Dynamic copula-based Markov chains at work: Theory, testing and performance in modeling daily stock returns

We generalize the score test for time-varying copula parameters proposed by [Abegaz & Naik-Nimbalkar, 2008] to a setting where more than one-parametric copulas can be tested for time variation in at least one parameter. In a next step we model the daily log returns of the Commerzbank stock using copula-based Markov chain models. We found evidence that compared to usual GARCH models the copula-based Markov chain models perform worse when daily stock returns are estimated. Thus we do not see any advantage of this model type when daily returns from financial data are modeled.