Numerical optimization of the likelihood function based on Kalman filter in the ARCH models

In this paper we elaborate an algorithm to estimate the parameters of a ARCH(p) model. This algorithm combines quasi-maximum likelihood method, the Kalman Filter, and the simulated annealing method, without any assumptions about initial values. In the aim to generalize the results found for ARCH(1) in the recent paper of Allal and Benmoumen (2014). Simulation results demonstrate that the algorithm is viable and promising.