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CONVERGENCE ANALYSIS OF THE LEAST-SQUARES ESTIMATES FOR INFINTE AR MODELS
Yulia Gel*, Andrey Barabanov**
* Saint-Petersburg State University, Russia and University of
Washington, Box 354320, Seattle, WA 98195, USA
** Saint-Petersburg State University, Bibliotechnaya sqr. 2,
198904 Saint-Petersburg, Russia
In this paper time series identification problem amounts to estimating the unknown parameters of an ARMA model, which is transformed to an infinite AR model and the Least-squares method is proposed for its identification. The convergence analysis of the LS estimates almost surely is carried out for an infinite case. Moreover, it is established the result on the estimate of the degree of convergence of the LS estimates for infinite AR model. Such an approach has been studied before for the “long” AR models but an overall convergence analysis has been lacking. In addition, a complimentary result on the convergence of semi-martingales is presented here, which is a corner-stone for proof of all theorems here, but is of interest by itself.
Keywords: ARMA models, autoregressive models, parameter estimation, identification, least-squares method
Session slot T-We-M21: Posters of Modelling, Identification and Discrete Systems/Area code 3a : Modelling, Identification and Signal Processing
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