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Biometrika 2005 92(2):477-484; doi:10.1093/biomet/92.2.477
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© 2005 Biometrika Trust

Miscellanea

Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors

Ngai Hang Chan1 and Liang Peng2

1 Department of Statistics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong nhchan{at}sta.cuhk.edu.hk, 2 School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, U.S.A.peng{at}math.gatech.edu

The weighted least absolute deviations estimator is studied for an AR(1) process with ARCH(1) errors {varepsilon}t. Unlike for the quasi maximum likelihood estimator, the estimator's, limiting distribution is shown to be normal even when E({varepsilon}t4) = {infty}. Furthermore, the estimator can be applied to examine the symmetry of the density of {varepsilon}t and to estimate the quantity E(log |{alpha} + {lambda}1/2 {varepsilon}t|), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators.

Key Words: Median; Symmetry; Weighted least absolute deviations estimator

Received November 2003. Revised October 2004.


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