Adaptive Prediction of Stationary Time Series by Modified Conjugate Direction Methods
Titel:
Adaptive Prediction of Stationary Time Series by Modified Conjugate Direction Methods
Auteur:
Friel, James O.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 4 (1975) nr. 1 pagina's 19-32
Jaar:
1975
Inhoud:
The problem considered is that of obtaining recursive estimates of the best finite memory linear one-step predictor for a non-deterministic weakly stationary stochastic process {ut : t = 0, ± 1, ± 2, ± …} with unknown covariance structure. If φ(k) = Eut ut+k is the covariance function for the process this problem reduces to solving iteratively a “moving” system of linear equations φ~n x = φ~n where φ~n and φ~n are consistent estimates of φ~ = (φ(1), φ(2), …, φ(d)) and φ~ = (φ(i-j));i, j=1, 2, …, d, based on the first n observations of the process. Two iterative procedures are developed for producing a sequence of estimators [image omitted] which converge almost surely to φ~, the solution of φ~ x~ = φ~. Both are modifications of conjugate direction methods originally proposed by Hestenes and Stiefel (1952).
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