Vine Copula Specifications for Stationary Multivariate Markov Chains

type="main" xml:id="jtsa12103-abs-0001">Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this article, we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher-order Markov chains. We propose a new vine structure, the M-vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M-vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae.