The ARIMA Model
ARIMA stands for autoregressive integrated moving average. It is a flexible linear model for a single stationary or differenced series.
The three orders
ARIMA is written with three numbers p, d, and q.
- p is the autoregressive order: how many past values feed the prediction.
- d is the degree of differencing needed to make the series stationary.
- q is the moving average order: how many past forecast errors feed the prediction.
How the pieces fit
The autoregressive part says the next value depends on a weighted sum of recent values. The moving average part says it also depends on recent errors. The integrated part handles trend by differencing before fitting and undoing it afterward.
Choosing the orders
- Inspect the ACF and PACF plots to suggest p and q.
- Use a test such as augmented Dickey Fuller to pick d.
- Compare candidate models with a score like the Akaike information criterion.
ARIMA captures trend well but has no built in seasonality, which motivates the seasonal extension.
Key idea
ARIMA fuses past values, past errors, and differencing into one linear forecaster tuned by the three orders p, d, and q.