Abstract
This paper focuses on the analysis of persistence properties of copula-based time series. We obtain theoretical results that demonstrate that Gaussian and Eyraud-Farlie-Gumbel-Morgenstern copulas always produce short memory stationary Markov processes. We further show via simulations that, in finite samples, stationary Markov processes, such as those generated by Clayton copulas, may exhibit a spurious long memory-like behavior on the level of copulas, as indicated by standard methods of inference and estimation for long memory time series. We also discuss applications of copula-based Markov processes to volatility modeling and the analysis of nonlinear dependence properties of returns in real financial markets that provide attractive generalizations of GARCH models. Among other conclusions, the results in the paper indicate non-robustness of the copula-level analogues of standard procedures for detecting long memory on the level of copulas and emphasize the necessity of developing alternative inference methods.
Highlights
Theory and applications of copulas and long range dependence are welldeveloped in economics, econometrics, statistics and probability
We provide an analysis of relations between different concepts of long memory, including those based on autocorrelations and copula functions
The theoretical results obtained in the paper demonstrate that Gaussian and Eyraud-FarlieGumbel-Morgenstern copulas always produce short memory stationary Markov processes
Summary
Dependence is one of the most fundamental concepts in econometrics, statistics and probability. In part, by empirical applications in economics and finance, many works provide examples of time series and stochastic processes that exhibit dependence and autocorrelation properties ranging from short to long memory (see, among others, Cont, 2001, and references therein). Stationary Markov processes are regarded as canonical examples of short memory processes. The value of such processes at a given time depends only on their value at the previous period. There are several definitions of long memory and persistence in a time series {Xt} available in the literature. These definitions differ in measures of dependence between the variables Xt and Xt+h they are based upon. The most commonly used notions of long memory employ the standard autocovariance or autocorrelation functions and take their slow decay to be the defining property of long memory processes (see, among others, Lo 1991, Baillie 1996, Hosking 1996, Doukhan, Oppenheim and Taqqu 2003 and Appendix A1 for a review of the commonly used definitions of long memory processes and their properties)
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