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

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Author Info
Myunghwan Seo

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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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Publisher Info
Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 494.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:494

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

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. 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. [Downloadable!]
    Other versions:
  3. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
  4. 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.
    Other versions:
  5. 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. [Downloadable!]
  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. [Downloadable!]
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  7. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05. [Downloadable!] (restricted)
  8. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Blackwell Publishing, vol. 24(4), pages 379-400, 07. [Downloadable!] (restricted)
  9. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
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  10. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  11. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November. [Downloadable!] (restricted)
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  12. 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.
  13. George Kapetanios & Yongcheol Shin, 2002. "Unit Root Tests in Three-Regime SETAR Models," Working Papers 465, Queen Mary, University of London, Department of Economics. [Downloadable!]
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Cited by:
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  1. 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. [Downloadable!]
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