1 Curved Gaussian Models with Application to the Modeling of Foreign Exchange Rates

Gaussian distributions lie at the heart of popular tools for capturing structure in high dimensional data. Standard techniques employ as models arbitrary linear transformations of spherical Gaussians. In this paper, we present a simple extension to a class of non{ linear, volume preserving transformations which provides an e cient local description of curvature. The resulting generalized Gaussian models give a simple statistical tool for measuring deviations from multivariate Gaussian distributions. Remarkably, there is a computationally e cient, analytic solution for tting the parameters of the non{linear models. The power of this approach is demonstrated in a curvature analysis of the Asian foreign exchange market.