Periodically Correlated Processes and Their Stationary Dilations

Abstract

An explicit form of a stationary dilation for periodically correlated random sequences is obtained. The spectrum of this dilation sequence is related to that of the original periodically correlated sequence in a fairly simple manner. These results are then used to give spectral conditions for a periodically correlated sequence to be deterministic, purely nondeterministic, minimal, and to have a positive angle between its past and future.