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, Jomes 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 obtaninig, rocursive estimates of the best finite cemory linear one-step predictor for a non-deterministic weakly stationary stochastic process ut+k a o, Z 2, ± 2, ± 2, ± … with unknown covariance structure. if u(k) x 3ut ut+k is the covariance function for the process this problem reduces to solring iteratively a 'coving' system of linear equations Pn x = Pn where Pn and Pn are consistent estimates of p = (0(1),p(2), …,p(d)) and p = (0(i-j)),i,j=1,2…, based on the first n observations of the process. Two iterative procedure are developed for producing a sequence fo estimators (-)n=1 which converge almost surely to 3 the solution of P x = 3 Both are modifications of conjugate direction methods originally proposed by Estenses and Stiefel (1952).
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