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Bootstrap Unit Root Tests

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  • Joon Y. Park

    (Seoul National University)

Abstract

We consider the bootstrap unit root tests based on autoregressive integrated models, 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 usual nonparametric 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 simulation, we investigate how effective is the bootstrap correction in small samples.

Suggested Citation

  • Joon Y. Park, 2000. "Bootstrap Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 1587, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1587
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    References listed on IDEAS

    as
    1. 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, July.
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    7. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
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