Time Series Regression with a Unit Root and Infinite Variance Errors
CFDP Revision Date
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.
Phillips, Peter C.B., "Time Series Regression with a Unit Root and Infinite Variance Errors" (1989). Cowles Foundation Discussion Papers. 1141.