Glossary

ARIMA (autoregressive integrated moving average)

A classical time-series forecasting model that combines a series' own past values, differencing, and past forecast errors.

Also called: ARIMA model, Box-Jenkins

ARIMA is a widely used class of statistical models for time series forecasting, combining three components in its name: the autoregressive part predicts a value from a weighted combination of its own recent past values; the integrated part applies differencing to make a non-stationary series stationary; and the moving-average part models the current value as a function of past forecast errors, not to be confused with a simple moving-average smoother.

An ARIMA model is specified with three parameters, written ARIMA(p, d, q): p is the number of past values used, d is the number of times the series is differenced to achieve stationarity, and q is the number of past error terms used. A seasonal variant, SARIMA, adds a parallel set of parameters at a seasonal lag to handle recurring seasonality directly, rather than requiring it to be removed beforehand. Choosing these parameters typically relies on inspecting the series' autocorrelation structure.

ARIMA matters as one of the standard baseline forecasting methods for demand, sales, and operational time series, particularly where the series is well-behaved and history is limited. Its main limitations are that it handles only a single series at a time, does not naturally incorporate external variables or multiple related series without extension, and requires more manual tuning than automated alternatives like exponential smoothing or modern machine-learning forecasters.

Last reviewed September 22, 2026

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Related terms

Stationarity The property of a time series whose statistical characteristics, such as mean and variance, stay constant over time. Autocorrelation The correlation of a time series with a lagged, delayed copy of itself, used to detect repeating patterns and dependence over time. Exponential smoothing A forecasting technique that weights recent observations more heavily than older ones, with the weight decaying exponentially with age. Time series forecasting Predicting future values of a metric using patterns found in its own historical sequence over time. Seasonality A regular, predictable pattern in data that repeats at a fixed calendar interval, such as daily, weekly, or annually.

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