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Wald Tests for Detecting Multiple Structural Changes in Persistence


  • Mohitosh Kejriwal
  • Pierre Perron
  • Jing Zhou


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 against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. 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) which allows the minimization of the sum of squared residuals under the alternative hypothesis while imposing within and cross regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed tests perform quite well in finite samples relative to those available in the literature.

Suggested Citation

  • Mohitosh Kejriwal & Pierre Perron & Jing Zhou, 2009. "Wald Tests for Detecting Multiple Structural Changes in Persistence," Purdue University Economics Working Papers 1223, Purdue University, Department of Economics.
  • Handle: RePEc:pur:prukra:1223

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    2. 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.
    3. 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.
    4. 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.
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    6. 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.
    7. 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.
    8. Vuyo Pikoko & Andrew Phiri, 2018. "Is there hysteresis in South African unemployment? Evidence form the post-recessionary period," Working Papers 1803, Department of Economics, Nelson Mandela University, revised Jan 2018.
    9. 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.
    10. Ghoshray, Atanu & Stamatogiannis, Michalis P., 2015. "Centurial evidence of breaks in the persistence of unemployment," Economics Letters, Elsevier, vol. 129(C), pages 74-76.
    11. 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.
    12. 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.
    13. Skrobotov, Anton, 2015. "Likelihood Ratio Test for Change in Persistence," Published Papers skr001, Russian Presidential Academy of National Economy and Public Administration.
    14. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai Leung, 2018. "Estimating Multiple Breaks in Nonstationary Autoregressive Models," MPRA Paper 92074, University Library of Munich, Germany.

    More about this item


    structural change; persistence; Wald tests; unit root; parameter restrictions;

    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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