COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 782R "Towards a Unified Asymptotic Theory for Autoregression" Peter C.B. Phillips February 1986 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. |
