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A Powerful Tuning Parameter Free Test Of The Autoregressive Unit Root Hypothesis

Author

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  • Morten Ø. Nielsen

    (Queen's University and CREATES)

Abstract

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing Breitung's (2002) test as the special case d = 1. It is shown that (i) each member of the family with d > 0 is consistent, (ii) the asymptotic distribution depends on d, and thus reflects the parameter chosen to implement the test, and (iii) since the asymptotic distribution depends on d and the test remains consistent for all d > 0, it is possible to analyze the power of the test for different values of d. The usual Phillips-Perron or Dickey-Fuller type tests are characterized by tuning parameters (bandwidth, lag length, etc.), i.e. parameters which change the test statistic but are not reflected in the asymptotic distribution, and thus have none of these three properties.It is shown that members of the family with d

Suggested Citation

  • Morten Ø. Nielsen, 2008. "A Powerful Tuning Parameter Free Test Of The Autoregressive Unit Root Hypothesis," Working Paper 1175, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1175
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1175.pdf
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    References listed on IDEAS

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    Cited by:

    1. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    2. Dechert, Andreas, 2014. "Fraktionale Kointegrationsbeziehungen zwischen Euribor-Zinssätzen," W.E.P. - Würzburg Economic Papers 93, University of Würzburg, Department of Economics.
    3. Nielsen, Morten Ørregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1515-1544, December.
    4. Morten Ø. Nielsen, 2008. "A Powerful Tuning Parameter Free Test Of The Autoregressive Unit Root Hypothesis," Working Paper 1175, Economics Department, Queen's University.
    5. Dechert, Andreas, 2012. "Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks," MPRA Paper 41044, University Library of Munich, Germany.

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    More about this item

    Keywords

    augmented Dickey-Fuller test; fractional integration; GLS detrending; nonparametric; nuisance parameter; tuning parameter; power envelope; unit root test; variance ratio;
    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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