Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

摘要

To model multivariate, possibly heavy-tailed data, we compare the multivariate normalmodel (N) with two versions of the multivariate Student model: the independent multivariateStudent (IT) and the uncorrelated multivariate Student (UT). After recalling some facts aboutthese distributions and models, known but scattered in the literature, we prove that the maximumlikelihood estimator of the covariance matrix in the UT model is asymptotically biased and proposean unbiased version. We provide implementation details for an iterative reweighted algorithm tocompute the maximum likelihood estimators of the parameters of the IT model. We present asimulation study to compare the bias and root mean squared error of the ensuing estimators of theregression coefficients and covariance matrix under several scenarios of the potential data-generatingprocess, misspecified or not. We propose a graphical tool and a test based on the Mahalanobisdistance to guide the choice between the competing models. We also present an application to modelvectors of financial assets returns.