Copula-Based Semiparametric Models for Multivariate Time Series

In this paper, we extend copula-based univariate time series models studied in Chen & Fan (2006) to multivariate time series. Doing so, we tackle at the same time serial dependence as well as interdependence between several time series. The proposed methodology is totally different from the usual time-varying copula modeling of time series in which only the dependence between the serially independent innovations is taken into account, time series have to be modeled, and residuals are used for inference. Here, no parametric modeling of time series is necessary, so there is no need of using residuals, which facilitates the statistical analysis. We discuss issues related to parameter estimation as well as tests of goodness-of-fit. We treat in greater detail two families, specifically the meta-elliptic copulas and Archimedean copulas. The methodology is then applied to model the dependence between the Canadian/US exchange rate and value of oil futures during the last ten years