A fitted ARMA model earns its place only when its conditional forecasts improve a decision: a hedge, a funding estimate, or a signal benchmark. This note shows how future shocks are replaced by their conditional expectation of zero, why forecast paths revert, and how to judge the resulting errors outside the estimation sample.
Learning objectives. By the end of this note you should be able to:
- compute AR and MA conditional forecasts;
- explain multi-step mean reversion;
- calculate RMSE;
- design a rolling out-of-sample comparison.
The forecasting rules below build on the AR, MA, and ARMA representations and assume that the model has survived the Box–Jenkins diagnostic loop.
In this lesson
- Conditional expectation is the forecasting engine
- Forecast uncertainty grows with the horizon
- Forecast evaluation
- Worked forecast and interval
Before you start
- AR, MA, and ARMA Models: Representation and the Wold Decomposition
- Box–Jenkins Methodology: Identification, Estimation, and Diagnostic Checking
The full lesson, with worked examples and exercise solutions, is for members.
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