The Conditional C-Convolution Model and the Three Stage Quasi Maximum Likelihood Estimator

In this paper, we present the asymptotic results of the quasi maximum likelihood estimator of the parameters of a C-convolution model based on the conditional copula (Patton [11]). The C-convolution operator determines the distribution of the sum of two dependent random variables with the dependence structure given by a copula function. We focus in particular on the case where the vector of parameters may be partitioned into elements relating only to the marginals and elements relating to the copula. We propose a three-stage quasi maximum likelihood estimator (3SQMLE) and we provide conditions under which the estimator is asymptotically normal. We examine the small sample properties via Monte Carlo simulation. Finally, we propose an empirical application to explain how our model works.