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Testing for unit roots in the presence of a possible break in trend and non-stationary volatility

Author

Listed:
  • Giuseppe Cavaliere
  • David I. Harvey
  • Stephen J. Leybourne
  • A. M. Robert Taylor

Abstract

In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2009) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T^-1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T^-1/2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of a one-time change in volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models.

Suggested Citation

  • Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2009. "Testing for unit roots in the presence of a possible break in trend and non-stationary volatility," Discussion Papers 09/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:09/05
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.
    2. Anton Skrobotov, 2013. "Local Structural Trend Break in Stationarity Testing," Working Papers 0074, Gaidar Institute for Economic Policy, revised 2013.
    3. repec:eee:ecmode:v:66:y:2017:i:c:p:81-100 is not listed on IDEAS
    4. Skrobotov Anton, 2018. "On Trend Breaks and Initial Condition in Unit Root Testing," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-15, January.
    5. Francesca Iorio & Stefano Fachin, 2014. "Savings and investments in the OECD: a panel cointegration study with a new bootstrap test," Empirical Economics, Springer, vol. 46(4), pages 1271-1300, June.
    6. Pershin, Vitaly & Molero, Juan Carlos & de Gracia, Fernando Perez, 2016. "Exploring the oil prices and exchange rates nexus in some African economies," Journal of Policy Modeling, Elsevier, vol. 38(1), pages 166-180.
    7. Skrobotov, Anton, 2015. "On Trend, Breaks and Initial Condition in Unit Root Testing," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.
    8. Sebastian Fossati, 2013. "Unit root testing with stationary covariates and a structural break in the trend function," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 368-384, May.
    9. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
    10. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    11. Apergis, Nicholas & Bowden, Nicholas & Payne, James E., 2015. "Downstream integration of natural gas prices across U.S. states: Evidence from deregulation regime shifts," Energy Economics, Elsevier, vol. 49(C), pages 82-92.
    12. Mohitosh Kejriwal & Claude Lopez, 2013. "Unit Roots, Level Shifts, and Trend Breaks in Per Capita Output: A Robust Evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 892-927, November.
    13. Harris, David & Leybourne, Stephen J. & Taylor, A.M. Robert, 2016. "Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point," Journal of Econometrics, Elsevier, vol. 192(2), pages 451-467.
    14. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2007. "Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]," Discussion Papers 06/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    15. Sun, Jingwei & Shi, Wendong, 2015. "Breaks, trends, and unit roots in spot prices for crude oil and petroleum products," Energy Economics, Elsevier, vol. 50(C), pages 169-177.
    16. Paulo M. M. Rodrigues, 2013. "Recursive adjustment, unit root tests and structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 62-82, January.
    17. Terence Mills, 2013. "Breaks and unit roots in global and hemispheric temperatures: an updated analysis," Climatic Change, Springer, vol. 118(3), pages 745-755, June.
    18. Neil Kellard & Denise Osborn & Jerry Coakley & Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2015. "Testing for Unit Roots Under Multiple Possible Trend Breaks and Non-Stationary Volatility Using Bootstrap Minimum Dickey–Fuller Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 603-629, September.

    More about this item

    Keywords

    Unit root tests; quasi difference de-trending; trend break; non-stationary volatility; wild bootstrap;

    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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