COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES
用连接函数刻画高阶马尔可夫过程，给出了给定阶数的马尔可夫过程具有m相依、r独立或条件对称的充要条件，并研究了不同连接函数族在构建具有这些依赖性质的高阶马尔可夫过程中的适用性和局限性。
In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibit m -dependence, r -independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness with m -dependence or r -independence in time series.