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Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis

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  • Michael Jansson

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract
This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinitedimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.

Suggested Citation

  • Michael Jansson, 2007. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," CREATES Research Papers 2007-12, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2007-12
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jansson Michael & Nielsen Morten Ørregaard, 2011. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-21, February.
    2. Werker, Bas J.M. & Zhou, Bo, 2022. "Semiparametric testing with highly persistent predictors," Journal of Econometrics, Elsevier, vol. 227(2), pages 347-370.
    3. Oliver Wichert & I. Gaia Becheri & Feike C. Drost & Ramon van den Akker, 2019. "Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing," Papers 1905.11184, arXiv.org.
    4. 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.
    5. Bo Zhou, 2023. "Semiparametrically Optimal Cointegration Test," Papers 2305.08880, arXiv.org.
    6. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, September.
    7. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
    8. repec:hal:journl:peer-00834424 is not listed on IDEAS
    9. Pierre Perron & Eduardo Zorita & Iliyan Georgiev & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2017. "Unit Root Tests and Heavy-Tailed Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 733-768, September.
    10. Becheri, I.G. & Drost, Feike C. & van den Akker, R., 2013. "Asymptotically UMP Panel Unit Root Tests," Discussion Paper 2013-017, Tilburg University, Center for Economic Research.
    11. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Other publications TiSEM bc68a2f2-3ca3-443c-b3ac-f, Tilburg University, School of Economics and Management.
    12. Dong Jin Lee, 2016. "Parametric and Semi-Parametric Efficient Tests for Parameter Instability," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 451-475, July.
    13. Becheri, I.G. & Drost, Feike C. & van den Akker, R., 2013. "Asymptotically UMP Panel Unit Root Tests," Other publications TiSEM e34b7d23-8e53-4cea-ba69-5, Tilburg University, School of Economics and Management.
    14. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2011. "A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)," Other publications TiSEM 004c9726-ec6a-4884-8238-d, Tilburg University, School of Economics and Management.
    15. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "Hypothesis Testing in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 75-104, September.
    16. Adam Lee, 2024. "Locally Regular and Efficient Tests in Non-Regular Semiparametric Models," Papers 2403.05999, arXiv.org.
    17. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    18. Zhang, Rongmao & Chan, Ngai Hang, 2018. "Portmanteau-type tests for unit-root and cointegration," Journal of Econometrics, Elsevier, vol. 207(2), pages 307-324.
    19. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.
    20. 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.
    21. Bas Werker & Bo Zhou, 2020. "Semiparametric Testing with Highly Persistent Predictors," Papers 2009.08291, arXiv.org.
    22. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    23. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
    24. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2021. "Local Projection Inference Is Simpler and More Robust Than You Think," Econometrica, Econometric Society, vol. 89(4), pages 1789-1823, July.
    25. Werker, Bas J.M. & Zhou, B., 2022. "Semiparametric testing with highly persistent predictors," Other publications TiSEM 2974ce9c-97c1-44cd-9331-0, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    Unit root testing; semiparametric efficiency;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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