Copula-based time series models implicitly assume a finite Markov order. In reality a time series may not follow the Markov property. We modify the copula-based time series models by introducing a moving aggregate (MAG) part into the model updating equation. The functional form of the MAG-part is given as the inverse of a conditional copula. The resulting MAG-modified Autoregressive Copula-Based Time Series model (MAGMAR-Copula) is discussed in detail and distributional properties are derived in a D-vine framework. The model nests the classical ARMA model and can be interpreted as a non-linear generalization of the ARMA-model. The modeling performance is evaluated by modeling US inflation. Our model is competitive with benchmark models in terms of information criteria.

翻译：基于Copula的时间序列模型隐含地假设了有限的马尔可夫阶数。现实中，时间序列可能并不遵循马尔可夫性质。我们通过将移动聚合（MAG）部分引入模型更新方程，对基于Copula的时间序列模型进行了修正。MAG部分的函数形式由条件Copula的逆函数给出。由此得到的MAG修正自回归Copula时间序列模型（MAGMAR-Copula）在D-vine框架下进行了详细讨论，并推导了其分布性质。该模型嵌套了经典的ARMA模型，可解释为ARMA模型的非线性推广。通过建模美国通货膨胀数据评估了模型的建模性能。在信息准则方面，我们的模型与基准模型相比具有竞争力。