@winner-fed/finmath

The complete collection of mathematical utility methods for FinTech , including:

• Moving averages
• MACD
• Bollinger bands
• Standard deviations
• Highest high values / Lowest low values

And all finmath methods also handle empty values.

Table of Contents

• simple Moving Average (MA)
• Dynamic weighted Moving Average (DMA)
• Exponential Moving Average (EMA)
• Smoothed Moving Average (SMA)
• Weighted Moving Average (WMA)
• MACD
• BOLLinger bands (BOLL)
• Standard Deviations (SD)
• Highest High Values (HHV)
• Lowest Low Values (LLV)

install

$ npm i @winner-fed/finmath

usage

import { ma, dma, ema, sma, wma, macd, boll, sd, hhv, llv, add, subtract, multiply, divide } from '@winner-fed/finmath';

ma([1, 2, 3, 4, 5], 2);
// [<1 empty item>, 1.5, 2.5, 3.5, 4.5]

Simple Moving Average: ma(data, size)

type Data = EmptyableArray<number>;

• data Data the collection of data inside which empty values are allowed. Empty values are useful if a stock is suspended.
• size number the size of the periods.

Returns Data

Type Array<number|Empty> represents an array of numbers or empty items. And every method of finmath does NOT accepts items that are not numbers.

[1, , 2, 3][(1, undefined, 2, 3)][(1, null, 2, 3)]; // OK ✅ // NOT OK ❌ // NOT OK ❌

Special Cases

// If the size is less than `1`
ma([1, 2, 3], 0.5); // [1, 2, 3]

// If the size is larger than data length
ma([1, 2, 3], 5); // [<3 empty items>]

ma([, 1, , 3, 4, 5], 2);
// [<2 empty items>, 0.5, 1.5, 3.5, 4.5]

And all of the other moving average methods have similar mechanism.

Dynamic Weighted Moving Average: dma(data, alpha, noHead)

• data
• alpha Data the coefficient or list of coefficients alpha represents the degree of weighting decrease for each datum.
  • If alpha is a number, then the weighting decrease for each datum is the same.
  • If alpha larger than 1 is invalid, then the return value will be an empty array of the same length of the original data.
  • If alpha is an array, then it could provide different decreasing degree for each datum.
• noHead Boolean= whether we should abandon the first DMA.

Returns Data

dma([1, 2, 3], 2); // [<3 empty items>]

dma([1, 2, 3], 0.5); // [1, 1.5, 2.25]

dma([1, 2, 3, 4, 5], [0.1, 0.2, 0.1]);
// [1, 1.2, 1.38]

Exponential Moving Average: ema(data, size)

Calulates the most frequent used exponential average which covers about 86% of the total weight (when alpha = 2 / (N + 1)).

• data
• size Number the size of the periods.

Returns Data

Smoothed Moving Average: sma(data, size, times)

Also known as the modified moving average or running moving average, with alpha = times / size.

• data
• size
• times? Number=1

Returns Data

Weighted Moving Average: wma(data, size)

Calculates convolution of the datum points with a fixed weighting function.

Returns Data

MACD: macd(data, slowPeriods?, fastPeriods?, signalPeriods?)

MACD, short for Moving Average Convergence / Divergence, is a trading indicator used in technical analysis of stock prices, created by Gerald Appel in the late 1970s.

• data Data the collection of prices
• slowPeriods? number=26 the size of slow periods. Defaults to 26
• fastPeriods? number=12 the size of fast periods. Defaults to 12
• signalPeriods? number=9 the size of periods to calculate the MACD signal line.

Returns MACDGraph

macd(data);

// which returns:
// {
//   MACD: <Array>,
//   signal: <Array>,
//   histogram: <Array>
// }

struct MACDGraph

• MACD Data the difference between EMAs of the fast periods and EMAs of the slow periods.
• signal Data the EMAs of the MACD
• histogram Data MACD minus signal

In some countries, such as China, the three series above are commonly known as:

MACD       -> DIF
signal     -> DEA
histogram  -> MACD

Bollinger Bands: boll(data, size?, times?, options?)

boll([1, 2, 4, 8], 2, 2);
// {
//   upper: [, 2.5, 5, 10],
//   mid  : [, 1.5, 3, 6],
//   lower: [, 0.5, 1, 2]
// }

• data Data the collection of data
• size? Number=20 the period size, defaults to 20
• times? Number=2 the times of standard deviation between the upper band and the moving average.
• options? Object= optional options
  • ma? Data= the moving averages of the provided datum and period size. This option is used to prevent duplicate calculation of moving average.
  • sd? Data= the standard average of the provided datum and period size

Returns Array<Band> the array of the Band object.

interface Band {
  // the value of the upper band
  upper: number;
  // the value middle band (simple moving average)
  mid: number;
  // the value of the lower band
  lower: number;
}

Standard deviations: sd(data, size)

• data Data the collection of data
• size number the sample size of

Returns Data the array of standard deviations.

sd([1, 2, 4, 8], 2); // [<1 empty item>, 0.5, 1, 2]

sd([1, 2, 3, 4, 5, 6], 4);
// [
//   <3 empty items>,
//   1.118033988749895,
//   1.118033988749895,
//   1.118033988749895
// ]

Highest High Values: hhv(data, periods)

• data Data the array of closing prices.
• periods number the size of periods

Returns Data the highest high values of closing prices over the preceding periods periods (periods includes the current time).

const array = [1, 2, 4, 1];

hhv(array, 2); // [, 2, 4, 4]
hhv(array); // 4
hhv(array, 5); // [<4 empty items>]
hhv(array, 1); // [1, 2, 4, 1]

hhv(array, 2); // [, 1, 2, 2]

Lowest Low Values: llv(data, periods)

Instead, returns Data the lowest low values.