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Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations

Author

Listed:
  • Si Zhang

    (School of Sciences, Xi’an University of Science and Technology, Xi’an 710054, China)

  • Hao Jin

    (School of Sciences, Xi’an University of Science and Technology, Xi’an 710054, China
    School of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an 710054, China)

  • Menglin Su

    (School of Sciences, Xi’an University of Science and Technology, Xi’an 710054, China)

Abstract

This paper investigates the properties of the change in persistence detection for observations with infinite variance. The innovations are assumed to be in the domain of attraction of a stable law with index κ ∈ ( 0 , 2 ] . We provide a new test statistic and show that its asymptotic distribution under the null hypothesis of non-stationary I ( 1 ) series is a functional of a stable process. When the change point in persistence is not known, the consistency is always given under the alternative, either from stationary I ( 0 ) to non-stationary I ( 1 ) or vice versa. The proposed tests can be used to identify the direction of change and do not over-reject against constant I ( 0 ) series, even in relatively small samples. Furthermore, we also consider the change point estimator which is consistent and the asymptotic behavior of the test statistic in the case of near-integrated time series. A block bootstrap method is suggested to determine critical values because the null asymptotic distribution contains the unknown tail index, which results in critical values depending on it. The simulation study demonstrates that the block bootstrap-based test is robust against change in persistence for heavy-tailed series with infinite variance. Finally, we apply our methods to the two series of the US inflation rate and USD/CNY exchange rate, and find significant evidence for persistence changes, respectively, from I ( 0 ) to I ( 1 ) and from I ( 1 ) to I ( 0 ) .

Suggested Citation

  • Si Zhang & Hao Jin & Menglin Su, 2024. "Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations," Mathematics, MDPI, vol. 12(2), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:258-:d:1318318
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    References listed on IDEAS

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    1. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.
    2. Philipp Sibbertsen & Juliane Willert, 2012. "Testing for a break in persistence under long-range dependencies and mean shifts," Statistical Papers, Springer, vol. 53(2), pages 357-370, May.
    3. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    4. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    5. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    6. Stephen J. Leybourne & Tae‐Hwan Kim & A. M. Robert Taylor, 2006. "Regression‐based Tests for a Change in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 595-621, October.
    7. Stephen Leybourne & Robert Taylor & Tae‐Hwan Kim, 2007. "CUSUM of Squares‐Based Tests for a Change in Persistence," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 408-433, May.
    8. 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.
    9. Ruibing Qin & Yang Liu, 2018. "Block bootstrap testing for changes in persistence with heavy-tailed innovations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1104-1116, March.
    10. Yushan Cheng & Yongchang Hui & Michael McAleer & Wing-Keung Wong, 2021. "Spurious Relationships for Nearly Non-Stationary Series," JRFM, MDPI, vol. 14(8), pages 1-24, August.
    11. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    12. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
    13. Jorge Belaire-Franch, 2019. "A note on the evidence of inflation persistence around the world," Empirical Economics, Springer, vol. 56(5), pages 1477-1487, May.
    14. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
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