() {
 		return 0
 	}
-	vi := inc.V.Index(i)
+	vi := inc.V.Last(i)
 	if vi == 0 {
 		return 0
 	}
-	return inc.PV.Index(i) / vi
+	return inc.PV.Last(i) / vi
 }
 
 func (inc *VWEMA) Length() int {
@@ -262,11 +262,11 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 		if s.heikinAshi.Close.Length() == 0 {
 			for _, kline := range window {
 				s.heikinAshi.Update(kline)
-				s.ccis.Update(getSource(window).Last())
+				s.ccis.Update(getSource(window).Last(0))
 			}
 		} else {
 			s.heikinAshi.Update(window[len(window)-1])
-			s.ccis.Update(getSource(window).Last())
+			s.ccis.Update(getSource(window).Last(0))
 		}
 	})
 	if s.UseEma {
@@ -283,7 +283,7 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 					ema34.Update(cloze)
 				}
 			} else {
-				cloze := getSource(window).Last()
+				cloze := getSource(window).Last(0)
 				ema5.Update(cloze)
 				ema34.Update(cloze)
 			}
@@ -306,7 +306,7 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 					sma34.Update(cloze)
 				}
 			} else {
-				cloze := getSource(window).Last()
+				cloze := getSource(window).Last(0)
 				sma5.Update(cloze)
 				sma34.Update(cloze)
 			}
@@ -330,14 +330,14 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 			vols := getVol(window)
 			if evwma5.PV.Length() == 0 {
 				for i := clozes.Length() - 1; i >= 0; i-- {
-					price := clozes.Index(i)
-					vol := vols.Index(i)
+					price := clozes.Last(i)
+					vol := vols.Last(i)
 					evwma5.UpdateVal(price, vol)
 					evwma34.UpdateVal(price, vol)
 				}
 			} else {
-				price := clozes.Last()
-				vol := vols.Last()
+				price := clozes.Last(0)
+				vol := vols.Last(0)
 				evwma5.UpdateVal(price, vol)
 				evwma34.UpdateVal(price, vol)
 			}
@@ -363,7 +363,7 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 					sig.Update(ewoValue)
 				}
 			} else {
-				sig.Update(s.ewo.Last())
+				sig.Update(s.ewo.Last(0))
 			}
 		})
 		s.ewoSignal = sig
@@ -381,7 +381,7 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 					sig.Update(ewoValue)
 				}
 			} else {
-				sig.Update(s.ewo.Last())
+				sig.Update(s.ewo.Last(0))
 			}
 		})
 		s.ewoSignal = sig
@@ -398,13 +398,13 @@ func (s *Strategy) SetupIndicators(store *bbgo.MarketDataStore) {
 				// lazy init
 				ewoVals := s.ewo.Reverse()
 				for i, ewoValue := range ewoVals {
-					vol := window.Volume().Index(i)
+					vol := window.Volume().Last(i)
 					sig.PV.Update(ewoValue * vol)
 					sig.V.Update(vol)
 				}
 			} else {
-				vol := window.Volume().Last()
-				sig.PV.Update(s.ewo.Last() * vol)
+				vol := window.Volume().Last(0)
+				sig.PV.Update(s.ewo.Last(0) * vol)
 				sig.V.Update(vol)
 			}
 		})
@@ -663,11 +663,13 @@ func (s *Strategy) GetLastPrice() fixedpoint.Value {
 // - TP by (lastprice < peak price - atr) || (lastprice > bottom price + atr)
 // - SL by s.StopLoss (Abs(price_diff / price) > s.StopLoss)
 // - entry condition on ewo(Elliott wave oscillator) Crosses ewoSignal(ma on ewo, signalWindow)
-//   * buy signal on (crossover on previous K bar and no crossunder on latest K bar)
-//   * sell signal on (crossunder on previous K bar and no crossunder on latest K bar)
+//   - buy signal on (crossover on previous K bar and no crossunder on latest K bar)
+//   - sell signal on (crossunder on previous K bar and no crossunder on latest K bar)
+//
 // - and filtered by the following rules:
-//   * buy: buy signal ON, kline Close > Open, Close > ma5, Close > ma34, CCI Stochastic Buy signal
-//   * sell: sell signal ON, kline Close < Open, Close < ma5, Close < ma34, CCI Stochastic Sell signal
+//   - buy: buy signal ON, kline Close > Open, Close > ma5, Close > ma34, CCI Stochastic Buy signal
+//   - sell: sell signal ON, kline Close < Open, Close < ma5, Close < ma34, CCI Stochastic Sell signal
+//
 // - or entry when ma34 +- atr * 3 gets touched
 // - entry price: latestPrice +- atr / 2 (short,long), close at market price
 // Cancel non-fully filled orders on new signal (either in same direction or not)
@@ -784,8 +786,8 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 	s.SetupIndicators(store)
 
 	// local peak of ewo
-	shortSig := s.ewo.Last() < s.ewo.Index(1) && s.ewo.Index(1) > s.ewo.Index(2)
-	longSig := s.ewo.Last() > s.ewo.Index(1) && s.ewo.Index(1) < s.ewo.Index(2)
+	shortSig := s.ewo.Last(0) < s.ewo.Last(1) && s.ewo.Last(1) > s.ewo.Last(2)
+	longSig := s.ewo.Last(0) > s.ewo.Last(1) && s.ewo.Last(1) < s.ewo.Last(2)
 
 	sellOrderTPSL := func(price fixedpoint.Value) {
 		lastPrice := s.GetLastPrice()
@@ -798,8 +800,8 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		}
 		balances := session.GetAccount().Balances()
 		quoteBalance := balances[s.Market.QuoteCurrency].Available
-		atr := fixedpoint.NewFromFloat(s.atr.Last())
-		atrx2 := fixedpoint.NewFromFloat(s.atr.Last() * 2)
+		atr := fixedpoint.NewFromFloat(s.atr.Last(0))
+		atrx2 := fixedpoint.NewFromFloat(s.atr.Last(0) * 2)
 		buyall := false
 		if s.bottomPrice.IsZero() || s.bottomPrice.Compare(price) > 0 {
 			s.bottomPrice = price
@@ -809,7 +811,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		spBack := s.sellPrice
 		reason := -1
 		if quoteBalance.Div(lastPrice).Compare(s.Market.MinQuantity) >= 0 && quoteBalance.Compare(s.Market.MinNotional) >= 0 {
-			base := fixedpoint.NewFromFloat(s.ma34.Last())
+			base := fixedpoint.NewFromFloat(s.ma34.Last(0))
 			// TP
 			if lastPrice.Compare(s.sellPrice) < 0 && (longSig ||
 				(!atrx2.IsZero() && base.Sub(atrx2).Compare(lastPrice) >= 0)) {
@@ -903,8 +905,8 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		}
 		balances := session.GetAccount().Balances()
 		baseBalance := balances[s.Market.BaseCurrency].Available
-		atr := fixedpoint.NewFromFloat(s.atr.Last())
-		atrx2 := fixedpoint.NewFromFloat(s.atr.Last() * 2)
+		atr := fixedpoint.NewFromFloat(s.atr.Last(0))
+		atrx2 := fixedpoint.NewFromFloat(s.atr.Last(0) * 2)
 		sellall := false
 		if s.peakPrice.IsZero() || s.peakPrice.Compare(price) < 0 {
 			s.peakPrice = price
@@ -915,7 +917,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		reason := -1
 		if baseBalance.Compare(s.Market.MinQuantity) >= 0 && baseBalance.Mul(lastPrice).Compare(s.Market.MinNotional) >= 0 {
 			// TP
-			base := fixedpoint.NewFromFloat(s.ma34.Last())
+			base := fixedpoint.NewFromFloat(s.ma34.Last(0))
 			if lastPrice.Compare(s.buyPrice) > 0 && (shortSig ||
 				(!atrx2.IsZero() && base.Add(atrx2).Compare(lastPrice) <= 0)) {
 				sellall = true
@@ -1089,10 +1091,10 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		balances := session.GetAccount().Balances()
 		baseBalance := balances[s.Market.BaseCurrency].Total()
 		quoteBalance := balances[s.Market.QuoteCurrency].Total()
-		atr := fixedpoint.NewFromFloat(s.atr.Last())
+		atr := fixedpoint.NewFromFloat(s.atr.Last(0))
 		if !s.Environment.IsBackTesting() {
 			log.Infof("Get last price: %v, ewo %f, ewoSig %f, ccis: %f, atr %v, kline: %v, balance[base]: %v balance[quote]: %v",
-				lastPrice, s.ewo.Last(), s.ewoSignal.Last(), s.ccis.ma.Last(), atr, kline, baseBalance, quoteBalance)
+				lastPrice, s.ewo.Last(0), s.ewoSignal.Last(0), s.ccis.ma.Last(0), atr, kline, baseBalance, quoteBalance)
 		}
 
 		if kline.Interval != s.Interval {
@@ -1104,21 +1106,21 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		priceChangeRate := (priceHighest - priceLowest) / priceHighest / 14
 		ewoHighest := types.Highest(s.ewoHistogram, 233)
 
-		s.ewoChangeRate = math.Abs(s.ewoHistogram.Last() / ewoHighest * priceChangeRate)
+		s.ewoChangeRate = math.Abs(s.ewoHistogram.Last(0) / ewoHighest * priceChangeRate)
 
 		longSignal := types.CrossOver(s.ewo, s.ewoSignal)
 		shortSignal := types.CrossUnder(s.ewo, s.ewoSignal)
 
-		base := s.ma34.Last()
-		sellLine := base + s.atr.Last()*3
-		buyLine := base - s.atr.Last()*3
+		base := s.ma34.Last(0)
+		sellLine := base + s.atr.Last(0)*3
+		buyLine := base - s.atr.Last(0)*3
 		clozes := getClose(window)
 		opens := getOpen(window)
 
 		// get trend flags
-		bull := clozes.Last() > opens.Last()
-		breakThrough := clozes.Last() > s.ma5.Last() && clozes.Last() > s.ma34.Last()
-		breakDown := clozes.Last() < s.ma5.Last() && clozes.Last() < s.ma34.Last()
+		bull := clozes.Last(0) > opens.Last(0)
+		breakThrough := clozes.Last(0) > s.ma5.Last(0) && clozes.Last(0) > s.ma34.Last(0)
+		breakDown := clozes.Last(0) < s.ma5.Last(0) && clozes.Last(0) < s.ma34.Last(0)
 
 		// kline breakthrough ma5, ma34 trend up, and cci Stochastic bull
 		IsBull := bull && breakThrough && s.ccis.BuySignal() && s.ewoChangeRate < s.EwoChangeFilterHigh && s.ewoChangeRate > s.EwoChangeFilterLow
@@ -1141,7 +1143,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 
 				// backup, since the s.sellPrice will be cleared when doing ClosePosition
 				sellPrice := s.sellPrice
-				log.Errorf("ewoChangeRate %v, emv %v", s.ewoChangeRate, s.emv.Last())
+				log.Errorf("ewoChangeRate %v, emv %v", s.ewoChangeRate, s.emv.Last(0))
 
 				// calculate report
 				if closeOrder, _ := s.PlaceBuyOrder(ctx, price); closeOrder != nil {
@@ -1175,7 +1177,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 
 				// backup, since the s.buyPrice will be cleared when doing ClosePosition
 				buyPrice := s.buyPrice
-				log.Errorf("ewoChangeRate: %v, emv %v", s.ewoChangeRate, s.emv.Last())
+				log.Errorf("ewoChangeRate: %v, emv %v", s.ewoChangeRate, s.emv.Last(0))
 
 				// calculate report
 				if closeOrder, _ := s.PlaceSellOrder(ctx, price); closeOrder != nil {
diff --git a/pkg/strategy/factorzoo/factors/momentum.go b/pkg/strategy/factorzoo/factors/momentum.go
index c9dc34877..827af0976 100644
--- a/pkg/strategy/factorzoo/factors/momentum.go
+++ b/pkg/strategy/factorzoo/factors/momentum.go
@@ -34,14 +34,14 @@ func (inc *MOM) Index(i int) float64 {
 	if inc.Values == nil {
 		return 0
 	}
-	return inc.Values.Index(i)
+	return inc.Values.Last(i)
 }
 
-func (inc *MOM) Last() float64 {
+func (inc *MOM) Last(int) float64 {
 	if inc.Values.Length() == 0 {
 		return 0
 	}
-	return inc.Values.Last()
+	return inc.Values.Last(0)
 }
 
 func (inc *MOM) Length() int {
@@ -51,7 +51,7 @@ func (inc *MOM) Length() int {
 	return inc.Values.Length()
 }
 
-//var _ types.SeriesExtend = &MOM{}
+// var _ types.SeriesExtend = &MOM{}
 
 func (inc *MOM) Update(open, close float64) {
 	if inc.SeriesBase.Series == nil {
@@ -62,7 +62,7 @@ func (inc *MOM) Update(open, close float64) {
 	inc.opens.Update(open)
 	inc.closes.Update(close)
 	if inc.opens.Length() >= inc.Window && inc.closes.Length() >= inc.Window {
-		gap := inc.opens.Last()/inc.closes.Index(1) - 1
+		gap := inc.opens.Last(0)/inc.closes.Index(1) - 1
 		inc.Values.Push(gap)
 	}
 }
@@ -72,11 +72,11 @@ func (inc *MOM) CalculateAndUpdate(allKLines []types.KLine) {
 		for _, k := range allKLines {
 			inc.PushK(k)
 		}
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
@@ -99,7 +99,7 @@ func (inc *MOM) PushK(k types.KLine) {
 
 	inc.Update(k.Open.Float64(), k.Close.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func calculateMomentum(klines []types.KLine, window int, valA KLineValueMapper, valB KLineValueMapper) (float64, error) {
diff --git a/pkg/strategy/factorzoo/factors/price_mean_reversion.go b/pkg/strategy/factorzoo/factors/price_mean_reversion.go
index 2d2bd5ce8..7143e547c 100644
--- a/pkg/strategy/factorzoo/factors/price_mean_reversion.go
+++ b/pkg/strategy/factorzoo/factors/price_mean_reversion.go
@@ -35,12 +35,12 @@ func (inc *PMR) Update(price float64) {
 	}
 	inc.SMA.Update(price)
 	if inc.SMA.Length() >= inc.Window {
-		reversion := inc.SMA.Last() / price
+		reversion := inc.SMA.Last(0) / price
 		inc.Values.Push(reversion)
 	}
 }
 
-func (inc *PMR) Last() float64 {
+func (inc *PMR) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
@@ -65,11 +65,11 @@ func (inc *PMR) CalculateAndUpdate(allKLines []types.KLine) {
 		for _, k := range allKLines {
 			inc.PushK(k)
 		}
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
@@ -92,7 +92,7 @@ func (inc *PMR) PushK(k types.KLine) {
 
 	inc.Update(indicator.KLineClosePriceMapper(k))
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func CalculateKLinesPMR(allKLines []types.KLine, window int) float64 {
diff --git a/pkg/strategy/factorzoo/factors/price_volume_divergence.go b/pkg/strategy/factorzoo/factors/price_volume_divergence.go
index 54b07a265..adc20e02a 100644
--- a/pkg/strategy/factorzoo/factors/price_volume_divergence.go
+++ b/pkg/strategy/factorzoo/factors/price_volume_divergence.go
@@ -47,7 +47,7 @@ func (inc *PVD) Update(price float64, volume float64) {
 	}
 }
 
-func (inc *PVD) Last() float64 {
+func (inc *PVD) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
@@ -72,11 +72,11 @@ func (inc *PVD) CalculateAndUpdate(allKLines []types.KLine) {
 		for _, k := range allKLines {
 			inc.PushK(k)
 		}
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
@@ -99,7 +99,7 @@ func (inc *PVD) PushK(k types.KLine) {
 
 	inc.Update(indicator.KLineClosePriceMapper(k), indicator.KLineVolumeMapper(k))
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func CalculateKLinesPVD(allKLines []types.KLine, window int) float64 {
diff --git a/pkg/strategy/factorzoo/factors/return_rate.go b/pkg/strategy/factorzoo/factors/return_rate.go
index 057f2ac5c..3fe3d4156 100644
--- a/pkg/strategy/factorzoo/factors/return_rate.go
+++ b/pkg/strategy/factorzoo/factors/return_rate.go
@@ -30,12 +30,12 @@ func (inc *RR) Update(price float64) {
 		inc.prices = types.NewQueue(inc.Window)
 	}
 	inc.prices.Update(price)
-	irr := inc.prices.Last()/inc.prices.Index(1) - 1
+	irr := inc.prices.Last(0)/inc.prices.Index(1) - 1
 	inc.Values.Push(irr)
 
 }
 
-func (inc *RR) Last() float64 {
+func (inc *RR) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
@@ -60,11 +60,11 @@ func (inc *RR) CalculateAndUpdate(allKLines []types.KLine) {
 		for _, k := range allKLines {
 			inc.PushK(k)
 		}
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
@@ -91,14 +91,14 @@ func (inc *RR) PushK(k types.KLine) {
 
 	inc.Update(indicator.KLineClosePriceMapper(k))
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *RR) LoadK(allKLines []types.KLine) {
 	for _, k := range allKLines {
 		inc.PushK(k)
 	}
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 //func calculateReturn(klines []types.KLine, window int, val KLineValueMapper) (float64, error) {
diff --git a/pkg/strategy/factorzoo/factors/volume_momentum.go b/pkg/strategy/factorzoo/factors/volume_momentum.go
index 602065273..87029ed9e 100644
--- a/pkg/strategy/factorzoo/factors/volume_momentum.go
+++ b/pkg/strategy/factorzoo/factors/volume_momentum.go
@@ -33,14 +33,14 @@ func (inc *VMOM) Index(i int) float64 {
 	if inc.Values == nil {
 		return 0
 	}
-	return inc.Values.Index(i)
+	return inc.Values.Last(i)
 }
 
-func (inc *VMOM) Last() float64 {
+func (inc *VMOM) Last(int) float64 {
 	if inc.Values.Length() == 0 {
 		return 0
 	}
-	return inc.Values.Last()
+	return inc.Values.Last(0)
 }
 
 func (inc *VMOM) Length() int {
@@ -59,7 +59,7 @@ func (inc *VMOM) Update(volume float64) {
 	}
 	inc.volumes.Update(volume)
 	if inc.volumes.Length() >= inc.Window {
-		v := inc.volumes.Last() / inc.volumes.Mean()
+		v := inc.volumes.Last(0) / inc.volumes.Mean()
 		inc.Values.Push(v)
 	}
 }
@@ -69,11 +69,11 @@ func (inc *VMOM) CalculateAndUpdate(allKLines []types.KLine) {
 		for _, k := range allKLines {
 			inc.PushK(k)
 		}
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	} else {
 		k := allKLines[len(allKLines)-1]
 		inc.PushK(k)
-		inc.EmitUpdate(inc.Last())
+		inc.EmitUpdate(inc.Last(0))
 	}
 }
 
@@ -96,7 +96,7 @@ func (inc *VMOM) PushK(k types.KLine) {
 
 	inc.Update(k.Volume.Float64())
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func calculateVolumeMomentum(klines []types.KLine, window int, valV KLineValueMapper, valP KLineValueMapper) (float64, error) {
@@ -110,7 +110,7 @@ func calculateVolumeMomentum(klines []types.KLine, window int, valV KLineValueMa
 		vma += valV(p)
 	}
 	vma /= float64(window)
-	momentum := valV(klines[length-1]) / vma //* (valP(klines[length-1-2]) / valP(klines[length-1]))
+	momentum := valV(klines[length-1]) / vma // * (valP(klines[length-1-2]) / valP(klines[length-1]))
 
 	return momentum, nil
 }
diff --git a/pkg/strategy/factorzoo/linear_regression.go b/pkg/strategy/factorzoo/linear_regression.go
index 80c84e687..670e4dcea 100644
--- a/pkg/strategy/factorzoo/linear_regression.go
+++ b/pkg/strategy/factorzoo/linear_regression.go
@@ -104,11 +104,11 @@ func (s *Linear) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.General
 
 		// use the last value from indicators, or the SeriesExtends' predict function. (e.g., look back: 5)
 		input := []float64{
-			s.divergence.Last(),
-			s.reversion.Last(),
-			s.drift.Last(),
-			s.momentum.Last(),
-			s.volume.Last(),
+			s.divergence.Last(0),
+			s.reversion.Last(0),
+			s.drift.Last(0),
+			s.momentum.Last(0),
+			s.volume.Last(0),
 		}
 		pred := model.Predict(input)
 		predLst.Update(pred)
diff --git a/pkg/strategy/fixedmaker/strategy.go b/pkg/strategy/fixedmaker/strategy.go
index d31633406..0910e536d 100644
--- a/pkg/strategy/fixedmaker/strategy.go
+++ b/pkg/strategy/fixedmaker/strategy.go
@@ -213,7 +213,7 @@ func (s *Strategy) generateSubmitOrders(ctx context.Context) ([]types.SubmitOrde
 	log.Infof("mid price: %+v", midPrice)
 
 	if s.ATRMultiplier.Float64() > 0 {
-		atr := fixedpoint.NewFromFloat(s.atr.Last())
+		atr := fixedpoint.NewFromFloat(s.atr.Last(0))
 		log.Infof("atr: %s", atr.String())
 		s.HalfSpreadRatio = s.ATRMultiplier.Mul(atr).Div(midPrice)
 		log.Infof("half spread ratio: %s", s.HalfSpreadRatio.String())
diff --git a/pkg/strategy/flashcrash/strategy.go b/pkg/strategy/flashcrash/strategy.go
index aff86f3ca..d4db38925 100644
--- a/pkg/strategy/flashcrash/strategy.go
+++ b/pkg/strategy/flashcrash/strategy.go
@@ -75,7 +75,7 @@ func (s *Strategy) updateBidOrders(orderExecutor bbgo.OrderExecutor, session *bb
 		return
 	}
 
-	var startPrice = fixedpoint.NewFromFloat(s.ewma.Last()).Mul(s.Percentage)
+	var startPrice = fixedpoint.NewFromFloat(s.ewma.Last(0)).Mul(s.Percentage)
 
 	var submitOrders []types.SubmitOrder
 	for i := 0; i < s.GridNum; i++ {
diff --git a/pkg/strategy/fmaker/A18.go b/pkg/strategy/fmaker/A18.go
index 6e7e603a0..35dc7368e 100644
--- a/pkg/strategy/fmaker/A18.go
+++ b/pkg/strategy/fmaker/A18.go
@@ -21,7 +21,7 @@ type A18 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *A18) Last() float64 {
+func (inc *A18) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -84,8 +84,8 @@ func calculateA18(klines []types.KLine, valClose KLineValueMapper) (float64, err
 		closes.Push(valClose(k))
 	}
 
-	delay5 := closes.Index(4)
-	curr := closes.Index(0)
+	delay5 := closes.Last(4)
+	curr := closes.Last(0)
 	alpha := curr / delay5
 
 	return alpha, nil
diff --git a/pkg/strategy/fmaker/A2.go b/pkg/strategy/fmaker/A2.go
index 0c9cc4b3b..cf674e1a6 100644
--- a/pkg/strategy/fmaker/A2.go
+++ b/pkg/strategy/fmaker/A2.go
@@ -21,7 +21,7 @@ type A2 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *A2) Last() float64 {
+func (inc *A2) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -88,8 +88,8 @@ func calculateA2(klines []types.KLine, valLow KLineValueMapper, valHigh KLineVal
 		closes.Push(valClose(k))
 	}
 
-	prev := ((closes.Index(1) - lows.Index(1)) - (highs.Index(1) - closes.Index(1))) / (highs.Index(1) - lows.Index(1))
-	curr := ((closes.Index(0) - lows.Index(0)) - (highs.Index(0) - closes.Index(0))) / (highs.Index(0) - lows.Index(0))
+	prev := ((closes.Last(1) - lows.Index(1)) - (highs.Index(1) - closes.Index(1))) / (highs.Index(1) - lows.Index(1))
+	curr := ((closes.Last(0) - lows.Index(0)) - (highs.Index(0) - closes.Index(0))) / (highs.Index(0) - lows.Index(0))
 	alpha := (curr - prev) * -1 // delta(1 interval)
 
 	return alpha, nil
diff --git a/pkg/strategy/fmaker/A3.go b/pkg/strategy/fmaker/A3.go
index 945b06b67..02118def8 100644
--- a/pkg/strategy/fmaker/A3.go
+++ b/pkg/strategy/fmaker/A3.go
@@ -22,7 +22,7 @@ type A3 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *A3) Last() float64 {
+func (inc *A3) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/A34.go b/pkg/strategy/fmaker/A34.go
index eb01799e3..ba60aeedd 100644
--- a/pkg/strategy/fmaker/A34.go
+++ b/pkg/strategy/fmaker/A34.go
@@ -21,7 +21,7 @@ type A34 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *A34) Last() float64 {
+func (inc *A34) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -83,7 +83,7 @@ func calculateA34(klines []types.KLine, valClose KLineValueMapper) (float64, err
 		closes.Push(valClose(k))
 	}
 
-	c := closes.Last()
+	c := closes.Last(0)
 
 	sumC := 0.
 	for i := 1; i <= 12; i++ {
diff --git a/pkg/strategy/fmaker/R.go b/pkg/strategy/fmaker/R.go
index d3aa0eca2..dc4f0eabf 100644
--- a/pkg/strategy/fmaker/R.go
+++ b/pkg/strategy/fmaker/R.go
@@ -25,7 +25,7 @@ type R struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *R) Last() float64 {
+func (inc *R) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/S0.go b/pkg/strategy/fmaker/S0.go
index 9c934ccd2..7d2eda158 100644
--- a/pkg/strategy/fmaker/S0.go
+++ b/pkg/strategy/fmaker/S0.go
@@ -21,7 +21,7 @@ type S0 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S0) Last() float64 {
+func (inc *S0) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -84,7 +84,7 @@ func calculateS0(klines []types.KLine, valClose KLineValueMapper) (float64, erro
 	}
 
 	sma := floats.Slice.Sum(closes[len(closes)-window:len(closes)-1]) / float64(window)
-	alpha := sma / closes.Last()
+	alpha := sma / closes.Last(0)
 
 	return alpha, nil
 }
diff --git a/pkg/strategy/fmaker/S1.go b/pkg/strategy/fmaker/S1.go
index 498efec63..68962a579 100644
--- a/pkg/strategy/fmaker/S1.go
+++ b/pkg/strategy/fmaker/S1.go
@@ -19,7 +19,7 @@ type S1 struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *S1) Last() float64 {
+func (inc *S1) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/S2.go b/pkg/strategy/fmaker/S2.go
index 960b3c5a8..d63488a98 100644
--- a/pkg/strategy/fmaker/S2.go
+++ b/pkg/strategy/fmaker/S2.go
@@ -19,7 +19,7 @@ type S2 struct {
 	UpdateCallbacks []func(value float64)
 }
 
-func (inc *S2) Last() float64 {
+func (inc *S2) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/S3.go b/pkg/strategy/fmaker/S3.go
index 238cc62ea..e00f83625 100644
--- a/pkg/strategy/fmaker/S3.go
+++ b/pkg/strategy/fmaker/S3.go
@@ -21,7 +21,7 @@ type S3 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S3) Last() float64 {
+func (inc *S3) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/S4.go b/pkg/strategy/fmaker/S4.go
index 9d122c473..b7f8cfd8c 100644
--- a/pkg/strategy/fmaker/S4.go
+++ b/pkg/strategy/fmaker/S4.go
@@ -21,7 +21,7 @@ type S4 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S4) Last() float64 {
+func (inc *S4) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
diff --git a/pkg/strategy/fmaker/S5.go b/pkg/strategy/fmaker/S5.go
index 046733b4f..8fd2edfb7 100644
--- a/pkg/strategy/fmaker/S5.go
+++ b/pkg/strategy/fmaker/S5.go
@@ -21,7 +21,7 @@ type S5 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S5) Last() float64 {
+func (inc *S5) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -83,7 +83,7 @@ func calculateS5(klines []types.KLine, valVolume KLineValueMapper) (float64, err
 		volumes.Push(valVolume(k))
 	}
 
-	v := volumes.Last()
+	v := volumes.Last(0)
 
 	sumV := 0.
 	for i := 1; i <= 10; i++ {
diff --git a/pkg/strategy/fmaker/S6.go b/pkg/strategy/fmaker/S6.go
index 4bb20b158..8c7f73c16 100644
--- a/pkg/strategy/fmaker/S6.go
+++ b/pkg/strategy/fmaker/S6.go
@@ -21,7 +21,7 @@ type S6 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S6) Last() float64 {
+func (inc *S6) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -90,10 +90,10 @@ func calculateS6(klines []types.KLine, valHigh KLineValueMapper, valLow KLineVal
 
 	}
 
-	H := highs.Last()
-	L := lows.Last()
-	C := closes.Last()
-	V := volumes.Last()
+	H := highs.Last(0)
+	L := lows.Last(0)
+	C := closes.Last(0)
+	V := volumes.Last(0)
 	alpha := (H + L + C) / 3 * V
 
 	return alpha, nil
diff --git a/pkg/strategy/fmaker/S7.go b/pkg/strategy/fmaker/S7.go
index 7000e6897..048078fe2 100644
--- a/pkg/strategy/fmaker/S7.go
+++ b/pkg/strategy/fmaker/S7.go
@@ -21,7 +21,7 @@ type S7 struct {
 	UpdateCallbacks []func(val float64)
 }
 
-func (inc *S7) Last() float64 {
+func (inc *S7) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0.0
 	}
@@ -86,8 +86,8 @@ func calculateS7(klines []types.KLine, valOpen KLineValueMapper, valClose KLineV
 
 	}
 
-	O := opens.Last()
-	C := closes.Last()
+	O := opens.Last(0)
+	C := closes.Last(0)
 	alpha := -(1 - O/C)
 
 	return alpha, nil
diff --git a/pkg/strategy/fmaker/strategy.go b/pkg/strategy/fmaker/strategy.go
index 0df9b68e2..d03b9bf37 100644
--- a/pkg/strategy/fmaker/strategy.go
+++ b/pkg/strategy/fmaker/strategy.go
@@ -341,7 +341,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		// }
 		r.Train(rdps...)
 		r.Run()
-		er, _ := r.Predict(floats2.Slice{s.S0.Last(), s.S1.Last(), s.S2.Last(), s.S4.Last(), s.S5.Last(), s.S6.Last(), s.S7.Last(), s.A2.Last(), s.A3.Last(), s.A18.Last(), s.A34.Last()})
+		er, _ := r.Predict(floats2.Slice{s.S0.Last(0), s.S1.Last(0), s.S2.Last(0), s.S4.Last(0), s.S5.Last(0), s.S6.Last(0), s.S7.Last(0), s.A2.Last(0), s.A3.Last(0), s.A18.Last(0), s.A34.Last(0)})
 		log.Infof("Expected Return Rate: %f", er)
 
 		q := new(regression.Regression)
@@ -399,7 +399,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 
 		q.Run()
 
-		log.Info(s.S0.Last(), s.S1.Last(), s.S2.Last(), s.S3.Last(), s.S4.Last(), s.S5.Last(), s.S6.Last(), s.S7.Last(), s.A2.Last(), s.A3.Last(), s.A18.Last(), s.A34.Last())
+		log.Info(s.S0.Last(0), s.S1.Last(0), s.S2.Last(0), s.S3.Last(0), s.S4.Last(0), s.S5.Last(0), s.S6.Last(0), s.S7.Last(0), s.A2.Last(0), s.A3.Last(0), s.A18.Last(0), s.A34.Last(0))
 
 		log.Infof("Return Rate Regression formula:\n%v", r.Formula)
 		log.Infof("Order Quantity Regression formula:\n%v", q.Formula)
@@ -416,7 +416,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		// a34 := preprocessing(s.A18.Values[len(s.A18.Values)-20 : len(s.A18.Values)-1-outlook])
 		// er, _ := r.Predict(types.Float64Slice{s0, s1, s2, s4, s5, a2, a3, a18, a34})
 		// eq, _ := q.Predict(types.Float64Slice{s0, s1, s2, s4, s5, a2, a3, a18, a34})
-		eq, _ := q.Predict(floats2.Slice{s.S0.Last(), s.S1.Last(), s.S2.Last(), s.S4.Last(), s.S5.Last(), s.S6.Last(), s.S7.Last(), s.A2.Last(), s.A3.Last(), s.A18.Last(), s.A34.Last(), er})
+		eq, _ := q.Predict(floats2.Slice{s.S0.Last(0), s.S1.Last(0), s.S2.Last(0), s.S4.Last(0), s.S5.Last(0), s.S6.Last(0), s.S7.Last(0), s.A2.Last(0), s.A3.Last(0), s.A18.Last(0), s.A34.Last(0), er})
 		log.Infof("Expected Order Quantity: %f", eq)
 		// if float64(s.Position.GetBase().Sign())*er < 0 {
 		//	s.ClosePosition(ctx, fixedpoint.One, kline.Close)
diff --git a/pkg/strategy/grid2/strategy.go b/pkg/strategy/grid2/strategy.go
index b8a614e17..dc45dffd0 100644
--- a/pkg/strategy/grid2/strategy.go
+++ b/pkg/strategy/grid2/strategy.go
@@ -1849,8 +1849,8 @@ func (s *Strategy) Run(ctx context.Context, _ bbgo.OrderExecutor, session *bbgo.
 		interval := s.AutoRange.Interval()
 		pivotLow := indicatorSet.PivotLow(types.IntervalWindow{Interval: interval, Window: s.AutoRange.Num})
 		pivotHigh := indicatorSet.PivotHigh(types.IntervalWindow{Interval: interval, Window: s.AutoRange.Num})
-		s.UpperPrice = fixedpoint.NewFromFloat(pivotHigh.Last())
-		s.LowerPrice = fixedpoint.NewFromFloat(pivotLow.Last())
+		s.UpperPrice = fixedpoint.NewFromFloat(pivotHigh.Last(0))
+		s.LowerPrice = fixedpoint.NewFromFloat(pivotLow.Last(0))
 		s.logger.Infof("autoRange is enabled, using pivot high %f and pivot low %f", s.UpperPrice.Float64(), s.LowerPrice.Float64())
 	}
 
diff --git a/pkg/strategy/harmonic/shark.go b/pkg/strategy/harmonic/shark.go
index 630d4f4bf..d7bc287c3 100644
--- a/pkg/strategy/harmonic/shark.go
+++ b/pkg/strategy/harmonic/shark.go
@@ -51,7 +51,7 @@ func (inc *SHARK) Update(high, low, price float64) {
 
 }
 
-func (inc *SHARK) Last() float64 {
+func (inc *SHARK) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
@@ -82,14 +82,14 @@ func (inc *SHARK) PushK(k types.KLine) {
 
 	inc.Update(indicator.KLineHighPriceMapper(k), indicator.KLineLowPriceMapper(k), indicator.KLineClosePriceMapper(k))
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *SHARK) LoadK(allKLines []types.KLine) {
 	for _, k := range allKLines {
 		inc.PushK(k)
 	}
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc SHARK) SharkLong(highs, lows floats.Slice, p float64, lookback int) float64 {
diff --git a/pkg/strategy/harmonic/strategy.go b/pkg/strategy/harmonic/strategy.go
index 4d98fda34..c73a3d736 100644
--- a/pkg/strategy/harmonic/strategy.go
+++ b/pkg/strategy/harmonic/strategy.go
@@ -145,7 +145,7 @@ func (r *AccumulatedProfitReport) DailyUpdate(tradeStats *types.TradeStats) {
 
 	// Accumulated profit MA
 	r.accumulatedProfitMA.Update(r.accumulatedProfit.Float64())
-	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last())
+	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last(0))
 
 	// Accumulated Fee
 	r.accumulatedFeePerDay.Update(r.accumulatedFee.Float64())
@@ -341,11 +341,11 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 	states.Update(0)
 	s.session.MarketDataStream.OnKLineClosed(types.KLineWith(s.Symbol, s.Interval, func(kline types.KLine) {
 
-		log.Infof("shark score: %f, current price: %f", s.shark.Last(), kline.Close.Float64())
+		log.Infof("shark score: %f, current price: %f", s.shark.Last(0), kline.Close.Float64())
 
 		nextState := hmm(s.shark.Array(s.Window), states.Array(s.Window), s.Window)
 		states.Update(nextState)
-		log.Infof("Denoised signal via HMM: %f", states.Last())
+		log.Infof("Denoised signal via HMM: %f", states.Last(0))
 
 		if states.Length() < s.Window {
 			return
diff --git a/pkg/strategy/irr/neg_return_rate.go b/pkg/strategy/irr/neg_return_rate.go
index 473f2ecdd..72fe420fe 100644
--- a/pkg/strategy/irr/neg_return_rate.go
+++ b/pkg/strategy/irr/neg_return_rate.go
@@ -44,16 +44,16 @@ func (inc *NRR) Update(openPrice, closePrice float64) {
 	irr := (closePrice - openPrice) / openPrice
 	if inc.prices.Length() >= inc.Window && inc.delay {
 		// D1
-		nirr = -1 * ((inc.prices.Last() / inc.prices.Index(inc.Window-1)) - 1)
-		irr = (inc.prices.Last() / inc.prices.Index(inc.Window-1)) - 1
+		nirr = -1 * ((inc.prices.Last(0) / inc.prices.Index(inc.Window-1)) - 1)
+		irr = (inc.prices.Last(0) / inc.prices.Index(inc.Window-1)) - 1
 	}
 
-	inc.Values.Push(nirr)                                                                  // neg ret here
-	inc.RankedValues.Push(inc.Rank(inc.RankingWindow).Last() / float64(inc.RankingWindow)) // ranked neg ret here
+	inc.Values.Push(nirr)                                                                   // neg ret here
+	inc.RankedValues.Push(inc.Rank(inc.RankingWindow).Last(0) / float64(inc.RankingWindow)) // ranked neg ret here
 	inc.ReturnValues.Push(irr)
 }
 
-func (inc *NRR) Last() float64 {
+func (inc *NRR) Last(int) float64 {
 	if len(inc.Values) == 0 {
 		return 0
 	}
@@ -84,12 +84,12 @@ func (inc *NRR) PushK(k types.KLine) {
 
 	inc.Update(indicator.KLineOpenPriceMapper(k), indicator.KLineClosePriceMapper(k))
 	inc.EndTime = k.EndTime.Time()
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
 
 func (inc *NRR) LoadK(allKLines []types.KLine) {
 	for _, k := range allKLines {
 		inc.PushK(k)
 	}
-	inc.EmitUpdate(inc.Last())
+	inc.EmitUpdate(inc.Last(0))
 }
diff --git a/pkg/strategy/irr/strategy.go b/pkg/strategy/irr/strategy.go
index 679c50ef5..0e7616c95 100644
--- a/pkg/strategy/irr/strategy.go
+++ b/pkg/strategy/irr/strategy.go
@@ -152,7 +152,7 @@ func (r *AccumulatedProfitReport) DailyUpdate(tradeStats *types.TradeStats) {
 
 	// Accumulated profit MA
 	r.accumulatedProfitMA.Update(r.accumulatedProfit.Float64())
-	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last())
+	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last(0))
 
 	// Accumulated Fee
 	r.accumulatedFeePerDay.Update(r.accumulatedFee.Float64())
diff --git a/pkg/strategy/linregmaker/strategy.go b/pkg/strategy/linregmaker/strategy.go
index 34ff4fb2d..b8e5f9be0 100644
--- a/pkg/strategy/linregmaker/strategy.go
+++ b/pkg/strategy/linregmaker/strategy.go
@@ -257,12 +257,12 @@ func (s *Strategy) isAllowOppositePosition() bool {
 		return false
 	}
 
-	if (s.mainTrendCurrent == types.DirectionUp && s.FastLinReg.Last() < 0 && s.SlowLinReg.Last() < 0) ||
-		(s.mainTrendCurrent == types.DirectionDown && s.FastLinReg.Last() > 0 && s.SlowLinReg.Last() > 0) {
-		log.Infof("%s allow opposite position is enabled: MainTrend %v, FastLinReg: %f, SlowLinReg: %f", s.Symbol, s.mainTrendCurrent, s.FastLinReg.Last(), s.SlowLinReg.Last())
+	if (s.mainTrendCurrent == types.DirectionUp && s.FastLinReg.Last(0) < 0 && s.SlowLinReg.Last(0) < 0) ||
+		(s.mainTrendCurrent == types.DirectionDown && s.FastLinReg.Last(0) > 0 && s.SlowLinReg.Last(0) > 0) {
+		log.Infof("%s allow opposite position is enabled: MainTrend %v, FastLinReg: %f, SlowLinReg: %f", s.Symbol, s.mainTrendCurrent, s.FastLinReg.Last(0), s.SlowLinReg.Last(0))
 		return true
 	}
-	log.Infof("%s allow opposite position is disabled: MainTrend %v, FastLinReg: %f, SlowLinReg: %f", s.Symbol, s.mainTrendCurrent, s.FastLinReg.Last(), s.SlowLinReg.Last())
+	log.Infof("%s allow opposite position is disabled: MainTrend %v, FastLinReg: %f, SlowLinReg: %f", s.Symbol, s.mainTrendCurrent, s.FastLinReg.Last(0), s.SlowLinReg.Last(0))
 
 	return false
 }
@@ -390,10 +390,10 @@ func (s *Strategy) getOrderQuantities(askPrice fixedpoint.Value, bidPrice fixedp
 	}
 
 	// Faster position decrease
-	if s.mainTrendCurrent == types.DirectionUp && s.SlowLinReg.Last() < 0 {
+	if s.mainTrendCurrent == types.DirectionUp && s.SlowLinReg.Last(0) < 0 {
 		sellQuantity = sellQuantity.Mul(s.FasterDecreaseRatio)
 		log.Infof("faster %s position decrease: sell qty %v", s.Symbol, sellQuantity)
-	} else if s.mainTrendCurrent == types.DirectionDown && s.SlowLinReg.Last() > 0 {
+	} else if s.mainTrendCurrent == types.DirectionDown && s.SlowLinReg.Last(0) > 0 {
 		buyQuantity = buyQuantity.Mul(s.FasterDecreaseRatio)
 		log.Infof("faster %s position decrease: buy qty %v", s.Symbol, buyQuantity)
 	}
@@ -475,12 +475,12 @@ func (s *Strategy) getCanBuySell(buyQuantity, bidPrice, sellQuantity, askPrice,
 	// Check TradeInBand
 	if s.TradeInBand {
 		// Price too high
-		if bidPrice.Float64() > s.neutralBoll.UpBand.Last() {
+		if bidPrice.Float64() > s.neutralBoll.UpBand.Last(0) {
 			canBuy = false
 			log.Infof("tradeInBand is set, skip buy due to the price is higher than the neutralBB")
 		}
 		// Price too low in uptrend
-		if askPrice.Float64() < s.neutralBoll.DownBand.Last() {
+		if askPrice.Float64() < s.neutralBoll.DownBand.Last(0) {
 			canSell = false
 			log.Infof("tradeInBand is set, skip sell due to the price is lower than the neutralBB")
 		}
@@ -700,7 +700,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 				closePrice = price
 			}
 		}
-		priceReverseEMA := fixedpoint.NewFromFloat(s.ReverseEMA.Last())
+		priceReverseEMA := fixedpoint.NewFromFloat(s.ReverseEMA.Last(0))
 
 		// Main trend by ReverseEMA
 		if closePrice.Compare(priceReverseEMA) > 0 {
@@ -715,7 +715,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 		// closePrice is the close price of current kline
 		closePrice := kline.GetClose()
 		// priceReverseEMA is the current ReverseEMA price
-		priceReverseEMA := fixedpoint.NewFromFloat(s.ReverseEMA.Last())
+		priceReverseEMA := fixedpoint.NewFromFloat(s.ReverseEMA.Last(0))
 
 		// Main trend by ReverseEMA
 		s.mainTrendPrevious = s.mainTrendCurrent
diff --git a/pkg/strategy/pivotshort/breaklow.go b/pkg/strategy/pivotshort/breaklow.go
index 91f9f0eed..55b6bed96 100644
--- a/pkg/strategy/pivotshort/breaklow.go
+++ b/pkg/strategy/pivotshort/breaklow.go
@@ -104,7 +104,7 @@ func (s *BreakLow) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gener
 	// update pivot low data
 	session.MarketDataStream.OnStart(func() {
 		if s.updatePivotLow() {
-			bbgo.Notify("%s new pivot low: %f", s.Symbol, s.pivotLow.Last())
+			bbgo.Notify("%s new pivot low: %f", s.Symbol, s.pivotLow.Last(0))
 		}
 
 		s.pilotQuantityCalculation()
@@ -117,7 +117,7 @@ func (s *BreakLow) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gener
 				return
 			}
 
-			bbgo.Notify("%s new pivot low: %f", s.Symbol, s.pivotLow.Last())
+			bbgo.Notify("%s new pivot low: %f", s.Symbol, s.pivotLow.Last(0))
 		}
 	}))
 
@@ -260,7 +260,7 @@ func (s *BreakLow) pilotQuantityCalculation() {
 }
 
 func (s *BreakLow) updatePivotLow() bool {
-	low := fixedpoint.NewFromFloat(s.pivotLow.Last())
+	low := fixedpoint.NewFromFloat(s.pivotLow.Last(0))
 	if low.IsZero() {
 		return false
 	}
@@ -273,7 +273,7 @@ func (s *BreakLow) updatePivotLow() bool {
 		s.pivotLowPrices = append(s.pivotLowPrices, low)
 	}
 
-	fastLow := fixedpoint.NewFromFloat(s.fastPivotLow.Last())
+	fastLow := fixedpoint.NewFromFloat(s.fastPivotLow.Last(0))
 	if !fastLow.IsZero() {
 		if fastLow.Compare(s.lastLow) < 0 {
 			s.lastLowInvalidated = true
diff --git a/pkg/strategy/pivotshort/failedbreakhigh.go b/pkg/strategy/pivotshort/failedbreakhigh.go
index 30ad0a32e..f60cddfe8 100644
--- a/pkg/strategy/pivotshort/failedbreakhigh.go
+++ b/pkg/strategy/pivotshort/failedbreakhigh.go
@@ -142,7 +142,7 @@ func (s *FailedBreakHigh) Bind(session *bbgo.ExchangeSession, orderExecutor *bbg
 	// update pivot low data
 	session.MarketDataStream.OnStart(func() {
 		if s.updatePivotHigh() {
-			bbgo.Notify("%s new pivot high: %f", s.Symbol, s.pivotHigh.Last())
+			bbgo.Notify("%s new pivot high: %f", s.Symbol, s.pivotHigh.Last(0))
 		}
 
 		s.pilotQuantityCalculation()
@@ -155,7 +155,7 @@ func (s *FailedBreakHigh) Bind(session *bbgo.ExchangeSession, orderExecutor *bbg
 				return
 			}
 
-			bbgo.Notify("%s new pivot high: %f", s.Symbol, s.pivotHigh.Last())
+			bbgo.Notify("%s new pivot high: %f", s.Symbol, s.pivotHigh.Last(0))
 		}
 	}))
 
@@ -237,7 +237,7 @@ func (s *FailedBreakHigh) Bind(session *bbgo.ExchangeSession, orderExecutor *bbg
 		}
 
 		if s.vwma != nil {
-			vma := fixedpoint.NewFromFloat(s.vwma.Last())
+			vma := fixedpoint.NewFromFloat(s.vwma.Last(0))
 			if kline.Volume.Compare(vma) < 0 {
 				bbgo.Notify("%s %s kline volume %f is less than VMA %f, skip failed break high short", kline.Symbol, kline.Interval, kline.Volume.Float64(), vma.Float64())
 				return
@@ -378,7 +378,7 @@ func (s *FailedBreakHigh) detectMacdDivergence() {
 }
 
 func (s *FailedBreakHigh) updatePivotHigh() bool {
-	high := fixedpoint.NewFromFloat(s.pivotHigh.Last())
+	high := fixedpoint.NewFromFloat(s.pivotHigh.Last(0))
 	if high.IsZero() {
 		return false
 	}
@@ -390,7 +390,7 @@ func (s *FailedBreakHigh) updatePivotHigh() bool {
 		s.pivotHighPrices = append(s.pivotHighPrices, high)
 	}
 
-	fastHigh := fixedpoint.NewFromFloat(s.fastPivotHigh.Last())
+	fastHigh := fixedpoint.NewFromFloat(s.fastPivotHigh.Last(0))
 	if !fastHigh.IsZero() {
 		if fastHigh.Compare(s.lastHigh) > 0 {
 			// invalidate the last low
diff --git a/pkg/strategy/pivotshort/resistance.go b/pkg/strategy/pivotshort/resistance.go
index 744abefba..357ff49ab 100644
--- a/pkg/strategy/pivotshort/resistance.go
+++ b/pkg/strategy/pivotshort/resistance.go
@@ -72,7 +72,7 @@ func (s *ResistanceShort) Bind(session *bbgo.ExchangeSession, orderExecutor *bbg
 	s.resistancePivot = session.StandardIndicatorSet(s.Symbol).PivotLow(s.IntervalWindow)
 
 	// use the last kline from the history before we get the next closed kline
-	s.updateResistanceOrders(fixedpoint.NewFromFloat(s.resistancePivot.Last()))
+	s.updateResistanceOrders(fixedpoint.NewFromFloat(s.resistancePivot.Last(0)))
 
 	session.MarketDataStream.OnKLineClosed(types.KLineWith(s.Symbol, s.Interval, func(kline types.KLine) {
 		// StrategyController
diff --git a/pkg/strategy/pricedrop/strategy.go b/pkg/strategy/pricedrop/strategy.go
index c8a9b1664..4d29330cd 100644
--- a/pkg/strategy/pricedrop/strategy.go
+++ b/pkg/strategy/pricedrop/strategy.go
@@ -74,8 +74,8 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 			return
 		}
 
-		if kline.Close.Float64() > ema.Last() {
-			log.Warnf("kline close price %v is above EMA %s %f", kline.Close, ema.IntervalWindow, ema.Last())
+		if kline.Close.Float64() > ema.Last(0) {
+			log.Warnf("kline close price %v is above EMA %s %f", kline.Close, ema.IntervalWindow, ema.Last(0))
 			return
 		}
 
diff --git a/pkg/strategy/rsmaker/strategy.go b/pkg/strategy/rsmaker/strategy.go
index 2dd477a8f..76f92438f 100644
--- a/pkg/strategy/rsmaker/strategy.go
+++ b/pkg/strategy/rsmaker/strategy.go
@@ -329,9 +329,9 @@ func (s *Strategy) placeOrders(ctx context.Context, midPrice fixedpoint.Value, k
 	// baseBalance, hasBaseBalance := balances[s.Market.BaseCurrency]
 	// quoteBalance, hasQuoteBalance := balances[s.Market.QuoteCurrency]
 
-	downBand := s.defaultBoll.DownBand.Last()
-	upBand := s.defaultBoll.UpBand.Last()
-	sma := s.defaultBoll.SMA.Last()
+	downBand := s.defaultBoll.DownBand.Last(0)
+	upBand := s.defaultBoll.UpBand.Last(0)
+	sma := s.defaultBoll.SMA.Last(0)
 	log.Infof("bollinger band: up %f sma %f down %f", upBand, sma, downBand)
 
 	bandPercentage := calculateBandPercentage(upBand, downBand, sma, midPrice.Float64())
diff --git a/pkg/strategy/schedule/strategy.go b/pkg/strategy/schedule/strategy.go
index a64759237..5137ae01a 100644
--- a/pkg/strategy/schedule/strategy.go
+++ b/pkg/strategy/schedule/strategy.go
@@ -127,7 +127,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 
 			match := false
 			// if any of the conditions satisfies then we execute order
-			if belowMA != nil && closePriceF < belowMA.Last() {
+			if belowMA != nil && closePriceF < belowMA.Last(0) {
 				match = true
 				if s.BelowMovingAverage != nil {
 					if s.BelowMovingAverage.Side != nil {
@@ -139,7 +139,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 						quantity = s.BelowMovingAverage.QuantityOrAmount.CalculateQuantity(closePrice)
 					}
 				}
-			} else if aboveMA != nil && closePriceF > aboveMA.Last() {
+			} else if aboveMA != nil && closePriceF > aboveMA.Last(0) {
 				match = true
 				if s.AboveMovingAverage != nil {
 					if s.AboveMovingAverage.Side != nil {
diff --git a/pkg/strategy/skeleton/strategy.go b/pkg/strategy/skeleton/strategy.go
index 536aaae10..6651151fb 100644
--- a/pkg/strategy/skeleton/strategy.go
+++ b/pkg/strategy/skeleton/strategy.go
@@ -98,7 +98,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 	// when a kline is closed, we will do something
 	callback := func(kline types.KLine) {
 		// get the latest ATR value from the indicator object that we just defined.
-		atrValue := atr.Last()
+		atrValue := atr.Last(0)
 		log.Infof("atr %f", atrValue)
 
 		// Update our counter and sync the changes to the persistence layer on time
diff --git a/pkg/strategy/supertrend/double_dema.go b/pkg/strategy/supertrend/double_dema.go
index e711f89f4..bbe1adde6 100644
--- a/pkg/strategy/supertrend/double_dema.go
+++ b/pkg/strategy/supertrend/double_dema.go
@@ -21,9 +21,9 @@ type DoubleDema struct {
 func (dd *DoubleDema) getDemaSignal(openPrice float64, closePrice float64) types.Direction {
 	var demaSignal types.Direction = types.DirectionNone
 
-	if closePrice > dd.fastDEMA.Last() && closePrice > dd.slowDEMA.Last() && !(openPrice > dd.fastDEMA.Last() && openPrice > dd.slowDEMA.Last()) {
+	if closePrice > dd.fastDEMA.Last(0) && closePrice > dd.slowDEMA.Last(0) && !(openPrice > dd.fastDEMA.Last(0) && openPrice > dd.slowDEMA.Last(0)) {
 		demaSignal = types.DirectionUp
-	} else if closePrice < dd.fastDEMA.Last() && closePrice < dd.slowDEMA.Last() && !(openPrice < dd.fastDEMA.Last() && openPrice < dd.slowDEMA.Last()) {
+	} else if closePrice < dd.fastDEMA.Last(0) && closePrice < dd.slowDEMA.Last(0) && !(openPrice < dd.fastDEMA.Last(0) && openPrice < dd.slowDEMA.Last(0)) {
 		demaSignal = types.DirectionDown
 	}
 
diff --git a/pkg/strategy/supertrend/linreg.go b/pkg/strategy/supertrend/linreg.go
index eb47c2c7b..65813aa7f 100644
--- a/pkg/strategy/supertrend/linreg.go
+++ b/pkg/strategy/supertrend/linreg.go
@@ -19,11 +19,11 @@ type LinReg struct {
 }
 
 // Last slope of linear regression baseline
-func (lr *LinReg) Last() float64 {
+func (lr *LinReg) Last(int) float64 {
 	if lr.Values.Length() == 0 {
 		return 0.0
 	}
-	return lr.Values.Last()
+	return lr.Values.Last(0)
 }
 
 // Index returns the slope of specified index
@@ -68,7 +68,7 @@ func (lr *LinReg) Update(kline types.KLine) {
 	startPrice := endPrice + slope*(length-1)
 	lr.Values.Push((endPrice - startPrice) / (length - 1))
 
-	log.Debugf("linear regression baseline slope: %f", lr.Last())
+	log.Debugf("linear regression baseline slope: %f", lr.Last(0))
 }
 
 func (lr *LinReg) BindK(target indicator.KLineClosedEmitter, symbol string, interval types.Interval) {
@@ -96,9 +96,9 @@ func (lr *LinReg) GetSignal() types.Direction {
 	var lrSignal types.Direction = types.DirectionNone
 
 	switch {
-	case lr.Last() > 0:
+	case lr.Last(0) > 0:
 		lrSignal = types.DirectionUp
-	case lr.Last() < 0:
+	case lr.Last(0) < 0:
 		lrSignal = types.DirectionDown
 	}
 
diff --git a/pkg/strategy/supertrend/strategy.go b/pkg/strategy/supertrend/strategy.go
index 1003c621e..ac3943456 100644
--- a/pkg/strategy/supertrend/strategy.go
+++ b/pkg/strategy/supertrend/strategy.go
@@ -110,7 +110,7 @@ func (r *AccumulatedProfitReport) DailyUpdate(tradeStats *types.TradeStats) {
 
 	// Accumulated profit MA
 	r.accumulatedProfitMA.Update(r.accumulatedProfit.Float64())
-	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last())
+	r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last(0))
 
 	// Accumulated Fee
 	r.accumulatedFeePerDay.Update(r.accumulatedFee.Float64())
@@ -606,14 +606,14 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 				s.currentStopLossPrice = kline.GetLow()
 			}
 			if s.TakeProfitAtrMultiplier > 0 {
-				s.currentTakeProfitPrice = closePrice.Add(fixedpoint.NewFromFloat(s.Supertrend.AverageTrueRange.Last() * s.TakeProfitAtrMultiplier))
+				s.currentTakeProfitPrice = closePrice.Add(fixedpoint.NewFromFloat(s.Supertrend.AverageTrueRange.Last(0) * s.TakeProfitAtrMultiplier))
 			}
 		} else if side == types.SideTypeSell {
 			if s.StopLossByTriggeringK {
 				s.currentStopLossPrice = kline.GetHigh()
 			}
 			if s.TakeProfitAtrMultiplier > 0 {
-				s.currentTakeProfitPrice = closePrice.Sub(fixedpoint.NewFromFloat(s.Supertrend.AverageTrueRange.Last() * s.TakeProfitAtrMultiplier))
+				s.currentTakeProfitPrice = closePrice.Sub(fixedpoint.NewFromFloat(s.Supertrend.AverageTrueRange.Last(0) * s.TakeProfitAtrMultiplier))
 			}
 		}
 
diff --git a/pkg/strategy/support/strategy.go b/pkg/strategy/support/strategy.go
index d59788a3a..b688d0cb4 100644
--- a/pkg/strategy/support/strategy.go
+++ b/pkg/strategy/support/strategy.go
@@ -477,19 +477,19 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 			}
 		}
 
-		if s.longTermEMA != nil && closePrice.Float64() < s.longTermEMA.Last() {
+		if s.longTermEMA != nil && closePrice.Float64() < s.longTermEMA.Last(0) {
 			bbgo.Notify("%s: closed price is below the long term moving average line %f, skipping this support",
 				s.Symbol,
-				s.longTermEMA.Last(),
+				s.longTermEMA.Last(0),
 				kline,
 			)
 			return
 		}
 
-		if s.triggerEMA != nil && closePrice.Float64() > s.triggerEMA.Last() {
+		if s.triggerEMA != nil && closePrice.Float64() > s.triggerEMA.Last(0) {
 			bbgo.Notify("%s: closed price is above the trigger moving average line %f, skipping this support",
 				s.Symbol,
-				s.triggerEMA.Last(),
+				s.triggerEMA.Last(0),
 				kline,
 			)
 			return
@@ -499,8 +499,8 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 			bbgo.Notify("Found %s support: the close price %s is below trigger EMA %f and above long term EMA %f and volume %s > minimum volume %s",
 				s.Symbol,
 				closePrice.String(),
-				s.triggerEMA.Last(),
-				s.longTermEMA.Last(),
+				s.triggerEMA.Last(0),
+				s.longTermEMA.Last(0),
 				kline.Volume.String(),
 				s.MinVolume.String(),
 				kline)
diff --git a/pkg/strategy/swing/strategy.go b/pkg/strategy/swing/strategy.go
index da85591ce..fdb1234b4 100644
--- a/pkg/strategy/swing/strategy.go
+++ b/pkg/strategy/swing/strategy.go
@@ -15,7 +15,7 @@ const ID = "swing"
 
 // Float64Indicator is the indicators (SMA and EWMA) that we want to use are returning float64 data.
 type Float64Indicator interface {
-	Last() float64
+	Last(int) float64
 }
 
 func init() {
@@ -104,7 +104,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 			return
 		}
 
-		movingAveragePrice := inc.Last()
+		movingAveragePrice := inc.Last(0)
 
 		// skip it if it's near zero
 		if movingAveragePrice < 0.0001 {
diff --git a/pkg/strategy/techsignal/strategy.go b/pkg/strategy/techsignal/strategy.go
index bf3326dd3..29a7c56be 100644
--- a/pkg/strategy/techsignal/strategy.go
+++ b/pkg/strategy/techsignal/strategy.go
@@ -187,7 +187,7 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
 				})
 			}
 
-			var lastMA = ma.Last()
+			var lastMA = ma.Last(0)
 
 			// skip if the closed price is above the moving average
 			if closePrice.Float64() > lastMA {
diff --git a/pkg/strategy/trendtrader/trend.go b/pkg/strategy/trendtrader/trend.go
index be12f575a..81876ef30 100644
--- a/pkg/strategy/trendtrader/trend.go
+++ b/pkg/strategy/trendtrader/trend.go
@@ -65,15 +65,15 @@ func (s *TrendLine) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gene
 	supportSlope2 := 0.
 
 	session.MarketDataStream.OnKLineClosed(types.KLineWith(s.Symbol, s.Interval, func(kline types.KLine) {
-		if s.pivotHigh.Last() != resistancePrices.Last() {
-			resistancePrices.Update(s.pivotHigh.Last())
+		if s.pivotHigh.Last(0) != resistancePrices.Last(0) {
+			resistancePrices.Update(s.pivotHigh.Last(0))
 			resistanceDuration.Update(pivotHighDurationCounter)
 			pivotHighDurationCounter = 0
 		} else {
 			pivotHighDurationCounter++
 		}
-		if s.pivotLow.Last() != supportPrices.Last() {
-			supportPrices.Update(s.pivotLow.Last())
+		if s.pivotLow.Last(0) != supportPrices.Last(0) {
+			supportPrices.Update(s.pivotLow.Last(0))
 			supportDuration.Update(pivotLowDurationCounter)
 			pivotLowDurationCounter = 0
 		} else {
@@ -95,8 +95,8 @@ func (s *TrendLine) Bind(session *bbgo.ExchangeSession, orderExecutor *bbgo.Gene
 
 		if converge(resistanceSlope, supportSlope) {
 			// y = mx+b
-			currentResistance := resistanceSlope*pivotHighDurationCounter + resistancePrices.Last()
-			currentSupport := supportSlope*pivotLowDurationCounter + supportPrices.Last()
+			currentResistance := resistanceSlope*pivotHighDurationCounter + resistancePrices.Last(0)
+			currentSupport := supportSlope*pivotLowDurationCounter + supportPrices.Last(0)
 			log.Info(currentResistance, currentSupport, kline.Close)
 
 			if kline.High.Float64() > currentResistance {
diff --git a/pkg/strategy/xmaker/strategy.go b/pkg/strategy/xmaker/strategy.go
index 7ff87ce99..a912cfeb1 100644
--- a/pkg/strategy/xmaker/strategy.go
+++ b/pkg/strategy/xmaker/strategy.go
@@ -302,8 +302,8 @@ func (s *Strategy) updateQuote(ctx context.Context, orderExecutionRouter bbgo.Or
 	var pips = s.Pips
 
 	if s.EnableBollBandMargin {
-		lastDownBand := fixedpoint.NewFromFloat(s.boll.DownBand.Last())
-		lastUpBand := fixedpoint.NewFromFloat(s.boll.UpBand.Last())
+		lastDownBand := fixedpoint.NewFromFloat(s.boll.DownBand.Last(0))
+		lastUpBand := fixedpoint.NewFromFloat(s.boll.UpBand.Last(0))
 
 		if lastUpBand.IsZero() || lastDownBand.IsZero() {
 			log.Warnf("bollinger band value is zero, skipping")
diff --git a/pkg/types/filter.go b/pkg/types/filter.go
index 58e0a966e..bdb9e5de0 100644
--- a/pkg/types/filter.go
+++ b/pkg/types/filter.go
@@ -7,11 +7,7 @@ type FilterResult struct {
 	c      []int
 }
 
-func (f *FilterResult) Last() float64 {
-	return f.Index(0)
-}
-
-func (f *FilterResult) Index(j int) float64 {
+func (f *FilterResult) Last(j int) float64 {
 	if j >= f.length {
 		return 0
 	}
@@ -37,6 +33,10 @@ func (f *FilterResult) Index(j int) float64 {
 	return 0
 }
 
+func (f *FilterResult) Index(j int) float64 {
+	return f.Last(j)
+}
+
 func (f *FilterResult) Length() int {
 	return f.length
 }
diff --git a/pkg/types/indicator.go b/pkg/types/indicator.go
index 92c751a2a..d8fe3870c 100644
--- a/pkg/types/indicator.go
+++ b/pkg/types/indicator.go
@@ -12,186 +12,17 @@ import (
 	"github.com/c9s/bbgo/pkg/datatype/floats"
 )
 
-// Super basic Series type that simply holds the float64 data
-// with size limit (the only difference compare to float64slice)
-type Queue struct {
-	SeriesBase
-	arr  []float64
-	size int
-}
-
-func NewQueue(size int) *Queue {
-	out := &Queue{
-		arr:  make([]float64, 0, size),
-		size: size,
-	}
-	out.SeriesBase.Series = out
-	return out
-}
-
-func (inc *Queue) Last() float64 {
-	if len(inc.arr) == 0 {
-		return 0
-	}
-	return inc.arr[len(inc.arr)-1]
-}
-
-func (inc *Queue) Index(i int) float64 {
-	if len(inc.arr)-i-1 < 0 {
-		return 0
-	}
-	return inc.arr[len(inc.arr)-i-1]
-}
-
-func (inc *Queue) Length() int {
-	return len(inc.arr)
-}
-
-func (inc *Queue) Clone() *Queue {
-	out := &Queue{
-		arr:  inc.arr[:],
-		size: inc.size,
-	}
-	out.SeriesBase.Series = out
-	return out
-}
-
-func (inc *Queue) Update(v float64) {
-	inc.arr = append(inc.arr, v)
-	if len(inc.arr) > inc.size {
-		inc.arr = inc.arr[len(inc.arr)-inc.size:]
-	}
-}
-
-var _ UpdatableSeriesExtend = &Queue{}
-
 // Float64Indicator is the indicators (SMA and EWMA) that we want to use are returning float64 data.
 type Float64Indicator interface {
-	Last() float64
-}
-
-// The interface maps to pinescript basic type `series`
-// Access the internal historical data from the latest to the oldest
-// Index(0) always maps to Last()
-type Series interface {
-	Last() float64
-	Index(int) float64
-	Length() int
-}
-
-type SeriesExtend interface {
-	Series
-	Sum(limit ...int) float64
-	Mean(limit ...int) float64
-	Abs() SeriesExtend
-	Predict(lookback int, offset ...int) float64
-	NextCross(b Series, lookback int) (int, float64, bool)
-	CrossOver(b Series) BoolSeries
-	CrossUnder(b Series) BoolSeries
-	Highest(lookback int) float64
-	Lowest(lookback int) float64
-	Add(b interface{}) SeriesExtend
-	Minus(b interface{}) SeriesExtend
-	Div(b interface{}) SeriesExtend
-	Mul(b interface{}) SeriesExtend
-	Dot(b interface{}, limit ...int) float64
-	Array(limit ...int) (result []float64)
-	Reverse(limit ...int) (result floats.Slice)
-	Change(offset ...int) SeriesExtend
-	PercentageChange(offset ...int) SeriesExtend
-	Stdev(params ...int) float64
-	Rolling(window int) *RollingResult
-	Shift(offset int) SeriesExtend
-	Skew(length int) float64
-	Variance(length int) float64
-	Covariance(b Series, length int) float64
-	Correlation(b Series, length int, method ...CorrFunc) float64
-	AutoCorrelation(length int, lag ...int) float64
-	Rank(length int) SeriesExtend
-	Sigmoid() SeriesExtend
-	Softmax(window int) SeriesExtend
-	Entropy(window int) float64
-	CrossEntropy(b Series, window int) float64
-	Filter(b func(i int, value float64) bool, length int) SeriesExtend
-}
-
-func NewSeries(a Series) SeriesExtend {
-	return &SeriesBase{
-		Series: a,
-	}
-}
-
-type UpdatableSeries interface {
-	Series
-	Update(float64)
-}
-
-type UpdatableSeriesExtend interface {
-	SeriesExtend
-	Update(float64)
-}
-
-func Clone(u UpdatableSeriesExtend) UpdatableSeriesExtend {
-	method, ok := reflect.TypeOf(u).MethodByName("Clone")
-	if ok {
-		out := method.Func.Call([]reflect.Value{reflect.ValueOf(u)})
-		return out[0].Interface().(UpdatableSeriesExtend)
-	}
-	panic("method Clone not exist")
-}
-
-func TestUpdate(u UpdatableSeriesExtend, input float64) UpdatableSeriesExtend {
-	method, ok := reflect.TypeOf(u).MethodByName("TestUpdate")
-	if ok {
-		out := method.Func.Call([]reflect.Value{reflect.ValueOf(u), reflect.ValueOf(input)})
-		return out[0].Interface().(UpdatableSeriesExtend)
-	}
-	panic("method TestUpdate not exist")
-}
-
-// The interface maps to pinescript basic type `series` for bool type
-// Access the internal historical data from the latest to the oldest
-// Index(0) always maps to Last()
-type BoolSeries interface {
-	Last() bool
-	Index(int) bool
-	Length() int
-}
-
-// Calculate sum of the series
-// if limit is given, will only sum first limit numbers (a.Index[0..limit])
-// otherwise will sum all elements
-func Sum(a Series, limit ...int) (sum float64) {
-	l := a.Length()
-	if len(limit) > 0 && limit[0] < l {
-		l = limit[0]
-	}
-	for i := 0; i < l; i++ {
-		sum += a.Index(i)
-	}
-	return sum
-}
-
-// Calculate the average value of the series
-// if limit is given, will only calculate the average of first limit numbers (a.Index[0..limit])
-// otherwise will operate on all elements
-func Mean(a Series, limit ...int) (mean float64) {
-	l := a.Length()
-	if l == 0 {
-		return 0
-	}
-	if len(limit) > 0 && limit[0] < l {
-		l = limit[0]
-	}
-	return Sum(a, l) / float64(l)
+	Last(i int) float64
 }
 
 type AbsResult struct {
 	a Series
 }
 
-func (a *AbsResult) Last() float64 {
-	return math.Abs(a.a.Last())
+func (a *AbsResult) Last(i int) float64 {
+	return math.Abs(a.a.Last(i))
 }
 
 func (a *AbsResult) Index(i int) float64 {
@@ -282,9 +113,9 @@ func (c *CrossResult) Last() bool {
 		return false
 	}
 	if c.isOver {
-		return c.a.Last()-c.b.Last() > 0 && c.a.Index(1)-c.b.Index(1) < 0
+		return c.a.Last(0)-c.b.Last(0) > 0 && c.a.Index(1)-c.b.Index(1) < 0
 	} else {
-		return c.a.Last()-c.b.Last() < 0 && c.a.Index(1)-c.b.Index(1) > 0
+		return c.a.Last(0)-c.b.Last(0) < 0 && c.a.Index(1)-c.b.Index(1) > 0
 	}
 }
 
@@ -328,7 +159,7 @@ func Highest(a Series, lookback int) float64 {
 	if lookback > a.Length() {
 		lookback = a.Length()
 	}
-	highest := a.Last()
+	highest := a.Last(0)
 	for i := 1; i < lookback; i++ {
 		current := a.Index(i)
 		if highest < current {
@@ -342,7 +173,7 @@ func Lowest(a Series, lookback int) float64 {
 	if lookback > a.Length() {
 		lookback = a.Length()
 	}
-	lowest := a.Last()
+	lowest := a.Last(0)
 	for i := 1; i < lookback; i++ {
 		current := a.Index(i)
 		if lowest > current {
@@ -354,7 +185,7 @@ func Lowest(a Series, lookback int) float64 {
 
 type NumberSeries float64
 
-func (a NumberSeries) Last() float64 {
+func (a NumberSeries) Last(_ int) float64 {
 	return float64(a)
 }
 
@@ -384,12 +215,12 @@ func Add(a interface{}, b interface{}) SeriesExtend {
 	return NewSeries(&AddSeriesResult{aa, bb})
 }
 
-func (a *AddSeriesResult) Last() float64 {
-	return a.a.Last() + a.b.Last()
+func (a *AddSeriesResult) Last(i int) float64 {
+	return a.a.Last(i) + a.b.Last(i)
 }
 
 func (a *AddSeriesResult) Index(i int) float64 {
-	return a.a.Index(i) + a.b.Index(i)
+	return a.Last(i)
 }
 
 func (a *AddSeriesResult) Length() int {
@@ -415,12 +246,12 @@ func Sub(a interface{}, b interface{}) SeriesExtend {
 	return NewSeries(&MinusSeriesResult{aa, bb})
 }
 
-func (a *MinusSeriesResult) Last() float64 {
-	return a.a.Last() - a.b.Last()
+func (a *MinusSeriesResult) Last(i int) float64 {
+	return a.a.Index(i) - a.b.Index(i)
 }
 
 func (a *MinusSeriesResult) Index(i int) float64 {
-	return a.a.Index(i) - a.b.Index(i)
+	return a.Last(i)
 }
 
 func (a *MinusSeriesResult) Length() int {
@@ -471,12 +302,12 @@ type DivSeriesResult struct {
 	b Series
 }
 
-func (a *DivSeriesResult) Last() float64 {
-	return a.a.Last() / a.b.Last()
+func (a *DivSeriesResult) Last(i int) float64 {
+	return a.a.Index(i) / a.b.Index(i)
 }
 
 func (a *DivSeriesResult) Index(i int) float64 {
-	return a.a.Index(i) / a.b.Index(i)
+	return a.Last(i)
 }
 
 func (a *DivSeriesResult) Length() int {
@@ -502,12 +333,12 @@ type MulSeriesResult struct {
 	b Series
 }
 
-func (a *MulSeriesResult) Last() float64 {
-	return a.a.Last() * a.b.Last()
+func (a *MulSeriesResult) Last(i int) float64 {
+	return a.a.Index(i) * a.b.Index(i)
 }
 
 func (a *MulSeriesResult) Index(i int) float64 {
-	return a.a.Index(i) * a.b.Index(i)
+	return a.Last(i)
 }
 
 func (a *MulSeriesResult) Length() int {
@@ -654,20 +485,17 @@ type ChangeResult struct {
 	offset int
 }
 
-func (c *ChangeResult) Last() float64 {
-	if c.offset >= c.a.Length() {
-		return 0
-	}
-	return c.a.Last() - c.a.Index(c.offset)
-}
-
-func (c *ChangeResult) Index(i int) float64 {
+func (c *ChangeResult) Last(i int) float64 {
 	if i+c.offset >= c.a.Length() {
 		return 0
 	}
 	return c.a.Index(i) - c.a.Index(i+c.offset)
 }
 
+func (c *ChangeResult) Index(i int) float64 {
+	return c.Last(i)
+}
+
 func (c *ChangeResult) Length() int {
 	length := c.a.Length()
 	if length >= c.offset {
@@ -692,20 +520,17 @@ type PercentageChangeResult struct {
 	offset int
 }
 
-func (c *PercentageChangeResult) Last() float64 {
-	if c.offset >= c.a.Length() {
-		return 0
-	}
-	return c.a.Last()/c.a.Index(c.offset) - 1
-}
-
-func (c *PercentageChangeResult) Index(i int) float64 {
+func (c *PercentageChangeResult) Last(i int) float64 {
 	if i+c.offset >= c.a.Length() {
 		return 0
 	}
 	return c.a.Index(i)/c.a.Index(i+c.offset) - 1
 }
 
+func (c *PercentageChangeResult) Index(i int) float64 {
+	return c.Last(i)
+}
+
 func (c *PercentageChangeResult) Length() int {
 	length := c.a.Length()
 	if length >= c.offset {
@@ -902,25 +727,21 @@ type ShiftResult struct {
 	offset int
 }
 
-func (inc *ShiftResult) Last() float64 {
-	if inc.offset < 0 {
-		return 0
-	}
-	if inc.offset > inc.a.Length() {
-		return 0
-	}
-	return inc.a.Index(inc.offset)
-}
-func (inc *ShiftResult) Index(i int) float64 {
+func (inc *ShiftResult) Last(i int) float64 {
 	if inc.offset+i < 0 {
 		return 0
 	}
 	if inc.offset+i > inc.a.Length() {
 		return 0
 	}
+
 	return inc.a.Index(inc.offset + i)
 }
 
+func (inc *ShiftResult) Index(i int) float64 {
+	return inc.Last(i)
+}
+
 func (inc *ShiftResult) Length() int {
 	return inc.a.Length() - inc.offset
 }
@@ -940,14 +761,16 @@ type SliceView struct {
 	length int
 }
 
-func (s *SliceView) Last() float64 {
-	return s.a.Index(s.start)
-}
-func (s *SliceView) Index(i int) float64 {
+func (s *SliceView) Last(i int) float64 {
 	if i >= s.length {
 		return 0
 	}
-	return s.a.Index(i + s.start)
+
+	return s.a.Last(i + s.start)
+}
+
+func (s *SliceView) Index(i int) float64 {
+	return s.Last(i)
 }
 
 func (s *SliceView) Length() int {
@@ -980,30 +803,6 @@ func Rolling(a Series, window int) *RollingResult {
 	return &RollingResult{a, window}
 }
 
-type SigmoidResult struct {
-	a Series
-}
-
-func (s *SigmoidResult) Last() float64 {
-	return 1. / (1. + math.Exp(-s.a.Last()))
-}
-
-func (s *SigmoidResult) Index(i int) float64 {
-	return 1. / (1. + math.Exp(-s.a.Index(i)))
-}
-
-func (s *SigmoidResult) Length() int {
-	return s.a.Length()
-}
-
-// Sigmoid returns the input values in range of -1 to 1
-// along the sigmoid or s-shaped curve.
-// Commonly used in machine learning while training neural networks
-// as an activation function.
-func Sigmoid(a Series) SeriesExtend {
-	return NewSeries(&SigmoidResult{a})
-}
-
 // SoftMax returns the input value in the range of 0 to 1
 // with sum of all the probabilities being equal to one.
 // It is commonly used in machine learning neural networks.
diff --git a/pkg/types/indicator_test.go b/pkg/types/indicator_test.go
index 458d9dcf2..19c265ea8 100644
--- a/pkg/types/indicator_test.go
+++ b/pkg/types/indicator_test.go
@@ -15,7 +15,7 @@ import (
 
 func TestQueue(t *testing.T) {
 	zeroq := NewQueue(0)
-	assert.Equal(t, zeroq.Last(), 0.)
+	assert.Equal(t, zeroq.Last(0), 0.)
 	assert.Equal(t, zeroq.Index(0), 0.)
 	zeroq.Update(1.)
 	assert.Equal(t, zeroq.Length(), 0)
@@ -23,7 +23,7 @@ func TestQueue(t *testing.T) {
 
 func TestFloat(t *testing.T) {
 	var a Series = Sub(3., 2.)
-	assert.Equal(t, a.Last(), 1.)
+	assert.Equal(t, a.Last(0), 1.)
 	assert.Equal(t, a.Index(100), 1.)
 }
 
@@ -47,7 +47,7 @@ func TestFloat64Slice(t *testing.T) {
 	var c Series = Sub(&a, &b)
 	a = append(a, 4.0)
 	b = append(b, 3.0)
-	assert.Equal(t, c.Last(), 1.)
+	assert.Equal(t, c.Last(0), 1.)
 }
 
 /*
@@ -128,7 +128,7 @@ func TestSigmoid(t *testing.T) {
 	out := Sigmoid(&a)
 	r := floats.Slice{0.9525741268224334, 0.7310585786300049, 0.8909031788043871}
 	for i := 0; i < out.Length(); i++ {
-		assert.InDelta(t, r.Index(i), out.Index(i), 0.001)
+		assert.InDelta(t, r.Index(i), out.Index(i), 0.001, "i=%d", i)
 	}
 }
 
@@ -142,7 +142,7 @@ func TestAdd(t *testing.T) {
 	var a NumberSeries = 3.0
 	var b NumberSeries = 2.0
 	out := Add(&a, &b)
-	assert.Equal(t, out.Last(), 5.0)
+	assert.Equal(t, out.Last(0), 5.0)
 	assert.Equal(t, out.Index(0), 5.0)
 	assert.Equal(t, out.Length(), math.MaxInt32)
 }
@@ -151,16 +151,16 @@ func TestDiv(t *testing.T) {
 	a := floats.Slice{3.0, 1.0, 2.0}
 	b := NumberSeries(2.0)
 	out := Div(&a, &b)
-	assert.Equal(t, out.Last(), 1.0)
-	assert.Equal(t, out.Length(), 3)
-	assert.Equal(t, out.Index(1), 0.5)
+	assert.Equal(t, 1.0, out.Last(0))
+	assert.Equal(t, 3, out.Length())
+	assert.Equal(t, 0.5, out.Index(1))
 }
 
 func TestMul(t *testing.T) {
 	a := floats.Slice{3.0, 1.0, 2.0}
 	b := NumberSeries(2.0)
 	out := Mul(&a, &b)
-	assert.Equal(t, out.Last(), 4.0)
+	assert.Equal(t, out.Last(0), 4.0)
 	assert.Equal(t, out.Length(), 3)
 	assert.Equal(t, out.Index(1), 2.0)
 }
@@ -183,11 +183,11 @@ func TestSwitchInterface(t *testing.T) {
 	var d float32 = 4.0
 	var df float64 = 4.0
 	var e float64 = 5.0
-	assert.Equal(t, switchIface(a).Last(), af)
-	assert.Equal(t, switchIface(b).Last(), bf)
-	assert.Equal(t, switchIface(c).Last(), cf)
-	assert.Equal(t, switchIface(d).Last(), df)
-	assert.Equal(t, switchIface(e).Last(), e)
+	assert.Equal(t, switchIface(a).Last(0), af)
+	assert.Equal(t, switchIface(b).Last(0), bf)
+	assert.Equal(t, switchIface(c).Last(0), cf)
+	assert.Equal(t, switchIface(d).Last(0), df)
+	assert.Equal(t, switchIface(e).Last(0), e)
 }
 
 // from https://en.wikipedia.org/wiki/Logistic_regression
@@ -223,8 +223,8 @@ func TestClone(t *testing.T) {
 	a.Update(3.)
 	b := Clone(a)
 	b.Update(4.)
-	assert.Equal(t, a.Last(), 3.)
-	assert.Equal(t, b.Last(), 4.)
+	assert.Equal(t, a.Last(0), 3.)
+	assert.Equal(t, b.Last(0), 4.)
 }
 
 func TestPlot(t *testing.T) {
@@ -244,6 +244,6 @@ func TestFilter(t *testing.T) {
 		return val > 0
 	}, 4)
 	assert.Equal(t, b.Length(), 4)
-	assert.Equal(t, b.Last(), 1000.)
+	assert.Equal(t, b.Last(0), 1000.)
 	assert.Equal(t, b.Sum(3), 1200.)
 }
diff --git a/pkg/types/kline.go b/pkg/types/kline.go
index 9f8dd5d72..fcc358176 100644
--- a/pkg/types/kline.go
+++ b/pkg/types/kline.go
@@ -597,7 +597,7 @@ type KLineSeries struct {
 	kv    KValueType
 }
 
-func (k *KLineSeries) Last() float64 {
+func (k *KLineSeries) Last(int) float64 {
 	length := len(*k.lines)
 	switch k.kv {
 	case kOpUnknown:
diff --git a/pkg/types/queue.go b/pkg/types/queue.go
new file mode 100644
index 000000000..5205f802f
--- /dev/null
+++ b/pkg/types/queue.go
@@ -0,0 +1,51 @@
+package types
+
+// Super basic Series type that simply holds the float64 data
+// with size limit (the only difference compare to float64slice)
+type Queue struct {
+	SeriesBase
+	arr  []float64
+	size int
+}
+
+func NewQueue(size int) *Queue {
+	out := &Queue{
+		arr:  make([]float64, 0, size),
+		size: size,
+	}
+	out.SeriesBase.Series = out
+	return out
+}
+
+func (inc *Queue) Last(i int) float64 {
+	if i < 0 || len(inc.arr)-i-1 < 0 {
+		return 0
+	}
+	return inc.arr[len(inc.arr)-1-i]
+}
+
+func (inc *Queue) Index(i int) float64 {
+	return inc.Last(i)
+}
+
+func (inc *Queue) Length() int {
+	return len(inc.arr)
+}
+
+func (inc *Queue) Clone() *Queue {
+	out := &Queue{
+		arr:  inc.arr[:],
+		size: inc.size,
+	}
+	out.SeriesBase.Series = out
+	return out
+}
+
+func (inc *Queue) Update(v float64) {
+	inc.arr = append(inc.arr, v)
+	if len(inc.arr) > inc.size {
+		inc.arr = inc.arr[len(inc.arr)-inc.size:]
+	}
+}
+
+var _ UpdatableSeriesExtend = &Queue{}
diff --git a/pkg/types/series.go b/pkg/types/series.go
new file mode 100644
index 000000000..1c4289ee2
--- /dev/null
+++ b/pkg/types/series.go
@@ -0,0 +1,123 @@
+package types
+
+import (
+	"reflect"
+
+	"github.com/c9s/bbgo/pkg/datatype/floats"
+)
+
+// The interface maps to pinescript basic type `series`
+// Access the internal historical data from the latest to the oldest
+// Index(0) always maps to Last()
+type Series interface {
+	Last(i int) float64
+	Index(i int) float64
+	Length() int
+}
+
+type SeriesExtend interface {
+	Series
+	Sum(limit ...int) float64
+	Mean(limit ...int) float64
+	Abs() SeriesExtend
+	Predict(lookback int, offset ...int) float64
+	NextCross(b Series, lookback int) (int, float64, bool)
+	CrossOver(b Series) BoolSeries
+	CrossUnder(b Series) BoolSeries
+	Highest(lookback int) float64
+	Lowest(lookback int) float64
+	Add(b interface{}) SeriesExtend
+	Minus(b interface{}) SeriesExtend
+	Div(b interface{}) SeriesExtend
+	Mul(b interface{}) SeriesExtend
+	Dot(b interface{}, limit ...int) float64
+	Array(limit ...int) (result []float64)
+	Reverse(limit ...int) (result floats.Slice)
+	Change(offset ...int) SeriesExtend
+	PercentageChange(offset ...int) SeriesExtend
+	Stdev(params ...int) float64
+	Rolling(window int) *RollingResult
+	Shift(offset int) SeriesExtend
+	Skew(length int) float64
+	Variance(length int) float64
+	Covariance(b Series, length int) float64
+	Correlation(b Series, length int, method ...CorrFunc) float64
+	AutoCorrelation(length int, lag ...int) float64
+	Rank(length int) SeriesExtend
+	Sigmoid() SeriesExtend
+	Softmax(window int) SeriesExtend
+	Entropy(window int) float64
+	CrossEntropy(b Series, window int) float64
+	Filter(b func(i int, value float64) bool, length int) SeriesExtend
+}
+
+func NewSeries(a Series) SeriesExtend {
+	return &SeriesBase{
+		Series: a,
+	}
+}
+
+type UpdatableSeries interface {
+	Series
+	Update(float64)
+}
+
+type UpdatableSeriesExtend interface {
+	SeriesExtend
+	Update(float64)
+}
+
+func Clone(u UpdatableSeriesExtend) UpdatableSeriesExtend {
+	method, ok := reflect.TypeOf(u).MethodByName("Clone")
+	if ok {
+		out := method.Func.Call([]reflect.Value{reflect.ValueOf(u)})
+		return out[0].Interface().(UpdatableSeriesExtend)
+	}
+	panic("method Clone not exist")
+}
+
+func TestUpdate(u UpdatableSeriesExtend, input float64) UpdatableSeriesExtend {
+	method, ok := reflect.TypeOf(u).MethodByName("TestUpdate")
+	if ok {
+		out := method.Func.Call([]reflect.Value{reflect.ValueOf(u), reflect.ValueOf(input)})
+		return out[0].Interface().(UpdatableSeriesExtend)
+	}
+	panic("method TestUpdate not exist")
+}
+
+// The interface maps to pinescript basic type `series` for bool type
+// Access the internal historical data from the latest to the oldest
+// Index(0) always maps to Last()
+type BoolSeries interface {
+	Last() bool
+	Index(int) bool
+	Length() int
+}
+
+// Calculate sum of the series
+// if limit is given, will only sum first limit numbers (a.Index[0..limit])
+// otherwise will sum all elements
+func Sum(a Series, limit ...int) (sum float64) {
+	l := a.Length()
+	if len(limit) > 0 && limit[0] < l {
+		l = limit[0]
+	}
+	for i := 0; i < l; i++ {
+		sum += a.Index(i)
+	}
+	return sum
+}
+
+// Calculate the average value of the series
+// if limit is given, will only calculate the average of first limit numbers (a.Index[0..limit])
+// otherwise will operate on all elements
+func Mean(a Series, limit ...int) (mean float64) {
+	l := a.Length()
+	if l == 0 {
+		return 0
+	}
+	if len(limit) > 0 && limit[0] < l {
+		l = limit[0]
+	}
+	return Sum(a, l) / float64(l)
+}
diff --git a/pkg/types/seriesbase_imp.go b/pkg/types/seriesbase_imp.go
index feb95645a..1e52ce544 100644
--- a/pkg/types/seriesbase_imp.go
+++ b/pkg/types/seriesbase_imp.go
@@ -1,6 +1,8 @@
 package types
 
-import "github.com/c9s/bbgo/pkg/datatype/floats"
+import (
+	"github.com/c9s/bbgo/pkg/datatype/floats"
+)
 
 // SeriesBase is a wrapper of the Series interface
 // You can assign a data container that implements the Series interface
@@ -13,14 +15,14 @@ func (s *SeriesBase) Index(i int) float64 {
 	if s.Series == nil {
 		return 0
 	}
-	return s.Series.Index(i)
+	return s.Series.Last(i)
 }
 
-func (s *SeriesBase) Last() float64 {
+func (s *SeriesBase) Last(int) float64 {
 	if s.Series == nil {
 		return 0
 	}
-	return s.Series.Last()
+	return s.Series.Last(0)
 }
 
 func (s *SeriesBase) Length() int {
diff --git a/pkg/types/sigmoid.go b/pkg/types/sigmoid.go
new file mode 100644
index 000000000..4b28bb23b
--- /dev/null
+++ b/pkg/types/sigmoid.go
@@ -0,0 +1,27 @@
+package types
+
+import "math"
+
+type SigmoidResult struct {
+	a Series
+}
+
+func (s *SigmoidResult) Last(i int) float64 {
+	return 1. / (1. + math.Exp(-s.a.Last(i)))
+}
+
+func (s *SigmoidResult) Index(i int) float64 {
+	return s.Last(i)
+}
+
+func (s *SigmoidResult) Length() int {
+	return s.a.Length()
+}
+
+// Sigmoid returns the input values in range of -1 to 1
+// along the sigmoid or s-shaped curve.
+// Commonly used in machine learning while training neural networks
+// as an activation function.
+func Sigmoid(a Series) SeriesExtend {
+	return NewSeries(&SigmoidResult{a})
+}