Towards a unified asymptotic theory for autoregression

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 alterna...

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Bibliographic Details
Published in:Biometrika 1987-09, Vol.74 (3), p.535-547
Main Author: Phillips, P. C. B.
Format: Article
Language:English
Subjects:
Asymptotic theory
Autoregression
Autoregressive moving average
Brownian motion
Diffusion
Diffusion theory
Estimators
Exact sciences and technology
Explosives
Generating function
Inference from stochastic processes
time series analysis
Mathematical moments
Mathematics
Near-integrated process
Noncentrality parameter
Probability and statistics
Sciences and techniques of general use
Statistical theories
Statistics
Time series
Unit root
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Summary: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 possibilities 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/74.3.535