Asymptotics for stationary very nearly unit root processes

doi:10.1111/j.1467-9892.2007.00552.x

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Wiley InterScience

Journal of Time Series Analysis

Volume 29 Issue 1, Pages 203 - 212

Published Online: 7 Sep 2007

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Asymptotics for stationary very nearly unit root processes

Donald W. K. Andrews ¹ and Patrik Guggenberger ¹

¹ Cowles Foundation, Yale University and Department of Economics, University of California-Los Angeles

Correspondence to Patrik Guggenberger, Department of Economics, UCLA. Tel: (310) 825-0849; Fax: (310) 825-9528; E-mail: guggenbe@econ.ucla.edu

KEYWORDS

Asymptotic distribution • autoregressive model • stationary very nearly unit root process

ABSTRACT

Abstract. This article considers a mean zero stationary first-order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter ρ_n is very near to one in the sense that 1 − ρ_n = o(n⁻¹).

First Version received December 2006

DIGITAL OBJECT IDENTIFIER (DOI)

10.1111/j.1467-9892.2007.00552.x About DOI

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