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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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    2. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    3. 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.
    4. Smeekes, S., 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).
    5. Xu, Deyi & Sheraz, Muhammad & Hassan, Arshad & Sinha, Avik & Ullah, Saif, 2022. "Financial development, renewable energy and CO2 emission in G7 countries: New evidence from non-linear and asymmetric analysis," Energy Economics, Elsevier, vol. 109(C).
    6. Harvey David I. & Leybourne Stephen J. & Whitehouse Emily J., 2018. "Testing for a unit root against ESTAR stationarity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-29, February.
    7. 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(2), pages 422-456, April.
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    9. 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.
    10. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    11. Saeid Mahdavi & Joakim Westerlund, 2017. "Are state–local government expenditures converging? New evidence based on sequential unit root tests," Empirical Economics, Springer, vol. 53(2), pages 373-403, September.
    12. 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.
    13. Andre M. Marques & Gilberto Tadeu Lima, 2021. "Testing for Granger Causality in Quantiles Between the Wage Share and Capacity Utilization," Working Papers, Department of Economics 2021_03, University of São Paulo (FEA-USP).
    14. Ghoshray, Atanu, 2022. "Trends and persistence of farm-gate coffee prices around the world," 96th Annual Conference, April 4-6, 2022, K U Leuven, Belgium 321166, Agricultural Economics Society - AES.
    15. 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.
    16. 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.
    17. Skrobotov, Anton (Скроботов, Антон), 2015. "About Trend, the Shift and the Initial Value in Testing of the Hypothesis of a Unit Root [О Тренде, Сдвиге И Начальном Значении В Тестировании Гипотезы О Наличии Единичного Корня]," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.
    18. Marques, André M. & Lima, Gilberto Tadeu, 2022. "Testing for Granger causality in quantiles between the wage share in income and productive capacity utilization," Structural Change and Economic Dynamics, Elsevier, vol. 62(C), pages 290-312.
    19. 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.
    20. 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.
    21. 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.

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    More about this item

    Keywords

    Unit root test; Trend uncertainty; Initial condition uncertainty; Asymptotic power; Union of rejections decision rule;
    All these keywords.

    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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