Block bootstrap methods in analysis of periodically correlated processes.

Seasonality appears naturally in economics, vibroacoustics, mechanics, hydrology and many other fields. Periodicity is often present not only in the mean but also in the covariance function.  Thus, to build statistical models periodically correlated (PC) processes are used. The purpose of the talk will be to present recent results concerning consistency of block bootstrap methods for the first and the second order characteristics of  PC time series such as seasonal means, seasonal variances,  autocovariance function and Fourier coefficients of the mean and the autocovariance functions. Two bootstrap methods will be used: the Moving Block Bootstrap (MBB) and the Generalized Seasonal Block Bootstrap (GSBB). For aforementioned cases the MBB and the GSBB estimators will be introduced and the consistency of both bootstrap techniques will be shown. In the second part of the presentation,   problem of the block length choice will be discussed. Finally, the heuristic method of the block length choice for the Fourier coefficients of the autocovariance function will be proposed.