Estimated Quasi-Likelihood Estimator on GARCH Models with Heavy-Tailed and Skewed Innovations and Its Applications

• Activity Number: 515
• Type: Contributed
• Date/Time: Wednesday, August 5, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Taewook Lee*+
• Companies: Hankuk University of Foreign Studies
• Keywords: Threshold GARCH model ; quasi maximum likelihood estimator ; estimated likelihood estimator ; consistency ; asymptotic normality ; Vale at Risk

Abstract

The generalized autoregressive conditional heteroscedastic (GARCH) model has gained a lot of popularity in the analysis of financial time series with high and changing volatility. In actual practice, it is conventional to use the Gaussian quasi-maximum likelihood for the parameter estimation in GARCH models. However, when the innovation terms have either heavy-tailed or skewed distributions, the quasi-maximum likelihood estimator (QMLE) does not function well. In order to remedy this defect, we extend their QMLE and propose the estimated quasi-likelihood estimator (QELE) to cope with the nuisance parameter, and demonstrate that the proposed QMLE and QELE are consistent and asymptotically normal. Finally, we provide the simulation results in order to illustrate our findings and apply our method to VaR (Value at Risk) estimation by using normal mixture density.