Numerical optimization of the likelihood function based on Kalman filter in the GARCH models
In this work, we propose a new estimate algorithm for the parameters of a $\mathrm{GARCH}(p,q)$ model. This algorithm turns out to be very reliable in estimating the true parameter’s values of a given model. It combines maximum likelihood method, Kalman filter algorithm and the simulated annealing (SA) method, without any assumptions about initial values. Simulation results demonstrate that the algorithm is liable and promising.