IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i2p258-d1318318.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/2/258/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/2/258/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    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. 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.
    10. 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.
    11. 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.
    12. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    13. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Soon, Siew-Voon & Baharumshah, Ahmad Zubaidi & Mohamad Shariff, Nurul Sima, 2017. "The persistence in real interest rates: Does it solve the intertemporal consumption behavior puzzle?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 50(C), pages 36-51.
    3. Chen, Wei & Huang, Zhuo & Yi, Yanping, 2015. "Is there a structural change in the persistence of WTI–Brent oil price spreads in the post-2010 period?," Economic Modelling, Elsevier, vol. 50(C), pages 64-71.
    4. Antonio Noriega & Carlos Capistrán & Manuel Ramos-Francia, 2013. "On the dynamics of inflation persistence around the world," Empirical Economics, Springer, vol. 44(3), pages 1243-1265, June.
    5. Kruse Robinson & Ventosa-Santaulària Daniel & Noriega Antonio E., 2017. "Changes in persistence, spurious regressions and the Fisher hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-28, June.
    6. Noriega Antonio E. & Ramos Francia Manuel, 2008. "A Note on the Dynamics of Persistence in US Inflation," Working Papers 2008-12, Banco de México.
    7. Frömmel, Michael & Kruse, Robinson, 2015. "Interest rate convergence in the EMS prior to European Monetary Union," Journal of Policy Modeling, Elsevier, vol. 37(6), pages 990-1004.
    8. Dilem Yıldırım & Dilan Aydın, 2021. "One Crisis After Another: A Dynamic Unemployment Persistence Analysis For The Gips Countries," ERC Working Papers 2102, ERC - Economic Research Center, Middle East Technical University, revised Apr 2021.
    9. 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.
    10. Mohitosh Kejriwal & Xuewen Yu & Pierre Perron, 2020. "Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 676-690, September.
    11. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    12. Leybourne, Stephen J. & Taylor, A.M. Robert, 2006. "Persistence change tests and shifting stable autoregressions," Economics Letters, Elsevier, vol. 91(1), pages 44-49, April.
    13. 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.
    14. 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.
    15. 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.
    16. Kruse, Robinson, 2011. "On European monetary integration and the persistence of real effective exchange rates," Finance Research Letters, Elsevier, vol. 8(1), pages 45-50, March.
    17. Philipp Sibbertsen & Robinson Kruse, 2009. "Testing for a break in persistence under long‐range dependencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 263-285, May.
    18. Daniel Chiquiar & Antonio Noriega & Manuel Ramos-Francia, 2010. "A time-series approach to test a change in inflation persistence: the Mexican experience," Applied Economics, Taylor & Francis Journals, vol. 42(24), pages 3067-3075.
    19. 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.
    20. Florian Heinen & Philipp Sibbertsen & Robinson Kruse, 2009. "Forecasting long memory time series under a break in persistence," CREATES Research Papers 2009-53, Department of Economics and Business Economics, Aarhus University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:258-:d:1318318. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.