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A Simple Unit Root Test Consistent Against Any Stationary Alternative

Author

Listed:
  • Frederique Bec

    (THEMA, CY Cergy Paris Université et CREST)

  • Alain Guay

    (University of Quebec in Montreal)

Abstract

This paper proposes t−like unit root tests which are consistent against any stationary alternatives, nonlinear or noncausal ones included. It departs from existing tests in that it uses an unbounded grid set including all possible values taken by the series. In our setup, thanks to the very simple nonlinear stationary alternative specification and the particular choice of the thresholds set, the proposed unit root test contains the standard ADF test as a special case. This, in turn, yields a sufficient condition for consistency against any ergodic stationary alternative. From a Monte-Carlo study, it turns out that the power of our unbounded non adaptive tests, in their average and exponential versions, outperforms existing bounded tests, either adaptive or not. This is illustrated by an application to interest rate spread data.

Suggested Citation

  • Frederique Bec & Alain Guay, 2020. "A Simple Unit Root Test Consistent Against Any Stationary Alternative," Working Papers 20-20, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    • Handle: RePEc:bbh:wpaper:20-20
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    References listed on IDEAS

    as
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    2. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    3. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    4. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    5. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
    6. Lof Matthijs, 2013. "Noncausality and asset pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 211-220, April.
    7. Fries, Sébastien & Zakoian, Jean-Michel, 2019. "Mixed Causal-Noncausal Ar Processes And The Modelling Of Explosive Bubbles," Econometric Theory, Cambridge University Press, vol. 35(6), pages 1234-1270, December.
    8. Christian Gouriéroux & Jean-Michel Zakoïan, 2017. "Local explosion modelling by non-causal process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 737-756, June.
    9. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    11. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Unit root test; Threshold autoregressive model; Interest rate spread.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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