Summary: Rank-Based Estimation for GARCH Processes
November 16, 2010
We consider a rank-based technique for estimating 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 L.A. Jaeckel
[Estimating regression coefficients by minimizing the dispersion of the residuals, Ann. Math.
Statist. 43 (1972) 14491458]. They are useful for GARCH order selection and preliminary
estimation. The limiting distribution for the rank estimators is given and used to show that
they 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.
The author is very grateful to co-editor Pentti Saikkonen and two anonymous referees for their helpful comments.
This work was supported in part by NSF Grant DMS0806104. Address correspondence to Beth Andrews, Department
of Statistics, Northwestern University, Evanston, Illinois 60208, USA; e-mail: firstname.lastname@example.org.
Rank Estimation for GARCH Processes 1