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Wald Tests For Detecting Multiple Structural Changes In Persistence


  • Kejriwal, Mohitosh
  • Perron, Pierre
  • Zhou, Jing


This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root throughout the sample against the alternative hypothesis that the process alternates between stationary and unit root regimes. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. We further show that the tests are inconsistent when directed against the incorrect alternative, thereby enabling identification of the nature of persistence in the initial regime. We also propose hybrid testing procedures that allow ruling out of stable stationary processes or ones that are subject to only stationary changes under the null, thereby aiding the researcher in interpreting a rejection as emanating from a switch between a unit root and stationary regime. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu ( 2006 , Journal of Econometrics 134, 373–399) which allows imposing within- and cross-regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed procedures perform well in finite samples relative to those available in the literature.

Suggested Citation

  • Kejriwal, Mohitosh & Perron, Pierre & Zhou, Jing, 2013. "Wald Tests For Detecting Multiple Structural Changes In Persistence," Econometric Theory, Cambridge University Press, vol. 29(02), pages 289-323, April.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:02:p:289-323_00

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    1. repec:cup:etheor:v:34:y:2018:i:05:p:985-1017_00 is not listed on IDEAS
    2. Ghoshray, Atanu & Stamatogiannis, Michalis P., 2015. "Centurial evidence of breaks in the persistence of unemployment," Economics Letters, Elsevier, vol. 129(C), pages 74-76.
    3. Constantin ANGHELACHE & Alexandru MANOLE & Madalina Gabriela ANGHEL & Georgiana NITU, 2016. "Some aspects regarding the extension of Edgeworth test to nonlinear restrictions," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(2), pages 83-86, February.
    4. Pang, Tianxiao & Tai-Leung Chong, Terence & Zhang, Danna & Liang, Yanling, 2018. "Structural Change In Nonstationary Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 34(05), pages 985-1017, October.
    5. Aleksei Netšunajev & Lars Winkelmann, 2014. "Inflation Expectations Spillovers between the United States and Euro Area," SFB 649 Discussion Papers SFB649DP2014-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. 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.
    7. Reiß, Markus & Todorov, Viktor & Tauchen, George, 2015. "Nonparametric test for a constant beta between Itô semi-martingales based on high-frequency data," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2955-2988.
    8. Skrobotov, Anton, 2015. "Likelihood Ratio Test for Change in Persistence," Published Papers skr001, Russian Presidential Academy of National Economy and Public Administration.
    9. Pikoko, Vuyokazi & Phiri, Andrew, 2018. "Is there hysteresis in South African unemployment? Evidence from the post-recessionary period," MPRA Paper 83962, University Library of Munich, Germany.
    10. repec:eee:intfin:v:58:y:2019:i:c:p:225-235 is not listed on IDEAS
    11. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert, 2017. "Improving the accuracy of asset price bubble start and end date estimators," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 121-138.
    12. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai Leung, 2018. "Estimating Multiple Breaks in Nonstationary Autoregressive Models," MPRA Paper 92074, University Library of Munich, Germany.
    13. Mohitosh Kejriwal, 2017. "A Robust Sequential Procedure for Estimating the Number of Structural Changes in Persistence," Purdue University Economics Working Papers 1303, Purdue University, Department of Economics.
    14. 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.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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