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

TL;DR

This paper establishes conditions under which the moving block bootstrap method is consistent for non-stationary time series with periodic or almost periodic structures, enabling reliable statistical inference in such contexts.

Contribution

It provides new theoretical conditions for the consistency of moving block bootstrap in non-stationary, periodic, and almost periodic time series, extending bootstrap applicability.

Findings

Consistency holds under periodic joint distributions with CLT and mixing.

Additional boundedness conditions are needed for almost periodic mean functions.

Simulation demonstrates diagnostic tests for frequencies and stationarity.

Abstract

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