Time Series Regression with a Unit Root and Infinite Variance Errors

Peter Phillips

No 897R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Integrated process; unit roots; random walk; time series (search for similar items in EconPapers)
Pages: 27 pages
Date: 1989, Revised 1989-08
Note: CFP 755.
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Published in Econometric Theory (1990), 6: 44-62

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Journal Article: Time Series Regression With a Unit Root and Infinite-Variance Errors (1990)
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