The Nonparametric Maximum Likelihood Estimation for Gaussian Mixture Innovations of GARCH Model

• Activity Number: 459
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Taewook Lee and Byungtae Seo*+
• Companies: Hankuk University of Foreign Studies and Texas Tech University
• Keywords: GARCH model ; Gaussian mixture ; NPMLE ; Quasi-maximum likelihood estimator ; Mixing distribution

Abstract

We study a new estimation method for Gaussian mixture innovations of GARCH model. Based on the residuals obtained from the quasi-maximum likelihood estimator (QMLE) of GARCH parameters, a mixing distribution of Gaussian mixture innovations is estimated by using the non-parametric maximum likelihood estimator (NPMLE). A recently developed algorithm for computing NPMLE proposed by Wang (2007) is adopted, as it is known to be fast and stable, compared with several other algorithms. Unlike Ausin and Galeano (2007) and Lee and Lee (2009), our estimation procedure does not assume that the number of Gaussian mixture components is finite and known. Instead we approximate the error distribution with nonparametric normal mixtures. A simulation result and a real data analysis are provided for illustration.