Optimization and Systems Theory Seminar
Friday, October 5, 2001, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Yulia Gel
St. Petersburg State University
St. Petersburg, Russia
Mälardalen University
Västerås, Sweden
E-mail: yulia.gel@mdh.se

The convergence analysis of the least-squares estimates for AR models of infinite order

The time series identification problem considered here 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 almost surely of the LS estimates is carried out for an infinite case. Moreover, the result is established on the estimate of the degree of convergence of the LS estimates for an 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, it is presented a complementary result on the convergence of semi-martingales, which is a corner-stone for proof of all theorems here, but is of interest by itself.
Calendar of seminars
Last update: September 27, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.