We deal with the problem of optimal estimation linear functionals constructed from unobserved values a continuous time stochastic process periodically correlated increments based on past observations this process. To solve problem, we construct corresponding to sequence functions which forms an infinite dimensional vector stationary increment sequence. In case known spectral density sequence, o...

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...