Probability Surveys

Copulas and long memory

Rustam Ibragimov and George Lentzas

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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.

Article information

Source
Probab. Surveys, Volume 14 (2017), 289-327.

Dates
Received: March 2014
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ps/1513069215

Digital Object Identifier
doi:10.1214/14-PS233

Mathematical Reviews number (MathSciNet)
MR3735284

Zentralblatt MATH identifier
06825001

Keywords
Long memory processes short memory processes copulas measures of dependence autocorrelations persistence volatility GARCH

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ibragimov, Rustam; Lentzas, George. Copulas and long memory. Probab. Surveys 14 (2017), 289--327. doi:10.1214/14-PS233. https://projecteuclid.org/euclid.ps/1513069215


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