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Econometrics Paper
Unit Root Test in a Threshold Autoregression: Asymptotic Theory and Residual-based Block Bootstrap
Myunghwan Seo
January 2005
Paper No' EM/2005/484:
Full Paper (pdf)

JEL Classification: C12; C15; C22

Tags: threshold autoregression; unit root test; threshold cointegration; 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.