Copula-Based Dependence Characteriztions and Modeling for Time Series

30 Pages Posted: 21 Sep 2005

See all articles by Rustam Ibragimov

Rustam Ibragimov

Harvard University - Department of Economics

Date Written: September 2005

Abstract

This paper develops a new unified approach to copula-based modeling and characterizations for time series and stochastic processes. We obtain complete characterizations of many time series dependence structures in terms of copulas corresponding to their finite-dimensional distributions. In particular, we focus on copula-based representations for Markov chains of arbitrary order, m-dependent and r-independent time series as well as martingales and conditionally symmetric processes. Our results provide new methods for modeling time series that have prescribed dependence structures such as, for instance, higher order Markov processes as well as non-Markovian processes that nevertheless satisfy Chapman-Kolmogorov stochastic equations. We also focus on the construction and analysis of new classes of copulas that have flexibility to combine many different dependence properties for time series. Among other results, we present a study of new classes of copulas based on expansions by linear functions (Eyraud-Farlie-Gumbel-Mongenstern copulas), power functions (power copulas) and Fourier polynomials (Fourier copulas) and introduce methods for modeling time series using these classes of dependence functions. We also focus on the study of weak convergence of empirical copula processes in the time series context and obtain new results on asymptotic gaussianity of such processes or a wide class of beta-mixing sequences.

Keywords: copulas, dependence, characterization, time series, Markov processes, m-dependence, r-indpendence, stochastic differential equations, Fourier copulas

JEL Classification: C14, C50, C52

Suggested Citation

Ibragimov, Rustam, Copula-Based Dependence Characteriztions and Modeling for Time Series (September 2005). Harvard Institute of Economic Research Discussion Paper No. 2094, Available at SSRN: https://ssrn.com/abstract=808024 or http://dx.doi.org/10.2139/ssrn.808024

Rustam Ibragimov (Contact Author)

Harvard University - Department of Economics ( email )

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