Patterns › Time series

ARIMA forecast (h-step + intervals)

ARIMA forecasting (automatic order selection or a fixed order) fits the model, projects h steps ahead, and returns a prediction interval as a fan chart.

What is ARIMA forecast (h-step + intervals)?

Automatic order selection searches over (p, d, q) — differencing to stationarity, then trading off AIC/BIC against parsimony — to pick an ARIMA model automatically, or you can fix the order yourself. The fitted model is then iterated forward to produce point forecasts.

The prediction interval widens with the horizon because forecast uncertainty compounds: each step inherits the variance of the ones before it. The band is model-based (Gaussian errors), so it captures parameter-conditional uncertainty, not model-selection or structural-break risk.

When should I use ARIMA forecast (h-step + intervals)?

Short-to-medium horizon forecasting of a single stationary-after-differencing series.
A quick automatic baseline before hand-tuning an ARIMA.

What data does it need?

One numeric series (row order = time) + forecast horizon h + automatic or fixed (p, d, q) + interval level.

What does it report?

Selected ARIMA order, AIC/BIC, a history-plus-forecast fan chart with the prediction band, and a table of point forecasts with lower/upper bounds.

What does it assume?

Series is regularly spaced and time-ordered.
Residuals are approximately white noise — check ACF/PACF first.
The band assumes the fitted structure holds over the horizon; it ignores regime change.

How do I interpret the result?

Point forecasts drift toward the series mean/trend as h grows; the widening band shows how quickly the forecast becomes uninformative.

References

Hyndman & Khandakar (2008). Automatic time series forecasting. JSS 27.
Hyndman & Athanasopoulos (2021). Forecasting: Principles and Practice, 3rd ed.