Abstract

http://ssrn.com/abstract=1540363
 
 

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Quasi Maximum Likelihood Estimation of GARCH Models with Heavy-Tailed Likelihoods


Jianqing Fan


Princeton University - Bendheim Center for Finance

Lei Qi


Princeton University - Bendheim Center for Finance

Dacheng Xiu


University of Chicago - Booth School of Business

July 2012


Abstract:     
The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing the heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter that is critical to the identification, and propose a two-step quasi maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach is consistent and asymptotically normal under weak moment conditions. Moreover, it achieves better efficiency than the Gaussian alternative, particularly when the innovation error has heavy tails. We also summarize and compare the values of the scale parameter and the asymptotic efficiency for estimators based on different choices of likelihood functions with an increasing level of heaviness in the innovation tails. Numerical studies confirm the advantages of the proposed approach.

Number of Pages in PDF File: 36

Keywords: quasi-likelihood, two-step estimator, heavy-tailed error

JEL Classification: C13, C22

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Date posted: January 24, 2010 ; Last revised: August 6, 2012

Suggested Citation

Fan, Jianqing and Qi, Lei and Xiu, Dacheng, Quasi Maximum Likelihood Estimation of GARCH Models with Heavy-Tailed Likelihoods (July 2012). Available at SSRN: http://ssrn.com/abstract=1540363 or http://dx.doi.org/10.2139/ssrn.1540363

Contact Information

Jianqing Fan
Princeton University - Bendheim Center for Finance ( email )
26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)
HOME PAGE: http://orfe.princeton.edu/~jqfan/
Lei Qi (Contact Author)
Princeton University - Bendheim Center for Finance ( email )
26 Prospect Avenue
Princeton, NJ 08540
United States
Dacheng Xiu
University of Chicago - Booth School of Business ( email )
5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
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