Limit Theory for Moderate Deviations from a Unit Root

Peter Phillips and Tassos Magdalinos
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Tassos Magdalinos: University of York

No 1471, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: An asymptotic theory is given for autoregressive time series with a root of the form rho_{n} = 1+c/n^{alpha}, which represents moderate deviations from unity when alpha in (0,1). The limit theory is obtained using a combination of a functional law to a diffusion on D[0,infinity) and a central limit law to a scalar normal variate. For c 0, the serial correlation coefficient is shown to have a n^{alpha}rho_{n}^{n} convergence rate and a Cauchy limit distribution without assuming Gaussian errors, so an invariance principle applies when rho_{n} > 1. This result links moderate deviation asymptotics to earlier results on the explosive autoregression proved under Gaussian errors for alpha = 0, where the convergence rate of the serial correlation coefficient is (1 + c)^{n} and no invariance principle applies.

Keywords: Central limit theory; Diffusion, Explosive autoregression, Local to unity, Moderate deviations, Unit root distribution (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2004-07
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Journal Article: Limit theory for moderate deviations from a unit root (2007)
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