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

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This CommonJS module includes:
- ARIMA (Autoregressive Integrated Moving Average)
- SARIMA (Seasonal ARIMA)
- SARIMAX (Seasonal ARIMA with exogenous variables)
- AutoARIMA (ARIMA with automatic parameters)

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``bash
npm install arima
`

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`javascript
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

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ARIMA, SARIMA, AutoARIMA:
`javascript
arima.train(ts) // Or arima.fit(ts)
arima.predict(10) // Predict 10 steps forward
`

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

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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:
`javascript
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.




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`javascript
// 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)
`

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`javascript
// 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)
`

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`javascript
// 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)
`

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

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

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`
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
`

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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.

`javascript
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
})
`

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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`.