 Bootstrap Unit Root TestsEconometrica, 2003, vol. 71, issue 6, 1845-1895 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 O(p) (n-super- - 1/4) and O(p) (n-super- - 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-super- - 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. Copyright The Econometric Society 2003. Date: 2003 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ecm:emetrp:v:71:y:2003:i:6:p:1845-1895 Ordering information: This journal article can be ordered from Access Statistics for this article Econometrica is currently edited by Guido Imbens More articles in Econometrica from Econometric Society Contact information at EDIRC. |
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