On convergence of least-squares identifiers for infinite AR models
نویسندگان
چکیده
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. A modification of the Least Squares method is proposed for the identification of an AR model of infinite order. The analysis of convergence of the LS estimates with probability 1 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. Moreover, an infinite AR model is a new identification object, which has not been considered before. In addition, in this paper it is presented a complimentary result on the convergence of semi-martingales, which is a corner-stone for proof of all theorems here, but is of interest by itself.
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Convergence Analysis of the Least-squares Estimates for Infinte Ar Models
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