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GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

Published online by Cambridge University Press:  22 January 2008

Peter C.B. Phillips  and
Chirok Han
Peter C.B. Phillips*
Affiliation:
Cowles Foundation, Yale UniversityUniversity of York and University of Auckland
Chirok Han
Affiliation:
University of Auckland
*
Address correspondence to Peter Phillips, Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520-8281, USA; e-mail: peter.phillips@yale.edu.
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Abstract

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This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 971–1001). The approach also has useful extensions to dynamic panels.

Information

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 631 - 650
Copyright
Copyright © Cambridge University Press 2008

References

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