  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.
