Decomposition of Time Series Dynamic Linear Models | Zendy

ODOLPHIN E. J. G | Zendy; JOHNSON S. E. | Zendy

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Decomposition of Time Series Dynamic Linear Models

Author(s) -

ODOLPHIN E. J. G,

JOHNSON S. E.

Publication year - 2003

Publication title -

journal of time series analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.576

H-Index - 54

eISSN - 1467-9892

pISSN - 0143-9782

DOI - 10.1111/1467-9892.00319

Subject(s) - mathematics , autoregressive model , diagonalizable matrix , decomposition , series (stratigraphy) , matrix decomposition , prime (order theory) , matrix (chemical analysis) , observable , polynomial , combinatorics , statistics , eigenvalues and eigenvectors , mathematical analysis , symmetric matrix , paleontology , biology , ecology , physics , materials science , quantum mechanics , composite material

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.

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