Copula-based time series models can model univariate and stationary time series in a flexible way by decomposing the joint distribution of consecutive observations into a copula and the stationary distribution. Implicitly this approach assumes 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 conditional quantile function corresponding to a 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. We show that the stationary distribution implied by the model is not standard-uniform. Hence we propose an adjustment transformation that recovers the desired standard-uniformity. 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的时间序列模型通过将连续观测值的联合分布分解为Copula和平稳分布，能够灵活地对单变量平稳时间序列进行建模。这种方法隐式假设了有限的马尔可夫阶数，但实际时间序列可能不满足马尔可夫性质。我们通过在模型更新方程中引入移动聚合（MAG）部分来改进基于Copula的时间序列模型。MAG部分的函数形式由对应于Copula的条件分位数函数给出。详细讨论了由此产生的MAG修正自回归Copula时间序列模型（MAGMAR-Copula），并在D-vine框架下推导了其分布性质。我们证明该模型隐含的平稳分布并非标准均匀分布，因此提出一种调整变换以恢复期望的标准均匀性。该模型嵌套经典ARMA模型，可视为ARMA模型的非线性泛化。通过建模美国通货膨胀评估了模型性能，结果表明我们的模型在信息准则方面与基准模型具有竞争力。