Asymptotic properties of the Bernstein density copula estimator for α-mixing data

  • Authors:

  • Taoufik Bouezmarni;Jeroen V. K. Rombouts;Abderrahim Taamouti

  • Affiliations:

  • Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, Canada, H3C 3J7 and Institute of Statistics, Universi ...;Institute of Applied Economics at HEC Montréal, CIRANO, CIRPEE, CORE (Université catholique de Louvain), 3000 Cote Sainte Catherine, Montréal (QC), Canada, H3T 2A7;Departamento de Economía, Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Madrid), Spain

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for @a-mixing data using Bernstein polynomials. We focus only on the dependence structure between stochastic processes, captured by the copula density defined on the unit cube, and not the complete distribution. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality. An empirical application is considered to illustrate the dependence structure among international stock markets (US and Canada) using the Bernstein density copula estimator.