ON THE EXISTENCE OF HILBERT VALUED PERIODICALLY CORRELATED AUTOREGRESSIVE PROCESSES

Abstract

In this paper we provide sufficient condition for existence of a unique Hilbert valued (H-valued) periodically correlated solution to the first order autoregressive model X-n = rho X-n(n-1) + Z(n), for n is an element of Z, and formulate the existing solution and its autocovariance operator. Also we specially investigate equivalent condition for the coordinate process < X-n, v >, for arbitrary element v in H, to satisfy in some autoregressive model. Finally, we extend our result to the autoregressive process with finite order.