This article is cited in 2 papers

Adaptive and Robust Systems

Convergence of the least-squares method with a polynomial regularizer for the infinite-dimensional autoregression equation

A. E. Barabanov, Yu. R. Gel'

Saint-Petersburg State University

Abstract: Consideration was given to the estimation of the unknown parameters of a stable infinite-dimensional autoregressive model from the observations of a random time series. The class of such models includes an autoregressive moving-average equation with a stable moving-average part. A modified procedure of the least-squares method was used to identify the unknown parameters. For the infinite-dimensional case, the estimates of the least-squares method were proved to be strong consistent. In addition, presented was a fact on convergence of the semimartingales that is of independent interest.

Presented by the member of Editorial Board: B. M. Miller

Received: 20.02.2003

 English version: Automation and Remote Control, 2005, 66:1, 92–107

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