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Power Functions And Envelopes For Unit Root Tests

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  • Juhl, Ted
  • Xiao, Zhijie

Abstract

This paper studies power functions and envelopes for covariate augmented unit root tests. The power functions are calculated by integrating the characteristic function, allowing accurate evaluation of the power envelope and the power functions. Using the power functions, we study the selection among point optimal invariant unit root tests. An “optimal” point optimal test is proposed based on minimizing the integrated power difference. We find that when there are covariate effects, optimal tests use a local alternative where the power envelope has an approximate value of 0.75.We thank Pentti Saikkonen and two referees for helpful comments.

Suggested Citation

  • Juhl, Ted & Xiao, Zhijie, 2003. "Power Functions And Envelopes For Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(2), pages 240-253, April.
    • Handle: RePEc:cup:etheor:v:19:y:2003:i:02:p:240-253_19
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    Cited by:

    1. Sebastian Fossati, 2013. "Unit root testing with stationary covariates and a structural break in the trend function," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 368-384, May.
    2. Cláudia Duarte, 2015. "Covariate-augmented unit root tests with mixed-frequency data," Working Papers w201507, Banco de Portugal, Economics and Research Department.
    3. Patrick Marsh, "undated". "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
    4. Clayton Webb & Suzanna Linn & Matthew J. Lebo, 2020. "Beyond the Unit Root Question: Uncertainty and Inference," American Journal of Political Science, John Wiley & Sons, vol. 64(2), pages 275-292, April.
    5. Kaddour Hadri & Eiji Kurozumi & Daisuke Yamazaki, 2015. "Synergy between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests," Manchester School, University of Manchester, vol. 83(6), pages 676-700, December.
    6. Eiji Kurozumi & Daisuke Yamazaki & Kaddour Hadri, 2012. "Covariate Unit Root Test for Cross-Sectionally Dependent Panel Data," Global COE Hi-Stat Discussion Paper Series gd12-256, Institute of Economic Research, Hitotsubashi University.
    7. Nadarajah, Saralees & Chan, Stephen & Afuecheta, Emmanuel, 2013. "On the characteristic function for asymmetric Student t distributions," Economics Letters, Elsevier, vol. 121(2), pages 271-274.
    8. Gordon Anderson & Teng Wah Leo, 2014. "Ranking Alternative Non-Combinable Prospects: A Stochastic Dominance Based Route to the Second Best Solution," Working Papers tecipa-520, University of Toronto, Department of Economics.

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