GeD spline estimation of multivariate Archimedean copulas

Dimitrova, D. S., Kaishev, V. K. & Penev, S. (2007). GeD spline estimation of multivariate Archimedean copulas (Report No. Actuarial Research Paper No. 179). London, UK: Faculty of Actuarial Science & Insurance, City University London.

[img]
Preview
PDF
Download (364kB) | Preview

Abstract

A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so called Geometrically Designed splines (GeD splines), recently introduced by Kaishev et al. (2006 a,b) [10] and [11], to represent the cdf of a random variable Wµ, obtained through the probability integral transform of an Archimedean copula with parameter µ. Sufficient conditions for the GeD spline estimator to posses the properties of the underlying theoretical cdf, K(µ; t), of Wµ, are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure,finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem, are separated. Thus, the resulting spline estimator ^K (^µ; t) is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d ¸ 2, as illustrated by the numerical examples presented.

Item Type: Monograph (Working Paper)
Uncontrolled Keywords: Archimedean copula, generator, Kendall's process, B- spline, geometrically designed regression splines, shape preserving
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance > Faculty of Actuarial Science & Insurance Actuarial Research Reports
URI: http://openaccess.city.ac.uk/id/eprint/2311

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics