Unit root test in a threshold autoregression: asymptotic theory and residual-based block bootstrap
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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- 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.
- Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
- 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.
- Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
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