This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourie...

In this paper, we introduce periodically correlated space-time autoregressive processes with values in Hilbert spaces. The existence conditions and the strong law of large numbers are established. Moreover, present an estimator for autocorrelation parameter such processes.

The extension of stationary process autocorrelation coefficient sequence is a classical problem in the field of spectral estimation. In this note, we treat this extension problem for the periodically correlated processes by using the partial autocorrelation function. We show that the theory of the non-stationary processes can be adapted to the periodically correlated processes. The partial auto...