Moving Aggregate Modified Autoregressive Copula‐Based Time Series Models (MAGMAR‐Copulas)

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 nonlinear 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.