Diagnostic Checking of Unobserved-Components Time Series Models.

Diagnostic checking of time-series models is normally carried out using the innovations, that is the one-step ahead prediction errors. In an unobserved components model, other sets of residuals are available. These auxiliary residuals are estimators of the disturbances associated.with the unobserved components. The article shows how the properties of the auxiliary residuals may be obtained, how they are related to each other and to the innovations, and how they can be used to construct test statistics. Applications are presented showing how residuals can be used to detect and distinguish between outliers and structural change.