An Extension Problem For Discrete-Time Periodically Correlated Stochastic Processes

Authors: Alpay, D.1; Chevreuil, A.1; Loubaton, P.1

Source: Journal of Time Series Analysis, Volume 22, Number 2, 1 March 2001 , pp. 1-11(11)

Publisher: Blackwell Publishing

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content

Abstract:

In the context of wide-sense stationary processes, the so-called Caratheodory-Fejer problem of extending a finite non-negative sequence of matrices has been much studied. We here investigate a similar extension problem in the setting of wide-sense periodically correlated processes: given the first N coefficients of T scalar-valued sequences, we study under which condition(s) it is possible to find T extensions which are the cyclocorrelaion sequences of a periodically correlated process with period T. Using a result of Gladysev, the problem is shifted to a Caratheodory-Fejer problem with symmetry constraints. The existence of extensions is proved. In nondegenerate cases, the set of all solutions is given in terms of a homographic transformation of some Schur function G. The choice G=0 leads to the maximum entropy solution. The associated Gaussian processes are then proved to have a periodic autoregressive structure.

Keywords: Periodically correlated processes; extension of a non-negative sequence; matrix-valued Szego polynomials

Document Type: Research article

Affiliations: 1: Ben-Gurion University and Universite de Marne la Vallee

The full text article is temporarily unavailable.

We apologise for the inconvenience. Please try again later.

Back to top

Key:
Free Content - Free Content
New Content - New Content
Subscribed Content - Subscribed Content
Free Trial Content - Free Trial Content
Page Help Click here for Page Help
Shopping cart
Tools
Sign in






Need to register?
Sign up here
Text size: A | A | A | A