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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Bouezmarni, Taoufik^2,3  Rombouts, Jeroen V. K.¹  Taamouti, Abderrahim⁴ 

[1] Catholic Univ Louvain, Inst Appl Econ, HEC Montreal, CIRANO,CIRPEE,CORE, Montreal, PQ H3T 2A7, Canada

[2] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[3] Catholic Univ Louvain, Inst Stat, Montreal, PQ H3T 2A7, Canada

[4] Univ Carlos III Madrid, Dept Econ, Madrid 28903, Spain

关键词: Nonparametric estimation;    Copula;    Bernstein polynomial;    alpha-mixing;    Asymptotic properties;    Boundary bias;   

DOI  :  10.1016/j.jmva.2009.02.014

来源: Elsevier

【 摘 要 】

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 alpha-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. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved,

【 授权许可】

Free