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

Bouezmarn, T.; Rombouts, Jeroen V.K.; Taamouti, A.

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 α-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.

Citation

Bouezmarn, T., Rombouts, J. V., & Taamouti, A. (2010). Asymptotic properties of the Bernstein density copula estimator for α-mixing data. Journal of Multivariate Analysis, 101(1), 1-10. https://doi.org/10.1016/j.jmva.2009.02.014

• Journal Article Type: Article
• Publication Date: 2010-01
• Deposit Date: Oct 16, 2014
• Journal: Journal of Multivariate Analysis
• Print ISSN: 0047-259X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Issue: 1
• Pages: 1-10
• DOI: https://doi.org/10.1016/j.jmva.2009.02.014
• Keywords: Nonparametric estimation, Copula, Bernstein polynomial, α-mixing, Asymptotic properties, Boundary bias.
• Public URL: https://durham-repository.worktribe.com/output/1452293