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

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.