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

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  • Chen, Zhanshou
  • Jin, Zi
  • Tian, Zheng
  • Qi, Peiyan

Abstract

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.

Suggested Citation

  • Chen, Zhanshou & Jin, Zi & Tian, Zheng & Qi, Peiyan, 2012. "Bootstrap testing multiple changes in persistence for a heavy-tailed sequence," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2303-2316.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2303-2316
    DOI: 10.1016/j.csda.2012.01.011
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    Cited by:

    1. Wagner, Martin & Wied, Dominik, 2014. "Monitoring Stationarity and Cointegration," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100386, Verein für Socialpolitik / German Economic Association.
    2. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    3. Zhanshou Chen & Yanting Xiao & Fuxiao Li, 2021. "Monitoring memory parameter change-points in long-memory time series," Empirical Economics, Springer, vol. 60(5), pages 2365-2389, May.
    4. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    5. Chen, Zhanshou & Xu, Qiongyao & Li, Huini, 2019. "Inference for multiple change points in heavy-tailed time series via rank likelihood ratio scan statistics," Economics Letters, Elsevier, vol. 179(C), pages 53-56.
    6. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    7. Fuxiao Li & Mengli Hao & Lijuan Yang, 2021. "Structural change detection in ordinal time series," PLOS ONE, Public Library of Science, vol. 16(8), pages 1-16, August.
    8. Chen, Zhanshou & Xing, Yuhong & Li, Fuxiao, 2016. "Sieve bootstrap monitoring for change from short to long memory," Economics Letters, Elsevier, vol. 140(C), pages 53-56.

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