Multivariate Student versus Multivariate Gaussian Regression Models with Applications to Finance and Political Economy
For modeling multivariate possibly heavy tailed data, we compare the multivariate normal regression model (N) with two versions of the multivariate Student regression model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). We recall some facts about these distributions and models, which are known but scattered in the literature. We complete the results by proposing an unbiased estimator of the covariance matrix in the UT model and giving an iterative reweighted least squares algorithm to compute the maximum likelihood estimators for the IT model. We present a simulation study to compare the bias and root mean square error of the ensuing estimators of the regression coefficients and covariance matrix under several scenarios of the potential data generating process, misspecified or not. We propose a graphical tool and a test based on the Mahalanobis distance to guide the choice between the competing models. We also present two small applications: one to model vectors of financial assets returns and the other to model vectors of party shares in an electoral process.