A numerical method for factorizing the rational spectral density matrix

作者：Hosoya Yuzo; Takimoto Taro^*

来源：Journal of Time Series Analysis, 2010, 31(4): 229-240.

DOI：10.1111/j.1467-9892.2010.00658.x

• Autoregressive-moving average representation
• causality
• one-step ahead prediction
• rational spectrum
• spectral density matrix factorization
• stationary process

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.

• 出版日期2010-7