Mathematics – Statistics Theory
Scientific paper
2007-11-28
Bernoulli 2007, Vol. 13, No. 4, 1151-1178
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.3150/07-BEJ102 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/07-BEJ102
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.
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