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The impact of the initial condition on covariate augmented unit root tests

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  • Chrystalleni Aristidou
  • David Harvey
  • Stephen Leybourne

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) and Elliott and Jansson (2003), 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

  • Chrystalleni Aristidou & David Harvey & Stephen Leybourne, 2016. "The impact of the initial condition on covariate augmented unit root tests," Discussion Papers 16/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:16/01
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    1. 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.
    2. 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.
    3. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July.
    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. 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.
    6. 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.
    7. 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.
    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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    1. 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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    More about this item

    Keywords

    Unit root tests; stationary covariates; initial condition uncertainty; asymptotic power.;
    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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