A test for second-order stationarity of time series based on unsystematic sub-samples

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In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximizing the difference in the second-order structure over pairs of randomly drawn intervals. The asymptotic normality of the test statistic is established for both Gaussian and a range of non-Gaussian time series, and a bootstrap procedure is proposed for estimating the variance of the main statistics. Further, we show the consistency of our test under local alternatives. Because of the flexibility inherent in the random, unsystematic sub-samples used for test statistic construction, the proposed method is able to identify the intervals of significant departure from the stationarity without any dyadic constraints, which is an advantage over other tests employing systematic designs. We demonstrate its good finite sample performance on both simulated and real data, particularly in detecting localized departure from the stationarity.
Original languageEnglish
Pages (from-to)262-277
Number of pages16
Issue number1
Early online date2 Nov 2016
Publication statusPublished - 17 Nov 2016


  • locally stationary wavelet process
  • non-stationarity
  • stationarity test


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