ARIMA. Time-series forecasting in browsers and Node.js

Emscripten port of the native C package ctsa for time series analysis and forecasting

This CommonJS module includes:

• ARIMA (Autoregressive Integrated Moving Average)
• SARIMA (Seasonal ARIMA)
• SARIMAX (Seasonal ARIMA with exogenous variables)
• AutoARIMA (ARIMA with automatic parameters)

Installation of the ARIMA module

npm install arima

Initialization

const ARIMA = require('arima')
const arima = new ARIMA(options)

Where the options object can include:

• auto - automatic ARIMA (default: false)
• p, d, q params for ARIMA (default: p: 1, d: 0, q: 1)
• P, D, Q, s seasonal params (default: 0s). Setting them to non-zero values makes the ARIMA model seasonal
• method - ARIMA method (default: 0, described below)
• optimizer - optimization method (default: 6, described below)
• transpose - transpose exogenous array when fitting SARIMAX (default: false)
• verbose - verbose output (default: true)

Also for AutoARIMA only:

• approximation - approximation method (default: 1),
• search - search method (default: 1)
• p, d, q, P, D, Q params define max values for a search algorithm

Train/Predict

ARIMA, SARIMA, AutoARIMA:

arima.train(ts) // Or arima.fit(ts)
arima.predict(10) // Predict 10 steps forward

SARIMAX:

arima.train(ts, exog) // or arima.fit(ts, exog)
arima.predict(10, exognew) // Predict 10 steps forwars using new exogenous variables

Running in browsers

As described in the issue #10 Chrome prevents compilation of wasm modules >4kB. There are two ways to overcome this:

• Load arima in a Web Worker
• Use the arima/async module

Example of async loading:

const ARIMAPromise = require('arima/async')

ARIMAPromise.then(ARIMA => {
  const ts = Array(10).fill(0).map((_, i) => i + Math.random() / 5)
  const arima = new ARIMA({ p: 2, d: 1, q: 2, P: 0, D: 0, Q: 0, S: 0, verbose: false }).train(ts)
  const [pred, errors] = arima.predict(10)
})

All following examples use synchronous compilation (Node.js, Firefox). They will not work in Chrome.

Example: ARIMA

// Load package
const ARIMA = require('arima')

// Synthesize timeseries
const ts = Array(24).fill(0).map((_, i) => i + Math.random() / 5)

// Init arima and start training
const arima = new ARIMA({
  p: 2,
  d: 1,
  q: 2,
  verbose: false
}).train(ts)

// Predict next 12 values
const [pred, errors] = arima.predict(12)

Example: SARIMA

// Init sarima and start training
const sarima = new ARIMA({
  p: 2,
  d: 1,
  q: 2,
  P: 1,
  D: 0,
  Q: 1,
  s: 12,
  verbose: false
}).train(ts)

// Predict next 12 values
const [pred, errors] = sarima.predict(12)

Example: SARIMAX

// Generate timeseries using exogenous variables
const f = (a, b) => a * 2 + b * 5
const exog = Array(30).fill(0).map(x => [Math.random(), Math.random()])
const exognew = Array(10).fill(0).map(x => [Math.random(), Math.random()])
const ts = exog.map(x => f(x[0], x[1]) + Math.random() / 5)

// Init and fit sarimax
const sarimax = new ARIMA({
  p: 1,
  d: 0,
  q: 1,
  transpose: true,
  verbose: false
}).fit(ts, exog)

// Predict next 12 values using exognew
const [pred, errors] = sarimax.predict(12, exognew)

Example: AutoARIMA

const autoarima = new ARIMA({ auto: true }).fit(ts)
const [pred, errors] = autoarima.predict(12)

ARIMA Method (method)

0 - Exact Maximum Likelihood Method (Default)
1 - Conditional Method - Sum Of Squares
2 - Box-Jenkins Method

Optimization Method (optimizer)

Method 0 - Nelder-Mead
Method 1 - Newton Line Search
Method 2 - Newton Trust Region - Hook Step
Method 3 - Newton Trust Region - Double Dog-Leg
Method 4 - Conjugate Gradient
Method 5 - BFGS
Method 6 - Limited Memory BFGS (Default)
Method 7 - BFGS Using More Thuente Method

Old functional API (still works)

The old interface of the arima package was only one function that took 3 arguments:

• a 1D array with observations over time
• a number of time steps to predict
• a javascript object with ARIMA parameters p, d, q and other options

It returned two vectors - predictions and mean square errors.

const arima = require('arima')
const [pred, errors] = arima(ts, 20, {
  method: 0, // ARIMA method (Default: 0)
  optimizer: 6, // Optimization method (Default: 6)
  p: 1, // Number of Autoregressive coefficients
  d: 0, // Number of times the series needs to be differenced
  q: 1, // Number of Moving Average Coefficients
  verbose: true // Output model analysis to console
})

Web demo

You can try ARIMA online in the StatSim Forecast app: https://statsim.com/forecast/. It uses the arima package under the hood and applies random search to find the best values of p, d and q.