Copulas and Long Memory

Abstract

This paper focuses on the analysis of long-memory properties of copula-based time series. We show via simulations that there exist Clayton copula-based stationary Markov processes that exhibit long memory on the level of copulas. This long memory is captured by an extremely slow hyperbolic decay of copula-based dependence measures between lagged values of the processes. In contrast, Gaussian and Eyraud-Farlie-Gumbel-Mongenstern copulas always produce short-memory stationary Markov processes. Application of copula-based Markov processes to volatility modeling captures both nonlinear conditional time variation as well as long memory, thus providing an attractive generalization of GARCH models.

Keywords: long-memory processes, copulas, measures of dependence, autocorrelations, persistence, volatility, GARCH

JEL Classification: C22, C51