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Unit Root Test in a Threshold Autoregression: Asymptotic Theory and Residual-based Block Bootstrap

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  • Myunghwan Seo

Abstract

There is a growing literature on unit root testing in threshold autoregressive models. This paper makes two contributions to the literature. First, an asymptotic theory is developed for unit root testing in a threshold autoregression, in which the errors are allowed to be dependent and heterogeneous, and the lagged level of the dependent variable is employed as the threshold variable. The asymptotic distribution of the proposed Wald test is non-standard and depends on nuisance parameters. Second, the consistency of the proposed residual-based block bootstrap is established based on a newly developed asymptotic theory for this bootstrap. It is demonstrated by a set of Monte Carlo simulations that the Wald test exhibits considerable power gains over the ADF test that neglects threshold effects. The law of one price hypothesis is investigated among used car markets in the US

Suggested Citation

  • Myunghwan Seo, 2004. "Unit Root Test in a Threshold Autoregression: Asymptotic Theory and Residual-based Block Bootstrap," Econometric Society 2004 North American Summer Meetings 494, Econometric Society.
  • Handle: RePEc:ecm:nasm04:494
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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. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Schweikert, Karsten, 2018. "Testing for cointegration with threshold adjustment in the presence of structural breaks," Hohenheim Discussion Papers in Business, Economics and Social Sciences 07-2018, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    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

    Keywords

    threshold autoregression; unit root test; threshold cointegration; residual-based block bootstrap;

    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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