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

Authors:
A. E. Barabanov;Yu. R. Gel'
Affiliations:
St. Petersburg State University, St. Petersburg, Russia;St. Petersburg State University, St. Petersburg, Russia
Venue:
Automation and Remote Control
Year:
2005

Citing 6
Cited 0

System identification: theory for the user

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The statistical theory of linear systems

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Linear robust control
Random Iterative Models

Random Iterative Models
A covariance extension approach to identification of time series

Automatica (Journal of IFAC)

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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.