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Bootstrap testing multiple changes in persistence for a heavy-tailed sequence

  • Chen, Zhanshou
  • Jin, Zi
  • Tian, Zheng
  • Qi, Peiyan
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    This paper tests the null hypothesis of stationarity against the alternative of changes in persistence for sequences in the domain of attraction of a stable law. The proposed moving ratio test is valid for multiple changes in persistence while the previous residual based ratio tests are designed for processes displaying only a single change. We show that the new test is consistent whether the process changes from I(0) to I(1) or vice versa. And it is easy to identify the direction of detected change points. In particular, a bootstrap approximation method is proposed to determine the critical values for the null distribution of the test statistic containing unknown tail index. We also propose a two step approach to estimate the change points. Numerical evidence suggests that our test performs well in finite samples. In addition, we show that our test is still powerful for changes between short and long memory, and displays no tendency to spuriously over-reject I(0) null in favor of a persistence change if the process is actually I(1) throughout. Finally, we illustrate our test using the US inflation rate data and a set of high frequency stock closing price data.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 7 ()
    Pages: 2303-2316

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2303-2316
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    1. Leybourne Stephen & Kim Tae-Hwan & Taylor A.M. Robert, 2007. "Detecting Multiple Changes in Persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 1-34, September.
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    15. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
    16. Chen, Zhanshou & Tian, Zheng & Wei, Yuesong, 2010. "Monitoring change in persistence in linear time series," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1520-1527, October.
    17. Sibbertsen, Philipp & Kruse, Robinson, 2007. "Testing for a break in persistence under long-range dependencies," Hannover Economic Papers (HEP) dp-381, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
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