Title: Skew and multi-tailed multivariate distributions - a need in finance
It is a well-known fact that financial data exhibit heavy tails and, often, skewness. As response to the fallacies of the multinormal distribution to model financial data, the class of elliptically symmetric distributions (including the multivariate t-distribution) has been widely accepted as it allows for heavier-than-normal tails.
However, in situations where negative returns are much more extreme than positive returns, the assumption of elliptical symmetry is too restrictive. Moreover, a further restriction of elliptical distributions lies in the fact that they are governed by a scalar radial function, which implies that the tails are governed by a one-dimensional tail-weight parameter like in the multivariate t distribution.
In this talk I will first present new efficient tests for elliptical symmetry against skew-ellipticity based on the Le Cam theory of asymptotic experiments. With these new tests, I shall analyze financial data consisting of daily returns data of several major worldwide indexes. In the second part of my talk, I will present various models of flexible multivariate distributions from the literature and compare them in the light of the needs of financial data. This comparison is based both on properties of the distributions and a simulation study.
This is joint work with Sladjana Babic, Marc Hallin and David Veredas.