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

2026-04-01

AI Summary

This study addresses the challenge of modeling long-range dependence in non-Gaussian, non-Markovian stationary time series by proposing a Copula-based time series model that integrates higher-order Markov and q-dependent structures. The approach leverages Copula functions to capture finite-dimensional temporal dependencies and establishes a rigorous framework for the model’s distributional properties and maximum likelihood estimation. Theoretical analysis reveals intrinsic connections between the proposed model and classical Gaussian ARMA and GARCH(1,1) processes. Empirical evaluations on probabilistic forecasting tasks—namely U.S. household inflation and German wind power generation—demonstrate that the model significantly outperforms conventional methods, highlighting its superior capacity to fit and predict complex dependence structures.

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.

Problem

• copula
• non-Gaussian
• non-Markovian
• stationary time series
• temporal dependence

Innovation

• copula-based time series
• non-Gaussian processes
• non-Markovian modeling
• MAG(1) process
• probabilistic forecasting