Bollinger Bands standard deviation calculation is different from othe…

…r implementations (#106)

Fixes #105

src/indicator/volatility/bollingerBands.test.ts

@@ -0,0 +1,40 @@
+// Copyright (c) 2022 Onur Cinar. All Rights Reserved.
+// https://github.com/cinar/indicatorts
+
+import { deepStrictEqual } from 'assert';
+import { roundDigitsAll } from '../../helper/numArray';
+import { bollingerBands } from './bollingerBands';
+
+describe('Bollinger Bands', () => {
+  it('should be able to compute the bollinger bands', () => {
+    const closings = [
+      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,
+    ];
+
+    const expectedUpperBand = [
+      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,
+    ];
+
+    const expectedMiddleBand = [
+      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,
+    ];
+
+    const expectedLowerBand = [
+      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,
+    ];
+
+    const actual = bollingerBands(closings);
+    deepStrictEqual(roundDigitsAll(2, actual.upperBand), expectedUpperBand);
+    deepStrictEqual(roundDigitsAll(2, actual.middleBand), expectedMiddleBand);
+    deepStrictEqual(roundDigitsAll(2, actual.lowerBand), expectedLowerBand);
+  });
+});

src/indicator/volatility/mstd.test.ts

@@ -8,8 +8,8 @@ import { mstd } from './mstd';
 describe('Standard deviation', () => {
   it('should be able to compute std', () => {
     const values = [2, 4, 6, 8, 12, 14, 16, 18, 20];
-    const expected = [0, 0, 0, 2.236, 2.958, 3.162, 2.958, 2.236, 2.236];
-    const period = 4;
+    const expected = [0, 1, 1, 1, 2, 1, 1, 1, 1];
+    const period = 2;
 
     const actual = mstd(period, values);
     deepStrictEqual(roundDigitsAll(3, actual), expected);

src/indicator/volatility/mstd.ts

@@ -1,6 +1,8 @@
 // Copyright (c) 2022 Onur Cinar. All Rights Reserved.
 // https://github.com/cinar/indicatorts
 
+import { sma } from '../trend/sma';
+
 /**
  * Moving strandard deviation function.
  *
@@ -10,27 +12,19 @@
  */
 export function mstd(period: number, values: number[]): number[] {
   const result = new Array<number>(values.length);
-
-  let sum = 0;
+  const averages = sma(period, values);
 
   for (let i = 0; i < values.length; i++) {
-    sum += values[i];
+    result[i] = 0;
 
     if (i >= period - 1) {
-      if (i >= period) {
-        sum -= values[i - period];
-      }
-
-      const average = sum / period;
-      let ss = 0;
+      let sum = 0;
 
-      for (let j = 0; j < period; j++) {
-        ss += Math.pow(values[i - j] - average, 2);
+      for (let k = i - (period - 1); k <= i; k++) {
+        sum += (values[k] - averages[i]) * (values[k] - averages[i]);
       }
 
-      result[i] = Math.sqrt(ss / period);
-    } else {
-      result[i] = 0;
+      result[i] = Math.sqrt(sum / period);
     }
   }