Econometric analysis of the relationships among the financial markets

A two-step optimization method called inference functions for margins (IFM) is broadly adopted to estimate Copula-GARCH models. However, IFM is subject to small-sample bias. This paper proposes to estimate Copula-GARCH models by applying Maximization by Parts (MBP), a multi-step optimization algorithm. This method decomposes the complicated log likelihood into two parts. In the decomposition, the first part is an easy likelihood consisting of only marginal likelihoods. The second part includes dependence parameters from a multivariate likelihood and is used to update the estimates from the first part. The results indicate that MBP can provide more efficient estimation than IFM.