- NON-ADMISSIBILITY AND THE SPECIFICATION OF UNOBSERVED COMPONENTS MODELS

We deal with the problem of decomposing a time series into the sum of unobserved components as in detrending or seasonal adjustment. In particular, we analyze the situation in which the decomposition into orthogonal balanced components as performed by the ARIMA-Model-Based method is non-admissible. We show that considering top-heavy models for the components can help to 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. Also, applying this procedure to a particular time series allows 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.