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Unit Root Test In A Threshold Autoregression: Asymptotic Theory And Residual-Based Block Bootstrap

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  • Seo, Myung Hwan

Abstract

This paper develops a test of the unit root null hypothesis against a stationary threshold process. This testing problem is nonstandard and complicated because a parameter is unidentified and the process is nonstationary under the null hypothesis. We derive an asymptotic distribution for the test, which is not pivotal without simplifying assumptions. A residual-based block bootstrap is proposed to calculate the asymptotic p -values. The asymptotic validity of the bootstrap is established, and a set of Monte Carlo simulations demonstrates its finite-sample performance. In particular, the test exhibits considerable power gains over the augmented Dickey–Fuller (ADF) test, which neglects threshold effects.

Suggested Citation

  • Seo, Myung Hwan, 2008. "Unit Root Test In A Threshold Autoregression: Asymptotic Theory And Residual-Based Block Bootstrap," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1699-1716, December.
  • Handle: RePEc:cup:etheor:v:24:y:2008:i:06:p:1699-1716_08
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    References listed on IDEAS

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    1. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    2. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    3. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    4. Pippenger, Michael K & Goering, Gregory E, 1993. "A Note on the Empirical Power of Unit Root Tests under Threshold Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(4), pages 473-481, November.
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    Cited by:

    1. Sephton, Peter & Mann, Janelle, 2013. "Further evidence of an Environmental Kuznets Curve in Spain," Energy Economics, Elsevier, vol. 36(C), pages 177-181.
    2. Kim, Hyeongwoo & Moh, Young-Kyu, 2010. "A century of purchasing power parity confirmed: The role of nonlinearity," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1398-1405, November.
    3. Dilem Yildirim & Ralf Becker & Denise R Osborn, 2009. "Bootstrap Unit Root Tests for Nonlinear Threshold Models," The School of Economics Discussion Paper Series 0915, Economics, The University of Manchester.
    4. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    5. Kim, Bong-Han & Min, Hong-Ghi & Moh, Young-Kyu, 2010. "Nonlinear dynamics in exchange rate deviations from the monetary fundamentals: An empirical study," Economic Modelling, Elsevier, vol. 27(5), pages 1167-1177, September.
    6. Peter Sephton & Janelle Mann, 2013. "Threshold Cointegration: Model Selection with an Application," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(2), pages 54-77.
    7. Mann, Janelle & Sephton, Peter, 2016. "Global relationships across crude oil benchmarks," Journal of Commodity Markets, Elsevier, vol. 2(1), pages 1-5.
    8. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    9. Hyeongwoo Kim & Young-Kyu Moh, 2012. "The Yen Real Exchange Rate May Not be Stationary After All: New Evidence from Non-linear Unit-Root Tests," Economic Analysis (Quarterly), Economic Research Institute, Bank of Korea, vol. 18(4), pages 1-22, December.
    10. Peter Sephton & Janelle Mann, 2015. "Nonlinear attractors and asymmetries between non-life insurance premiums and financial markets," Empirical Economics, Springer, vol. 49(3), pages 783-799, November.
    11. Daiki Maki & Shin-ichi Kitasaka, 2015. "Residual-based tests for cointegration with three-regime TAR adjustment," Empirical Economics, Springer, vol. 48(3), pages 1013-1054, May.
    12. Thanabalasingam Vinayagathasan, 2013. "Monetary Policy and the Real Economy: A Structural VAR Approach for Sri Lanka," GRIPS Discussion Papers 13-13, National Graduate Institute for Policy Studies.
    13. Mann, Janelle M., 2013. "Is there a Global Relationship Across Crude Oil Benchmarks?," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150368, Agricultural and Applied Economics Association.
    14. Peter Sephton & Janelle Mann, 2016. "Compelling Evidence of an Environmental Kuznets Curve in the United Kingdom," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(2), pages 301-315, June.
    15. repec:taf:jnlbes:v:35:y:2017:i:2:p:250-264 is not listed on IDEAS
    16. Laurent Callot & Mehmet Caner & Anders Bredahl Kock & Juan Andres Riquelme, 2017. "Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 250-264, April.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation 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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