An ARMA fit with an inadmissible root has no stable economic interpretation: an old shock can grow rather than decay, or distinct MA parameterisations can describe the same data. This derivation records the root restrictions that make the forecasting representations in the parent ARMA lesson unique and well behaved.
Learning objectives. By the end of this note you should be able to:
- derive the AR(1) stationary representation;
- derive the MA(1) invertible representation;
- state the general characteristic-root tests.
In this lesson
- The two questions the root tests answer
- AR stationarity
- MA invertibility
- Why invertibility selects a unique MA model
- Applying the test without losing the convention
Before you start
- Stationarity, White Noise, and the ACF/PACF
- AR, MA, and ARMA Models: Representation and the Wold Decomposition
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