The power of tests for equivalent ARMA models: The implications for practitioners

Analysts frequently find it convenient to use the same ARMA model to make forecasts for multiple time series. The trick is to know when it is safe to assume that multiple series are generated by the same underlying process. Although several authors have developed statistical procedures for testing whether two models are equivalent, no one has shown how to determine the power of these tests. This paper shows how to determine the power of the most general test for equivalent ARMA models. It also shows how to quantify the effect of model misspecification errors on the accuracy of the forecast. An illustrative example and flowchart are then used to show how calculating the power of the test can enable the practitioner to safeguard against a serious degradation in the accuracy of the forecast.