### 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

and

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.
*