 Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed LikelihoodsJianqing Fan, Lei Qi and Dacheng Xiu Journal of Business & Economic Statistics, 2014, vol. 32, issue 2, 178-191 Abstract: The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing 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 η f that is critical to the identification for consistency and propose a three-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. Date: 2014 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:32:y:2014:i:2:p:178-191 Ordering information: This journal article can be ordered from DOI: 10.1080/07350015.2013.840239 Access Statistics for this article Journal of Business & Economic Statistics is currently edited by Eric Sampson, Rong Chen and Shakeeb Khan More articles in Journal of Business & Economic Statistics from Taylor & Francis Journals |
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