Bootstrap Unit Root Tests

Joon Park

Working Papers from Rice University, Department of Economics

Abstract: We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey-Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op(n-1/4) and Op(n-1/2), and involve functionals of Brownian motions and normal random variates. The asymptotic expansions for the bootstrap tests are also derived and compared with those of the Dickey-Fuller tests. We show in particular that the bootstrap offers asymptotic refinements for the Dickey-Fuller tests, i.e., it corrects their second-order errors. More precisely, it is shown that the critical values obtained by the bootstrap resampling are correct up to the second-order terms, and the errors in rejection probabilities are of order o(n-1/2) if the tests are based upon the bootstrap critical values. Through simulations, we investigate how effective is the bootstrap correction in small samples.

Date: 2002-10
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http://www.ruf.rice.edu/~econ/papers/2003papers/04Park.pdf

Related works:
Journal Article: Bootstrap Unit Root Tests (2003)
Working Paper: Bootstrap Unit Root Tests (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:ecl:riceco:2003-04

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