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Testing for unit roots in the presence of uncertainty over both the trend and initial condition

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  • Harvey, David I.
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert

Abstract

In this paper we provide a joint treatment of two major problems that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, and uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. We suggest decision rules based on the union of rejections of four standard unit root tests (OLS and quasi-differenced demeaned and detrended ADF unit root tests), along with information regarding the magnitude of the trend and initial condition, to allow simultaneously for both trend and initial condition uncertainty.

Suggested Citation

  • Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
  • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:188-195
    DOI: 10.1016/j.jeconom.2012.01.018
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Milda Norkute, 2015. "Can the sectoral New Keynesian Phillips curve explain inflation dynamics in the Euro Area?," Empirical Economics, Springer, vol. 49(4), pages 1191-1216, December.
    3. 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.
    4. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 28(02), pages 422-456, April.
    5. 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.
    6. Anton Skrobotov, 2015. "Trend and Initial Condition in Stationarity Tests: The Asymptotic Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(2), pages 254-273, April.
    7. Smeekes Stephan, 2011. "Bootstrap Sequential Tests to Determine the Stationary Units in a Panel," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
    9. David I. Harvey & Stephen J. Leybourne & Emily J. Whitehouse, "undated". "Testing for a unit root against ESTAR stationarity," Discussion Papers 17/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    10. repec:spr:empeco:v:53:y:2017:i:2:d:10.1007_s00181-016-1123-3 is not listed on IDEAS
    11. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    12. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Stephan Smeekes, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 398-415, May.
    13. Jeremy Nguyen & Jen-je Su, 2015. "Combining linear and nonlinear unit root tests with an application to PPP," Economics Bulletin, AccessEcon, vol. 35(4), pages 2796-2801.
    14. Su, Jen-Je & Nguyen, Jeremy K., 2013. "Alternative unit root testing strategies using the Fourier approximation," Economics Letters, Elsevier, vol. 121(1), pages 8-11.

    More about this item

    Keywords

    Unit root test; Trend uncertainty; Initial condition uncertainty; Asymptotic power; Union of rejections decision rule;

    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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