The hierarchical-likelihood approach to autoregressive stochastic volatility models

Many volatility models used in financial research belong to a class of hierarchical generalized linear models with random effects in the dispersion. Therefore, the hierarchical-likelihood (h-likelihood) approach can be used. However, the dimension of the Hessian matrix is often large, so techniques of sparse matrix computation are useful to speed up the procedure of computing the inverse matrix. Using numerical studies we show that the h-likelihood approach gives better long-term prediction for volatility than the existing MCMC method, while the MCMC method gives better short-term prediction. We show that the h-likelihood approach gives comparable estimations of fixed parameters to those of existing methods.