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

Other versions of this item:

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

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References listed on IDEAS
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  1. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
    Other versions:
  2. 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:
  3. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
  4. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  5. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November. [Downloadable!] (restricted)
    Other versions:
  6. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, May. [Downloadable!]
  7. 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:
  8. 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.
  9. 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)
  10. 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!]
  11. 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)
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