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 arimaInitialization
const ARIMA = require('arima')
const arima = new ARIMA(options)Where the options object can include:
auto- automatic ARIMA (default:false)p,d,qparams for ARIMA (default:p: 1, d: 0, q: 1)P,D,Q,sseasonal params (default:0s). Setting them to non-zero values makes the ARIMA model seasonalmethod- 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,Qparams 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 forwardSARIMAX:
arima.train(ts, exog) // or arima.fit(ts, exog)
arima.predict(10, exognew) // Predict 10 steps forwars using new exogenous variablesRunning in browsers
As described in the issue #10 Chrome prevents compilation of wasm modules >4kB. There are two ways to overcome this:
- Load
arimain a Web Worker - Use the
arima/asyncmodule
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,qand 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.