Pair circulas modelling for multivariate circular time series

Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence structure, we decompose a multivariate circula density to a product of several pair circula densities. Moreover, to reduce the number of pair circula densities, we consider strictly stationary multi-order Markov processes. The real data analysis, in which the proposed model is fitted to multivariate time series wind direction data is also given.