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On testing for unit roots and the initial observation

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Listed:
  • David I. Harvey
  • Stephen J. Leybourne

Abstract

Recent work has highlighted the crucial dependence of the power of existing unit root tests on the deviation of the initial observation from the deterministic component of the series. In practical applications, it is useful to have a test available with power more robust to the initial condition. In this paper, we propose such a procedure based on a data-dependent weighted average of the standard Dickey--Fuller and Elliott--Rothenberg--Stock tests. Simulation of the new test's power reveals very good performance across different magnitudes of the initial condition, and the procedure's value is further highlighted by application to U.S. producer price inflation. Copyright 2005 Royal Economic Society

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne, 2005. "On testing for unit roots and the initial observation," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 97-111, March.
    • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:1:p:97-111
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    Citations

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    Cited by:

    1. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2010. "The impact of the initial condition on robust tests for a linear trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 292-302, July.
    2. Meng, Ming & Lee, Hyejin & Cho, Myeong Hyeon & Lee, Junsoo, 2013. "Impacts of the initial observation on unit root tests using recursive demeaning and detrending procedures," Economics Letters, Elsevier, vol. 120(2), pages 195-199.
    3. Sven Otto, 2020. "Unit Root Testing with Slowly Varying Trends," Papers 2003.04066, arXiv.org, revised Aug 2020.
    4. 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(3), pages 587-636, June.
    5. Kerry Patterson & Michael A. Thornton, 2013. "A review of econometric concepts and methods for empirical macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 2, pages 4-42, Edward Elgar Publishing.
    6. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Sakkas, Nikolaos D., 2010. "Local Asymptotic Power Of The Im-Pesaran-Shin Panel Unit Root Test And The Impact Of Initial Observations," Econometric Theory, Cambridge University Press, vol. 26(1), pages 311-324, February.
    7. 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.
    8. Sven Otto, 2021. "Unit root testing with slowly varying trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 85-106, January.
    9. Karavias, Yiannis & Tzavalis, Elias, 2013. "The Power Performance of Fixed-T Panel Unit Root Tests allowing for Structural Breaks," MPRA Paper 46012, University Library of Munich, Germany.
    10. Niklas Ahlgren & Mikael Juselius, 2012. "Tests for cointegration rank and the initial condition," Empirical Economics, Springer, vol. 42(3), pages 667-691, June.
    11. 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.
    12. 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.
    13. Kajal Lahiri & Zhongwen Liang & Huaming Peng, 2017. "The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends," CESifo Working Paper Series 6313, CESifo.
    14. Yiannis Karavias & Elias Tzavalis, 2017. "Local power of panel unit root tests allowing for structural breaks," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1123-1156, November.
    15. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    16. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    17. Yaya, OlaOluwa Simon & Gil-Alana, Luis Alberiko & Carcel, Hector, 2015. "Testing fractional persistence and non-linearities in the natural gas market: An application of non-linear deterministic terms based on Chebyshev polynomials in time," Energy Economics, Elsevier, vol. 52(PA), pages 240-245.
    18. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    19. Anton Skrobotov, 2013. "Double Unit Roots Testing, GLS-detrending and Uncertainty over the Initial Conditions," Working Papers 0083, Gaidar Institute for Economic Policy, revised 2013.
    20. David I. Harvey & Stephen J. Leybourne & Nikolaos D. Sakkas, 2008. "Panel root tests and the impact of initial observations," Discussion Papers 06/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    21. 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.
    22. Aristidou Chrystalleni & Harvey David I. & Leybourne Stephen J., 2017. "The Impact of the Initial Condition on Covariate Augmented Unit Root Tests," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-23, January.

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