Limit theory for moderate deviations from a unit root

Phillips, Peter Charles Bonest and Magdalinos, Tassos (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics, 136 (1), 115-130. (doi:10.1016/j.jeconom.2005.08.002).

Record type: Article

Abstract

An asymptotic theory is given for autoregressive time series with a root of the form , which represents moderate deviations from unity when is a deterministic sequence increasing to infinity at a rate slower than n, so that as . For , the results provide a rate of convergence and asymptotic normality for the first order serial correlation, partially bridging the and n convergence rates for the stationary () and conventional local to unity () cases. For the serial correlation coefficient is shown to have a convergence rate and a Cauchy limit distribution without assuming Gaussian errors, so an invariance principle applies when . This result links moderate deviation asymptotics to earlier results on the explosive autoregression proved under Gaussian errors for , where the convergence rate of the serial correlation coefficient is and no invariance principle applies.

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