Copula-Based Time Series for Non-Gaussian and Non-Markovian Stationary Processes

Sven Pappert; Harry Joe

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arXiv · 2604.01500

Copula-Based Time Series for Non-Gaussian and Non-Markovian Stationary Processes

Sven Pappert·Harry Joe

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Abstract

In the copula-based approach to univariate time series modeling, the finite dimensional temporal dependence of a stationary time series is captured by a copula. Recent studies investigate how copula-based time series models can be generalized to have long-term autoregressive effects. We study a generalization that comes from a Markov sequence of order p and a q-dependent sequence. We derive the relation of the model to Gaussian-ARMA models and to the Gaussian-GARCH(1,1) model. We investigate distributional properties of the process and discuss the maximum likelihood estimation (MLE). Additionally we analyze the copula moving aggregate process of order one, or MAG(1), as it is a basic building block. Last we test the model in probabilistic forecasting studies on US inflation and German wind energy production.

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Sven Pappert, Harry Joe. 2026-04-02. Copula-Based Time Series for Non-Gaussian and Non-Markovian Stationary Processes. https://arxiv.org/abs/2604.01500

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