‎in this work we introduce and study discrete time periodically correlated stable‎ ‎processes and multivariate stationary stable processes related to periodic and cyclic‎ ‎flows‎. ‎our study involves producing a spectral representation and a‎ ‎spectral identification for such processes‎. ‎we show that the third‎ ‎component of a periodically correlated stable process has a component related to a...

‎In this work we introduce and study discrete time periodically correlated stable‎ ‎processes and multivariate stationary stable processes related to periodic and cyclic‎ ‎flows‎. ‎Our study involves producing a spectral representation and a‎ ‎spectral identification for such processes‎. ‎We show that the third‎ ‎component of a periodically correlated stable process has a component related to a...

The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.

simple harmonizable processes (shp) introduced by soltani and parvardeh (2006) are a large class of nonstationary processes which includes stationary and periodically correlated (pc) processes. detection and estimation of shp structure are important problems when dealing with nonstationary data. in this paper, we study the spectral properties of simple processes and propose a method to detect a...

the existence of shift for periodically correlated processes and its boundedness are investigated. spectral criteria for these non-stationary processes to have such shifts are obtained.

This paper focuses on the empirical autocovariance operator of H-valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.