This paper proposes a method for estimation of a class of copula-based semiparametric stationary Markov vector time series models, namely, the two-stage semiparametric pseudo
maximum likelihood estimation (2SSPPMLE). These Markov vector time series models are characterized
by nonparametric marginal distributions and parametric copula functions of temporal
and contemporaneous dependence, while the copulas capture two classes of dependence relationships
of Markov time series. We provide simple estimators of marginal distribution and two
classes of copulas parameters and establish their asymptotic properties following conclusions in
Chen and Fan (2006) and some easily verifiable conditions. Moreover, we obtain the estimation of
conditional moment and conditional quantile functions for the bivariate Markov time series model.