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The Impact of the Initial Condition on Covariate Augmented Unit Root Tests

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  • Aristidou Chrystalleni

    (School of Economics, University of Nottingham, Nottingham, United Kingdom of Great Britain and Northern Ireland)

  • Harvey David I.

    (School of Economics, University of Nottingham, Nottingham, United Kingdom of Great Britain and Northern Ireland)

  • Leybourne Stephen J.

    (School of Economics, University of Nottingham, Nottingham, United Kingdom of Great Britain and Northern Ireland)

Abstract

We examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.” Econometric Theory 11:1148–71) and Elliott and Jansson (2003, “Testing for Unit Roots with Stationary Covariates.” Journal of Econometrics 115:75–89), respectively, in situations where the magnitude of the initial condition of the time series under consideration may be non-negligible. We show that the asymptotic power of such tests is very sensitive to the initial condition; OLS- and GLS-based tests achieve relatively high power for large and small magnitudes of the initial condition, respectively. Combining information from both types of test via a simple union of rejections strategy is shown to effectively capture the higher power available across all initial condition magnitudes.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jtsmet:v:9:y:2017:i:1:p:23:n:3
    DOI: 10.1515/jtse-2015-0013
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    References listed on IDEAS

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    1. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    2. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July.
    3. 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.
    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    5. 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.
    6. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1148-1171, October.
    7. Joakim Westerlund, 2013. "A computationally convenient unit root test with covariates, conditional heteroskedasticity and efficient detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 477-495, July.
    8. 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.
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    2. 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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    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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