Consistency and application of moving block bootstrap for non-stationary time series with periodic and almost periodic structure

摘要

The aim of this paper it to establish sufficient conditions for consistencyof moving block bootstrap for non-stationary time series with periodic andalmost periodic structure. The parameter of the study is the mean value of theexpectation function. Consistency holds in quite general situations: if alljoint distributions of the series are periodic, then it suffices to assume thecentral limit theorem and strong mixing property, together with summability ofthe autocovariance function. In the case where the mean function is almostperiodic, we additionally need uniform boundedness of the fourth moments of theroot statistics. It is shown that these theoretical results can be applied instatistical inference concerning the Fourier coefficients of periodically (PC)and almost periodically (APC) correlated time series. A simulation exampleshows how to use a graphical diagnostic test for significant frequencies andstationarity within these classes of time series.