Decomposition of Time Series Dynamic Linear Models

This paper derives the admissible decompositions for a time series dynamic linear model, assuming only that the model is observable. The decompositions depend on factorizations of the characteristic polynomial of the state evolution matrix G into relatively prime factors. This generalizes the method of West (1997) which considers one decomposition in the particular case where G is diagonalizable. Conditions are derived for a decomposition to be independent. These results show that no autoregressive process of order d has an independent decomposition for any integer d. Two illustrations of this procedure are discussed in detail. Copyright 2003 Blackwell Publishing Ltd.

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