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RANK-BASED ESTIMATION FOR GARCH PROCESSES

Published online by Cambridge University Press:  27 April 2012

Beth Andrews
Beth Andrews*
Affiliation:
Northwestern University
*
*Address correspondence to Beth Andrews, Department of Statistics, Northwestern University, Evanston, IL 60208, USA; e-mail: [email protected].
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Abstract

We consider a rank-based technique for estimating generalized autoregressive conditionally heteroskedastic (GARCH) model parameters, some of which are scale transformations of conventional GARCH parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in Jaeckel (1972, Annals of Mathematical Statistics43, 1449–1458). They are useful for GARCH order selection and preliminary estimation. We give a limiting distribution for the rank estimators that holds when the true parameter vector is in the interior of its parameter space and when some GARCH parameters are zero. The limiting theory is used to show that the rank estimators are robust, can have the same asymptotic efficiency as maximum likelihood estimators, and are relatively efficient compared to traditional Gaussian and Laplace quasi-maximum likelihood estimators. The behavior of the estimators for finite samples is studied via simulation, and we use rank estimation to fit a GARCH model to exchange rate log-returns.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1037 - 1064
Copyright
Copyright © Cambridge University Press 2012

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