On a property of one-sided moving average random sequences. (English. Russian original) Zbl 0625.62069

Moklyachuk, M. P.

Theory Probab. Math. Stat. 32, 95-102 (1986); translation from Teor. Veroyatn. Mat. Stat. 32, 86-93 (1985).

The problem of minimum mean square error estimation of \(\sum^{\infty}_{k=0}a(k)\xi (k)\) based on observations of the process \(\xi (k)+\eta (k)\), \(k=-1,-2,...\), where \(\xi\) (k) and \(\eta\) (k) are uncorrelated stationary processes is considered. It is shown that under specific conditions on the sequence \(\{\) a(k)\(\}\) the maximum value of this minimum mean square error occurs when \(\{\xi\) (k)\(\}\) is a one-sided moving average process.

Reviewer: E.McKenzie

MSC:

62M09	Non-Markovian processes: estimation
60G10	Stationary stochastic processes
62G05	Nonparametric estimation

Keywords:

maximal error; stationary random sequence; minimum mean square error estimation; uncorrelated stationary processes; one-sided moving average process