Parameters estimation for GARCH (p,q) model: QL and AQL approaches

In this paper, estimation for the generalized autoregressive conditional heteroscedasticity (GARCH) model is conducted. The Quasi likelihood (QL) and Asymptotic Quasi-likelihood (AQL) estimation methods are suggested in this paper. The QL approach relaxes the distributional assumptions of GARCH processes. The AQL technique obtains out the QL method when the conditional variance of process is unknown. The AQL methodology, merging the kernel technique used for parameter estimation of the GARCH model. This AQL methodology enables a substitute technique for parameter estimation when the conditional variance of process is unknown. Application of the QL and AQL methods to weekly prices changes of crude oil modelled by GARCH model is considered.