## Bernoulli

• Bernoulli
• Volume 13, Number 4 (2007), 1151-1178.

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

Rafal Synowiecki

#### 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.

#### Article information

Source
Bernoulli, Volume 13, Number 4 (2007), 1151-1178.

Dates
First available in Project Euclid: 9 November 2007

https://projecteuclid.org/euclid.bj/1194625606

Digital Object Identifier
doi:10.3150/07-BEJ102

Mathematical Reviews number (MathSciNet)
MR2364230

Zentralblatt MATH identifier
1129.62082

#### Citation

Synowiecki, Rafal. Consistency and application of moving block bootstrap for non-stationary time series with periodic and almost periodic structure. Bernoulli 13 (2007), no. 4, 1151--1178. doi:10.3150/07-BEJ102. https://projecteuclid.org/euclid.bj/1194625606

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