Copulas and Long Memory

53 Pages Posted: 30 Jul 2008

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

George Lentzas

Morgan Stanley

Date Written: July 29, 2008


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

Suggested Citation

Ibragimov, Rustam and Lentzas, George, Copulas and Long Memory (July 29, 2008). Harvard Institute of Economic Research Discussion Paper No. 2160, Available at SSRN: or

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

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Cambridge, MA 02138
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George Lentzas

Morgan Stanley ( email )

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New York, NY 10036
United States

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