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

TL;DR

This paper introduces a copula-based framework for modeling non-Gaussian, non-Markovian stationary time series, extending existing models to include long-term dependencies and applying it to economic and energy data.

Contribution

It generalizes copula-based time series models to incorporate Markov and q-dependent structures, relating them to Gaussian ARMA and GARCH models, and demonstrates their application in forecasting.

Findings

Model captures long-term dependencies in non-Gaussian time series.

The approach relates to Gaussian ARMA and GARCH models.

Forecasting performance on US inflation and wind energy data is evaluated.

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.