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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.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/484.

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Date of creation: Jan 2005
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Handle: RePEc:cep:stiecm:/2005/484

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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

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  1. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 533-576, September.
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  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 473-81, November.
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  8. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, 07.
  9. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
  10. Frédérique Bec & Alain Guay & Emmanuel Guerre, 2002. "Adaptive Consistent Unit Root Tests Based on Autoregressive Threshold Model," Working Papers 2002-46, Centre de Recherche en Economie et Statistique.
  11. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
  12. 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, 07.
  13. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
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  15. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
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Cited by:
  1. 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," Auburn Economics Working Paper Series auwp2012-02, Department of Economics, Auburn University.
  2. 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.
  3. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
  4. 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.
  5. Hwan Seo, Myung, 2011. "Estimation Of Nonlinear Error Correction Models," Econometric Theory, Cambridge University Press, vol. 27(02), pages 201-234, April.
  6. 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.
  7. 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.
  8. Peter Sephton & Janelle Mann, 2013. "Threshold Cointegration: Model Selection with an Application," Journal of Economics and Econometrics, Economics and Econometrics Research Institute (EERI), Brussels, vol. 56(2), pages 54-77.
  9. 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.

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