ARIMA

Install and import#

npm install fintech-algorithms

import { forecastARIMA } from "fintech-algorithms/statistical-time-series/forecast-models/arima";

Signature#

forecastARIMA(values, ar, ma, intercept, differenceOrder, horizon)

ARMA on a differenced series, with forecasts integrated back to the original level. The integration step is where sign and level errors hide, so both the differenced and the level forecast are returned.

Parameters#

Returns#

{ forecast, fitted, residuals, state, differenced_forecast }

Both the differenced forecast and the integrated one, so the reconstruction can be checked.

Errors#

• When the sample is shorter than the differencing and model order require — throws

Complexity: time O(n × (p + q)), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

[100, 102, 105, 109, 114, 120]

[0.5]

[]

1

1

2

Call#

forecastARIMA(values, ar, ma, intercept, differenceOrder, horizon)

Returns#

object with 1 field: forecast

{
  "forecast": [124, 127]
}

Diagrams#

Calculation flow#

flowchart LR
    A["Finalized equally spaced training series"] --> B["Validate cutoff and frozen parameters"]
    B --> C["Build selected state or transformed series"]
    C --> D["Calculate horizon h conditional mean"]
    D --> E{"More horizons?"}
    E -- "yes" --> F["Append forecast and zero future innovation"]
    F --> D
    E -- "no" --> G["Publish path and state trace"]
    G --> H["Reveal holdout only for evaluation"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Forecasting: Principles and Practice — ARIMA models — Rob J. Hyndman and George Athanasopoulos
• statsmodels.tsa.arima.model.ARIMA — statsmodels developers
• Forecasting: Principles and Practice — Evaluating point forecast accuracy — Rob J. Hyndman and George Athanasopoulos
• Forecasting: Principles and Practice — Time series cross-validation — Rob J. Hyndman and George Athanasopoulos
• Forecasting: Principles and Practice — Evaluating regression and residual behavior — Rob J. Hyndman and George Athanasopoulos

The rest of the Forecast Models family#

• AutoRegForecasts from an autoregression with supplied coefficients.
• ARMAARMA forecasting with supplied coefficients: autoregressive terms on past values, moving-average terms on past errors.
• SARIMA/SARIMAXSeasonal ARIMA with optional exogenous regressors.
• Holt-WintersAdditive Holt-Winters: exponential smoothing of level, trend and seasonality.
• Theta ForecastThe Theta method: decompose, extrapolate, recombine.