The asymptotic convexity of the negative likelihood function of GARCH models

Authors:
W. C. Ip;Heung Wong;J. Z. Pan;D. F. Li
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong;LMAM and Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China;LMAM and Department of Probability and Statistics, School of Mathematical Sciences, Peking University, Beijing 100871, China
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH. A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign exchange rates is also given.