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.

翻译：本文研究多元循环时间序列的建模问题。通过引入循环圆环（即圆分布对应的联结函数）来描述横截面与序列相关性。为简化相依结构表达式，我们将多元循环圆环密度分解为若干配对循环圆环密度的乘积，并进一步通过严格平稳多阶马尔可夫过程降低配对循环圆环密度数量。最后结合实际数据分析，将所提模型应用于多元时间序列风向数据的拟合。