Towards a Unified Asymptotic Theory for Autoregression

Peter Phillips

No 782R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the unit root case appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion process. The theory has applications to continuous time estimation and to the analysis of the asymptotic power of tests for a unit root under a sequence of local alternatives.

Keywords: Autoregression; Brownian motion; diffusion; near-integrated process; noncentrality parameters; unit root (search for similar items in EconPapers)
Pages: 13 pages
Date: 1986-02, Revised 1986-08
Note: CFP 685.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Biometrika (1987), 74: 535-547

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