castiilg and time series analysis Exact factorization of the spectral density ann its application to wrf

Let f be the spectral density function of a purely nondeter-minis tic stationary stochastic process and be the optimal (canonical) factor of f. The role of the coefficients cnand dn (n 0) of J) and respectively, in prediction, filtering and control theory is well-known. We show that the c ns and d ns can be obtained recursively in terms of the Fourier coefficients of log f. Also, recursive and updating formulae for the Kolmogorov-Wiener predictor similar to those of Box-Jenkins are provided. 1983, Taylor & Francis Group, LLC. All rights reserved.

Exact factorization of the spectral density ann its application to wrf,castiilg and time series analysis Academic Article