Automation and Remote Control

, Volume 66, Issue 1, pp 92–107 | Cite as

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

  • A. E. Barabanov
  • Yu. R. Gel’
Adaptive and Robust Systems
Received:

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.

Keywords

Time Series Mechanical Engineer System Theory Unknown Parameter Autoregressive Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Pleiades Publishing, Inc. 2005

Authors and Affiliations

  • A. E. Barabanov
    • 1
  • Yu. R. Gel’
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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