World Conference Econometric Society, 2000, Seattle

Joon Y. Park, Seoul National University |

Bootstrap Unit Root Tests |

Session: C-9-16 Monday 14 August 2000 by Park, Joon Y. |

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. |

Submitted paper full-text in .pdf |

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