IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i7p2303-2316.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000308
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.01.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. 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.
    5. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
    6. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
    7. Rosadi, Dedi, 2009. "Testing for independence in heavy-tailed time series using the codifference function," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4516-4529, October.
    8. 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.
    9. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    10. 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.
    11. Uwe Hassler & Jan Scheithauer, 2011. "Detecting changes from short to long memory," Statistical Papers, Springer, vol. 52(4), pages 847-870, November.
    12. 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.
    13. 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.
    14. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2006. "Modified tests for a change in persistence," Journal of Econometrics, Elsevier, vol. 134(2), pages 441-469, October.
    15. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy‐tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, March.
    16. Stephen Leybourne & Tae-Hwan Kim & Vanessa Smith & Paul Newbold, 2003. "Tests for a change in persistence against the null of difference-stationarity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 291-311, December.
    17. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    18. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Assaf, Ata & Bhandari, Avishek & Charif, Husni & Demir, Ender, 2022. "Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19," International Review of Financial Analysis, Elsevier, vol. 82(C).
    6. 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.
    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. Taipalus, Katja, 2012. "Signaling asset price bubbles with time-series methods," Research Discussion Papers 7/2012, Bank of Finland.
    9. repec:zbw:bofrdp:2012_007 is not listed on IDEAS
    10. Gabriel Zsurkis & JoÃo Nicolau & Paulo M. M. Rodrigues, 2021. "A Re‐Examination of Inflation Persistence Dynamics in OECD Countries: A New Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 935-959, August.
    11. Mohitosh Kejriwal, 2020. "A Robust Sequential Procedure for Estimating the Number of Structural Changes in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(3), pages 669-685, June.
    12. 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.
    13. 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.
    14. Luis F. Martins & Paulo M. M. Rodrigues, 2022. "Tests for segmented cointegration: an application to US governments budgets," Empirical Economics, Springer, vol. 63(2), pages 567-600, August.
    15. repec:zbw:bofism:2012_047 is not listed on IDEAS
    16. Taipalus, Katja, 2012. "Signaling asset price bubbles with time-series methods," Bank of Finland Research Discussion Papers 7/2012, Bank of Finland.
    17. Leone, Vitor & de Medeiros, Otavio Ribeiro, 2015. "Signalling the Dotcom bubble: A multiple changes in persistence approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 55(C), pages 77-86.
    18. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs, Bank of Finland, number 2012_047.
    19. Heinen, Florian & Willert, Juliane, 2011. "Monitoring a change in persistence of a long range dependent time series," Hannover Economic Papers (HEP) dp-479, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    20. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    21. 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.
    22. Eiji Kurozumi, 2005. "Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 181-206, April.

    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:eee:csdana:v:56:y:2012:i:7:p:2303-2316. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.