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.