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A note on estimating a structural change in persistence


  • Kejriwal, Mohitosh
  • Perron, Pierre


This paper studies issues related to the estimation of a structural change in the persistence of a univariate time series. The break is such that the process has a unit root [i.e., is I(1)] in the pre-break regime but reverts to a stationary [i.e., I(0)] process in the post-break regime or vice versa. Chong (2001) develops the limit theory for the estimation of such autoregressive processes and shows that the rate of convergence of the breakpoint estimator in the I(1)–I(0) case is faster than that in the I(0)–I(1) case, which enables the break date to be estimated much more precisely in the former case. In this paper, we show that the faster rate is an artifact of the assumed data generating process that is characterized by a spurious jump at the true breakpoint. Based on a reformulation that avoids this jump, the same rate of convergence prevails in both cases. An important implication of this result is that existing confidence intervals in the I(1)–I(0) case have asymptotically zero coverage rates when the break magnitude is fixed. A small simulation study confirms the relevance of the asymptotic results in finite samples.

Suggested Citation

  • Kejriwal, Mohitosh & Perron, Pierre, 2012. "A note on estimating a structural change in persistence," Economics Letters, Elsevier, vol. 117(3), pages 932-935.
  • Handle: RePEc:eee:ecolet:v:117:y:2012:i:3:p:932-935
    DOI: 10.1016/j.econlet.2012.07.020

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    References listed on IDEAS

    1. Chong, Terence Tai-Leung, 2001. "Structural Change In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 17(01), pages 87-155, February.
    2. 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.
    3. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    4. 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.
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    Cited by:

    1. 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.

    More about this item


    Structural change; Break date; Persistence; Unit root; Autoregressive model;

    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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