COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Post Office Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 897R

"Time Series Regression with Unit Root and Infinite Variance Errors"

Peter C.B. Phillips

August 1989

Chan and Tran give the limit theory for the least squares coefficient in a random walk with the iid errors that are in the domain of attraction of a stable law. This note discusses their results and provides generalizations to the case of I(q) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the semiparametric corrections suggested by the author for the finite variance case continue to work when the errors have infinite variance. The limit laws are expressed in terms of ratios of quadratic functionals of a stable process rather than Brownian motion. The correction terms that eliminate nuisance parameter dependencies are random in the limit and involve multiple stochastic integrals that may be written in terms of the quadratic variation of the limiting stable process.

JE Classification: 211

Keywords: Integrated process, unit roots, random walk, time series