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Decomposition of Time Series Dynamic Linear Models

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  • E. J. G ODOLPHIN
  • S. E. JOHNSON

Abstract

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.

Suggested Citation

  • E. J. G Odolphin & S. E. Johnson, 2003. "Decomposition of Time Series Dynamic Linear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 513-527, September.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:513-527
    DOI: 10.1111/1467-9892.00319
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    References listed on IDEAS

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    1. C. K. Carter & R. Kohn, 1997. "Semiparametric Bayesian Inference for Time Series with Mixed Spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 255-268.
    2. Gabriel Huerta & Mike West, 1999. "Bayesian Inference on Periodicities and Component Spectral Structure in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(4), pages 401-416, July.
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    Cited by:

    1. Godolphin, E.J. & Triantafyllopoulos, Kostas, 2006. "Decomposition of time series models in state-space form," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2232-2246, May.

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