Multivariate reduced rank regression in non-Gaussian contexts, using copulas

A new procedure is proposed that performs reduced rank regression (RRR) in non-Gaussian contexts based on multivariate dispersion models. Reduced-rank multivariate dispersion models (RR-MDM) generalize RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, inverse Gaussian, and discrete distributions like the Poisson, the binomial and the negative binomial. A multivariate distribution is created with the help of the Gaussian copula and estimation is performed using maximum likelihood. It is shown how this method can be amended to deal with the case of discrete data. A Monte Carlo simulation shows that the new estimator is more efficient than the traditional Gaussian RRR. In the framework of MDM's a procedure analogous to canonical correlations is introduced, which takes into account the distribution of the data. Finally, the method is applied to the number of trades of five US department stores on the New York Stock Exchange during the year 1999 and determine the existence of a common factor which represents sector specific news. This analysis is helpful in microstructure analysis to identify leaders from the point of view of dissemination of sectorial information.