Copulas and long memory

Abstract

This paper focuses on the analysis of persistence propertiesof copula-based time series. We obtain theoretical results that demonstratethat Gaussian and Eyraud-Farlie-Gumbel-Morgenstern copulas always pro-duce short memory stationary Markov processes. We further show via sim-ulations that, in finite samples, stationary Markov processes, such as thosegenerated by Clayton copulas, may exhibit a spurious long memory-like be-havior on the level of copulas, as indicated by standard methods of inferenceand estimation for long memory time series. We also discuss applicationsof copula-based Markov processes to volatility modeling and the analysisof nonlinear dependence properties of returns in real financial markets thatprovide attractive generalizations of GARCH models. Among other conclu-sions, the results in the paper indicate non-robustness of the copula-levelanalogues of standard procedures for detecting long memory on the levelof copulas and emphasize the necessity of developing alternative inferencemethods.