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Copula-Based Dependence Characterizations and Modeling for Time Series

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  • Rustam Ibragimov

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 cop- ulas 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 for a wide class of beta mixing sequences.

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Bibliographic Info

Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2094.

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Date of creation: 2005
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Handle: RePEc:fth:harver:2094

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Cited by:
  1. Rosario Romera & Elisa M. Molanes, 2008. "Copulas in finance and insurance," Statistics and Econometrics Working Papers ws086321, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Beare, Brendan K., 2009. "Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt87p829d4, Department of Economics, UC San Diego.
  3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Economics Series Working Papers 655, University of Oxford, Department of Economics.
  4. Beare, Brendan, 2008. "Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt2880q2jq, Department of Economics, UC San Diego.

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