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.
- maximum likelihood estimation
- iterative algorithm
- foreign exchange rates
- data analysis
Ip, W., Wong, H., Pan, J., & Li, D. F. (2006). The asymptotic convexity of the negative likelihood function of GARCH models. Computational Statistics and Data Analysis, 50(2), 311-331. https://doi.org/10.1016/j.csda.2004.08.012