Multivariate time series models for mixed data

We introduce a general approach which unifies some previous attempts for modeling the dynamic of multivariate time series or regression analysis when data are mixed type (binary/count/continuous). Our is quite flexible since conditionally on past values, each coordinate at t can have distribution compatible with standard univariate model such as GARCH, ARMA, INGARCH logistic models whereas values other coordinates play role exogenous covariates in dynamic. The simultaneous dependence be modeled copula. Additional also allowed first study usual stability properties these and then show that autoregressive parameters consistently estimated equation-by-equation using pseudo-maximum likelihood method, leading to fast implementation even number large. Moreover, we prove consistency results parametric copula fitted case Gaussian copulas, estimator correlation matrix strongly consistent. carefully check all our assumptions two prototypical examples: GARCH/INGARCH logistic/log-linear model. illustrated numerical experiments well real sets.