Premium
A numerical method for factorizing the rational spectral density matrix
Author(s) -
Hosoya Yuzo,
Takimoto Taro
Publication year - 2010
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/j.1467-9892.2010.00658.x
Subject(s) - invertible matrix , mathematics , factorization , rational function , algebraic number , matrix decomposition , representation (politics) , matrix (chemical analysis) , canonical form , algebra over a field , causality (physics) , calculus (dental) , pure mathematics , algorithm , mathematical analysis , medicine , eigenvalues and eigenvectors , physics , materials science , dentistry , quantum mechanics , politics , political science , law , composite material
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.