ARMA

Install and import#

npm install fintech-algorithms

import { forecastARMA } from "fintech-algorithms/statistical-time-series/forecast-models/arma";

Signature#

forecastARMA(values, ar, ma, intercept, horizon)

ARMA forecasting with supplied coefficients: autoregressive terms on past values, moving-average terms on past errors.

Parameters#

Returns#

{ forecast, fitted, residuals, state }

Forecasts, fitted values and residuals.

Errors#

• When the sample is shorter than the model order — 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#

[10, 12, 11]

[0.5]

[0.25]

5

2

Call#

forecastARMA(values, ar, ma, intercept, horizon)

Returns#

object with 1 field: forecast

{
  "forecast": [10.375, 10.1875]
}

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#

• statsmodels.tsa.arima.model.ARIMA — statsmodels developers
• Forecasting: Principles and Practice — ARIMA models — Rob J. Hyndman and George Athanasopoulos
• 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.
• ARIMAARMA on a differenced series, with forecasts integrated back to the original level.
• 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.