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A numerical method for factorizing the rational spectral density matrix

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  • Yuzo Hosoya
  • Taro Takimoto

Abstract

Improving Rozanov (1967, Stationary Random Processes. San Francisco: Holden‐day.)’s algebraic‐analytic solution to the canonical factorization problem of the rational spectral density matrix, this article presents a feasible computational procedure for the spectral factorization. We provide numerical comparisons of our procedure with the Bhansali's (1974, Journal of the Statistical Society, B36, 61.) and Wilson's (1972 SIAM Journal on Applied Mathematics, 23, 420) methods and illustrate its application in estimation of invertible MA representation. The proposed procedure is usefully applied to linear predictor construction, causality analysis and other problems where a canonical transfer function specification of a stationary process in question is required.

Suggested Citation

  • Yuzo Hosoya & Taro Takimoto, 2010. "A numerical method for factorizing the rational spectral density matrix," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 229-240, July.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:4:p:229-240
    DOI: 10.1111/j.1467-9892.2010.00658.x
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    References listed on IDEAS

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    1. Li, Lei M., 2005. "Factorization of moving-average spectral densities by state-space representations and stacking," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 425-438, October.
    2. Taro Takimoto & Yuzo Hosoya, 2004. "A Three‐Step Procedure For Estimating And Testing Cointegrated Armax Models," The Japanese Economic Review, Japanese Economic Association, vol. 55(4), pages 418-450, December.
    3. Wilson, G. Tunnicliffe, 1978. "A convergence theorem for spectral factorization," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 222-232, June.
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