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Unit root test in a threshold autoregression: asymptotic theory and residual-based block bootstrap

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  • Myung Hwan 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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File URL: http://eprints.lse.ac.uk/6836/
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Bibliographic Info

Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 6836.

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Length: 29 pages
Date of creation: Jan 2005
Date of revision:
Handle: RePEc:ehl:lserod:6836

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

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References

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  1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  2. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
  3. 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.
  4. 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.
  5. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics 381, Boston College Department of Economics.
  6. 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.
  7. Horvath, Michael T.K. & Watson, Mark W., 1995. "Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified," Econometric Theory, Cambridge University Press, vol. 11(05), pages 984-1014, October.
  8. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
  9. 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.
  10. Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
    • 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.
  11. 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.
  12. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  13. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  14. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  15. 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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Citations

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Cited by:
  1. Kim, Hyeongwoo & Moh, Young-Kyu, 2009. "A Century of Purchasing Power Parity Confirmed: The Role of Nonlinearity," MPRA Paper 17488, University Library of Munich, Germany.
  2. Myung Hwan Seo, 2007. "Estimation of Nonlinear Error CorrectionModels," STICERD - Econometrics Paper Series /2007/517, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.

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