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Bootstrap procedures for variance breaks test in time series with a changing trend

Author

Listed:
  • Hao Jin
  • Si Zhang
  • Jinsuo Zhang
  • Shougang Zhang

Abstract

In this article, we consider the problem of testing for variance breaks in time series in the presence of a changing trend. In performing the test, we employ the cumulative sum of squares (CUSSQ) test introduced by Inclán and Tiao (1994, J. Amer. Statist. Assoc., 89, 913 − 923). It is shown that CUSSQ test is not robust in the case of broken trend and its asymptotic distribution does not convergence to the sup of a standard Brownian bridge. As a remedy, a bootstrap approximation method is designed to alleviate the size distortions of test statistic while preserving its high power. Via a bootstrap functional central limit theorem, the consistency of these bootstrap procedures is established under general assumptions. Simulation results are provided for illustration and an empirical example of application to a set of high frequency real data is given.

Suggested Citation

  • Hao Jin & Si Zhang & Jinsuo Zhang & Shougang Zhang, 2018. "Bootstrap procedures for variance breaks test in time series with a changing trend," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(18), pages 4609-4627, September.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:18:p:4609-4627
    DOI: 10.1080/03610926.2017.1377256
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