Efficient estimation of copula-GARCH models

An iterative (fixed-point) algorithm for the maximum-likelihood estimation of copula-based models that circumvents the need to compute second-order derivatives of the full likelihood function is adapted and examined. The algorithm exploits the structure of copula-based models that yield a natural decomposition of a potentially complicated likelihood function into two parts. The first part is a working likelihood that only involves the parameters of the marginals and the residual part is used to update estimates from the first part. A modified algorithm based on a working likelihood that accounts for some degree of correlation between the marginals is proposed. Compared to the original algorithm based on the working likelihood with the independent correlation, the modified one provides a better approximation to the full likelihood and overcomes convergence difficulties. A numerical example illustrates the efficiency gains of the estimation algorithms in the context of a benchmark copula-GARCH model. The modified algorithm is illustrated by an application to daily returns on two major stock market indices.