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Overcoming Nonadmissibility in ARIMA-Model-Based Signal Extraction

We analyze the situation in which the decomposition of a time series into orthogonal balanced components as performed by the AR IMA-model-based (AMB) method is nonadmissible. We show that considering top-heavy models for the components can solve the problem. The top-heavy decomposition is derived and the improvement achieved is illustrated by an application to a class of models often encountered in practice. Two empirical applications allow us to draw a comparison with the results yielded by the AMB decomposition of an approximated model by using an ad hoc filter such as X11-ARIMA and by direct specification of the structural time series models.