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LEAST ABSOLUTE DEVIATION ESTIMATION FOR UNIT ROOT PROCESSES WITH GARCH ERRORS

Published online by Cambridge University Press:  01 October 2009

Guodong Li  and
Wai Keung Li
Guodong Li
Affiliation:
Nanyang Technological University and University of Hong Kong
Wai Keung Li*
Affiliation:
University of Hong Kong
*
*Address correspondence to Wai Keung Li, Department of Statistics and Actuarial Sciences, University of Hong Kong, Pokfulam Road, Hong Kong; e-mail: hrntlwk@hku.hk.
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Abstract

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distribution of the estimated unit root is shown to be a functional of a bivariate Brownian motion, and then two unit root tests are derived. The simulation results demonstrate that the tests outperform those based on the Gaussian quasi maximum likelihood estimators with heavy-tailed innovations and those based on the simple least absolute deviation estimators.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 5 , October 2009 , pp. 1208 - 1227
Copyright
Copyright © Cambridge University Press 2009

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