In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.