(Very) Fast estimation and testing of (very) large dimensional heavy-tailed elliptical distributions
by David Veredas
Abstract: We estimate the parameters of an elliptical distribution by means of a multivariate extension of the Method of Simulated Quantiles (MSQ) of Dominicy and Veredas (2010). The multivariate extension entails the construction of a function of quantiles that is informative about the codispersion parameters: the interquantile range of a projection of pairwise random variables onto the 45 degree line. Moreover, due to the properties of the elliptical distributions we circumvent the curse of dimensionality as we provide a very fast methodology to estimate the parameters of any dimension. We also provide a quantile-based criterion to choose the elliptical distribution. A Monte Carlo study to 20, 200 and 2000 dimensions reveals good finite sample properties of the estimators. Two empirical applications to 22 worldwide financial market returns and 490 asset returns illustrate the usefulness of the method.
(Joint work Yves Dominicy and Hiroaki Ogata)
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