Do stock returns have an Archimedean copula?

Abstract

The flexible class of Archimedean copulas plays an important role in multivariate statistics. While there is a large number of goodness-of-fit tests for copulas and parametric families of copulas, the question if a given data set belongs to an arbitrary Archimedean copula or not has not yet received much attention in the literature. This paper suggests a new, straightforward method to test whether a copula is an Archimedean copula without the need to specify its parametric family. We conduct Monte Carlo simulations to assess the power of the test. The approach is applied to (bivariate) joint distributions of stock asset returns. We find that, in general, stock returns may have Archimedean copulas.

Keywords:

• Archimedean copulas
• joint stock return distribution

JEL :

• G11
• C51

Notes

The methods may, of course, be transferred by substituting U _i for Û _i and V _i for [Vcirc] _i .

The number of bootstrap replications is set to B=100 to economize on computing time.

Since copulas are invariant to monotone transformations, the test results do not change if the returns are defined as percentage changes.

The models have been estimated by the garchFit command of the R package fGarch.

The grid size has been chosen such that the average number of points in each grid field is about 40.