Skew-t Copula-Based Semiparametric Markov Chains

Without specifying the structure of a time series, we model the distribution of a multivariate Markov process in discrete time by the corresponding multivariate Markov family and the one-dimensional flows of marginal distributions. Such models tackle simultaneously temporal dependence and contemporaneous dependence between time series. A specific parametric form of stationary copula, namely skew-t copula, is assumed. Skew-t copulas are capable of modeling asymmetry, skewness, and heavy tails. An empirical study with unfiltered daily returns for three stock indices shows that the skew-t copula Markov model provides a better fit than the skew-Normal copula Markov or t-copula Markov model, and the skew-t copula model without Markov property.