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...

We consider the maximum entropy extention of a partially specified autocovariance sequence of a periodically correlated process. The sequence may be specified on a non-contiguous set. We give a method which solves the problem completely—it gives the positive definite solution when it exists and reports that it does not exist otherwise. The method is numerically reliable even when the solution i...

This research is dedicated to the study of periodic characteristics of periodically correlated time series such as seasonal means, seasonal variances and autocovariance functions. Two bootstrap methods are used: the extension of the usual Moving Block Bootstrap (EMBB) and the Generalized Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual MBB does not preserve the...

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...