### Optimization and Systems Theory Seminar

Friday, June 1, 2001, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Anders Dahlén**

Optimization and Systems Theory

KTH

E-mail: anders.dahlen@math.kth.se

####
Identification of stochastic systems: Subspace methods and covariance
extension

This talk will be an overview of my thesis which has the same title.
A class of methods called subspace methods has attracted a lot of
attention due to their advantages in modeling time series and
especially multivariate time series. However, these methods are based
on an unnatural assumption and therefore an alternative identification
procedure is presented. It is based on identification of a high-order
Maximum Entropy model (AR model) followed by Stochastically balanced
Truncation (MEST). The MEST procedure is described using just linear
algebraic operations, and therefore it inherits the nice properties of
subspace methods. Actually, MEST is very closely related to the
subspace methods. The essential differences between the CCA subspace
method of Larimore and MEST are: CCA estimates all covariances in a
block Hankel matrix directly from data, whereas MEST uses covariance
extension when constructing the Hankel matrix. By increasing the
AR-model order in a proper manner, strong consistency and asymptotic
normality of MEST is obtained. In fact, MEST and the CCA subspace
method are asymptotically equivalent, which implies that they have the
same asymptotic normal distribution. However, simulations indicate
that MEST has a better performance than CCA in practice.

Calendar of seminars

*Last update: May 23, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*