The asymptotic convexity of the negative likelihood function of GARCH models
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.
convexity garch convergence maximum likelihood estimation iterative algorithm foreign exchange rates