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: false)

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(12).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(30).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

Cleanup

When you're done with a model instance, call .destroy() to free WASM memory:

const arima = new ARIMA({ p: 2, d: 1, q: 2 }).train(ts)
const [pred, errors] = arima.predict(12)
arima.destroy()

This is especially important when creating many model instances (e.g. in a loop or optimization). Re-training an existing instance (calling .train() again) automatically frees the previous model.

Minimum series length

The input time series must be long enough for the model parameters. If the series is too short, .train() will throw an error with the required minimum length. As a rule of thumb, provide at least 10 observations for simple ARIMA, and at least 2*s observations for seasonal models.

Known AutoARIMA limitations

AutoARIMA (Issues #7, #12) may produce inaccurate results with certain data patterns. If predictions seem wrong, try manually specifying p, d, q (and seasonal P, D, Q, s) instead of using auto: true.

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: false // Output model analysis to console (Default: false)
})

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.