Bollinger Bands standard deviation calculation is different from othe…

…r implementations (#103)

* Bollinger Bands standard deviation calculation is different from other implementations
Fixes #102

* Bollinger bands test case.

volatility_indicators.go

@@ -117,20 +117,16 @@ func ChandelierExit(high, low, closing []float64) ([]float64, []float64) {
 func Std(period int, values []float64) []float64 {
 	result := make([]float64, len(values))
 	sma := Sma(period, values)
-	sum := float64(0)
 
-	for i, value := range values {
-		d1 := math.Pow(value-sma[i], 2)
-		count := i + 1
-		sum += d1
-
-		if i >= period {
-			first := i - period
-			sum -= math.Pow(values[first]-sma[first], 2)
-			count = period
+	for i := range values {
+		result[i] = 0.0
+		if i >= period-1 {
+			sum := float64(0)
+			for k := i - (period - 1); k <= i; k++ {
+				sum += (values[k] - sma[i]) * (values[k] - sma[i])
+			}
+			result[i] = math.Sqrt(sum / float64(period))
 		}
-
-		result[i] = math.Sqrt(sum / float64(count))
 	}
 
 	return result

volatility_indicators_test.go

@@ -9,9 +9,44 @@ import (
 	"testing"
 )
 
+func TestBollingerBands(t *testing.T) {
+	closing := []float64{
+		2, 4, 6, 8, 12, 14, 16, 18, 20,
+		2, 4, 6, 8, 12, 14, 16, 18, 20,
+		2, 4, 6, 8, 12, 14, 16, 18, 20,
+		2, 4, 6, 8, 12, 14, 16, 18, 20,
+	}
+
+	expectedMiddleBand := []float64{
+		2, 3, 4, 5, 6.4, 7.67, 8.86, 10, 11.11,
+		10.2, 9.64, 9.33, 9.23, 9.43, 9.73, 10.13, 10.59, 11.11,
+		10.63, 10.3, 10.5, 10.7, 11, 11.3, 11.5, 11.7, 11.9,
+		11.1, 10.3, 10.5, 10.7, 11, 11.3, 11.5, 11.7, 11.9,
+	}
+
+	expectedUpperBand := []float64{
+		2, 3, 4, 5, 6.4, 7.67, 8.86, 10, 11.11, 10.2,
+		9.64, 9.33, 9.23, 9.43, 9.73, 10.13, 10.59, 11.11,
+		10.63, 22.78, 22.56, 22.45, 22.56, 22.84, 23.22, 23.72, 24.32,
+		23.9, 22.78, 22.56, 22.45, 22.56, 22.84, 23.22, 23.72, 24.32,
+	}
+
+	expectedLowerBand := []float64{
+		2, 3, 4, 5, 6.4, 7.67, 8.86, 10, 11.11,
+		10.2, 9.64, 9.33, 9.23, 9.43, 9.73, 10.13, 10.59, 11.11,
+		10.63, -2.18, -1.56, -1.05, -0.56, -0.24, -0.22, -0.32, -0.52,
+		-1.7, -2.18, -1.56, -1.05, -0.56, -0.24, -0.22, -0.32, -0.52,
+	}
+
+	actualMiddleBand, actualUpperBand, actualLowerBand := BollingerBands(closing)
+	testEquals(t, roundDigitsAll(actualMiddleBand, 2), expectedMiddleBand)
+	testEquals(t, roundDigitsAll(actualUpperBand, 2), expectedUpperBand)
+	testEquals(t, roundDigitsAll(actualLowerBand, 2), expectedLowerBand)
+}
+
 func TestStd(t *testing.T) {
 	values := []float64{2, 4, 6, 8, 12, 14, 16, 18, 20}
-	expected := []float64{0, 0.707, 1, 1, 1.581, 1.581, 1, 1, 1}
+	expected := []float64{0, 1, 1, 1, 2, 1, 1, 1, 1}
 	period := 2
 
 	actual := Std(period, values)