Multi-modality in the Likelihood Function of GARCH Model

It is shown empirically that likelihood function of the GARCH is multi-modal. Hence, the maximum likelihood estimates at local and global maxima will be quantitatively different. Therefore, it is important to start an estimation method with consistent starting value that converge to global maxima. This study compares two estimation methods, BFGS and DE, on the basis of simulation and surface constructed by changing the value of GARCH [Formula: see text] model. DE is superior and consistent throughout the surface, and across distributions. PSX is used as real-world application and it has been found that the estimates obtained from DE are best and unbiased.