Publication Date
11-17-1972
Abstract
We consider the problem of obtaining finite memory linear one-step predictors for a non-deterministic weakly stationary stochastic process {ut : t = 0, ± 1, ± 2, ± ···} which have minimum mean square error. If φ(k) = Ɛ ut ut+k is the (unknown) covariance function for the process this problem reduces to solving the system of linear equations φ x = φ where φ = (φ(1), φ(2), ..., φ(d)), φ = (φ(i - j)) i, j = 1, 2, ..., d. Two iterative procedures are developed for producing a sequence of estimators {xn}n=1∞ which converge almost surely to Ө, the solution of φ x = φ. Both are modifications of conjugate direction methods originally proposed by Hestenes and Stiefel. A convergence rate for almost sure convergence is obtained for the first modification when the process has a finite moving average representation.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Lambert Herman Koopmans
Second Committee Member
Julius Rubin Blum
Third Committee Member
Herbert Thaddeus Davis III
Language
English
Document Type
Dissertation
Recommended Citation
Friel, James Otto. "Adaptive Prediction of Stationary Time Series by Modified Conjugate Direction Methods." (1972). https://digitalrepository.unm.edu/math_etds/246