Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

Thi Huong An Nguyen, Anne Ruiz-Gazen, Christine Thomas-Agnan and Thibault Laurent
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Thi Huong An Nguyen: Toulouse School of Economics, University of Toulouse Capitole, 21 allée de Brienne, 31000 Toulouse, France
Thibault Laurent: Toulouse School of Economics, CNRS, University of Toulouse Capitole, 31000 Toulouse, France

JRFM, 2019, vol. 12, issue 1, 1-21

Abstract: To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recalling some facts about these distributions and models, known but scattered in the literature, we prove that the maximum likelihood estimator of the covariance matrix in the UT model is asymptotically biased and propose an unbiased version. We provide implementation details for an iterative reweighted algorithm to compute the maximum likelihood estimators of the parameters of the IT model. We present a simulation study to compare the bias and root mean squared 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 an application to model vectors of financial assets returns.

Keywords: multivariate regression models; heavy-tailed data; Mahalanobis distances; maximum likelihood estimator; independent multivariate Student distribution; uncorrelated multivariate Student distribution (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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