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Wiener-Kolmogorov Filtering and Smoothing for Multivariate Series With State-Space Structure


  • Víctor Gómez


Wiener-Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi-infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state-space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener-Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

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  • Víctor Gómez, 2007. "Wiener-Kolmogorov Filtering and Smoothing for Multivariate Series With State-Space Structure," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 361-385, May.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:361-385

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    References listed on IDEAS

    1. Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, vol. 24(03), pages 823-828, June.
    2. Henghsiu Tsai & K. S. Chan, 2007. "A Note on Non-Negative Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 350-360, May.
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