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

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  • Nielsen, Morten Ørregaard

Abstract

This paper presents a family of simple nonparametric unit root tests indexed by one parameter, d, and containing the Breitung (2002, Journal of Econometrics 108, 342–363) test as the special case d = 1. It is shown that (a) each member of the family with d > 0 is consistent, (b) the asymptotic distribution depends on d and thus reflects the parameter chosen to implement the test, and (c) because 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 and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.It is shown that members of the family with d

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:06:p:1515-1544_99
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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. Burak Alparslan Eroğlu & Barış Soybilgen, 2018. "On the Performance of Wavelet Based Unit Root Tests," JRFM, MDPI, vol. 11(3), pages 1-22, August.
    3. In Choi, 2014. "Unit root tests for dependent and heterogeneous micropanels," Working Papers 1404, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    4. Eroğlu, Burak Alparslan & Göğebakan, Kemal Çağlar & Trokić, Mirza, 2018. "Powerful nonparametric seasonal unit root tests," Economics Letters, Elsevier, vol. 167(C), pages 75-80.
    5. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    6. 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.
    7. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    8. Karsten Reichold, 2022. "A Residuals-Based Nonparametric Variance Ratio Test for Cointegration," Papers 2211.06288, arXiv.org, revised Dec 2022.
    9. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    10. Karsten Reichold, 2024. "A residual‐based nonparametric variance ratio no‐cointegration test," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(5), pages 847-856, September.
    11. Eroğlu, Burak Alparslan, 2019. "Wavelet variance ratio cointegration test and wavestrapping," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 298-319.
    12. Hassler, Uwe & Hosseinkouchack, Mehdi, 2025. "Joint Hypothesis Testing from Heterogeneous Samples under Cross-dependence," Econometrics and Statistics, Elsevier, vol. 35(C), pages 41-54.
    13. Dechert, Andreas, 2014. "Fraktionale Kointegrationsbeziehungen zwischen Euribor-Zinssätzen," W.E.P. - Würzburg Economic Papers 93, University of Würzburg, Department of Economics.
    14. Nielsen, Morten Ørregaard & Seo, Won-Ki & Seong, Dakyung, 2023. "Inference On The Dimension Of The Nonstationary Subspace In Functional Time Series," Econometric Theory, Cambridge University Press, vol. 39(3), pages 443-480, June.
    15. Eroğlu, Burak Alparslan & Yiğit, Taner, 2016. "A nonparametric unit root test under nonstationary volatility," Economics Letters, Elsevier, vol. 140(C), pages 6-10.
    16. Nielsen, Morten, 2008. "A Powerful Tuning Parameter Free Test of the Autoregressive Unit Root Hypothesis," Working Papers 08-05, Cornell University, Center for Analytic Economics.
    17. Babatunde Sunday Eweade & Ada Chigozie Akadiri & Kehinde O. Olusoga & Ruth Oluyemi Bamidele, 2024. "The symbiotic effects of energy consumption, globalization, and combustible renewables and waste on ecological footprint in the United Kingdom," Natural Resources Forum, Blackwell Publishing, vol. 48(1), pages 274-291, February.
    18. Burak Eroglu, 2017. "Wavelet Variance Ratio Test And Wavestrapping For The Determination Of The Cointegration Rank," Working Papers 1706, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    19. Mehdi Hosseinkouchack & Uwe Hassler, 2016. "Powerful Unit Root Tests Free of Nuisance Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 533-554, July.
    20. In Choi, 2019. "Unit Root Tests for Dependent Micropanels," The Japanese Economic Review, Japanese Economic Association, vol. 70(2), pages 145-167, June.
    21. Burak Eroglu & Kemal Caglar Gogebakan & Mirza Trokic, 2017. "Fractional Seasonal Variance Ratio Unit Root Tests," Working Papers 1707, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    22. 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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    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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