Pseudo maximum likelihood estimation of the univariate GARCH (2, 2) and asymptotic normality under dependent innovations. Issue 23 (2nd December 2017)

• Record Type: Journal Article
• Authors: Kouassi, Eugene; Soh Takam, Patrice; Brou, Jean Marcelin Bosson; Ndoumbe, Emile Herve
• Is Part Of: Communications in statistics. Volume 46:Issue 23(2017)
• Page Start: 11558
• Page End: 11574
• Publication Date: 2017-12-02
• Subjects: Asymptotic normality -- Pseudo-maximum likelihood estimator -- Quadratic exponential family -- Univariate GARCH (2, 2) model.; 60G; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1275694
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, we first consider the pseudo maximum likelihood estimation of the univariate GARCH (2, 2) model and derive the underlying estimator. Then, we make use of the technique of martingales to establish the asymptotic normality of the pseudo-maximum likelihood estimator (PMLE) of the univariate GARCH (2, 2) model. Contrary to previous approaches encountered in the statistical literature, the pseudo-likelihood function uses the general form of the density laws of the quadratic exponential family.