IDEAS home Printed from
   My bibliography  Save this article

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance


  • Thi Huong An Nguyen

    () (Toulouse School of Economics, University of Toulouse Capitole, 21 allée de Brienne, 31000 Toulouse, France
    Department of Economics, DaNang Architecture University, Da Nang 550000, Vietnam
    These authors contributed equally to this work.)

  • Anne Ruiz-Gazen

    () (Toulouse School of Economics, University of Toulouse Capitole, 21 allée de Brienne, 31000 Toulouse, France
    These authors contributed equally to this work.)

  • Christine Thomas-Agnan

    () (Toulouse School of Economics, University of Toulouse Capitole, 21 allée de Brienne, 31000 Toulouse, France
    These authors contributed equally to this work.)

  • Thibault Laurent

    () (Toulouse School of Economics, CNRS, University of Toulouse Capitole, 31000 Toulouse, France
    These authors contributed equally to this work.)


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.

Suggested Citation

  • Thi Huong An Nguyen & Anne Ruiz-Gazen & Christine Thomas-Agnan & Thibault Laurent, 2019. "Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(1), pages 1-21, February.
  • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:1:p:28-:d:204457

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Nguyen, T.H.A & Laurent, Thibault & Thomas-Agnan, Christine & Ruiz-Gazen, Anne, 2018. "Analyzing the impacts of socio-economic factors on French departmental elections with CODA methods," TSE Working Papers 18-961, Toulouse School of Economics (TSE).
    3. Christophe Croux & Mohammed Fekri & Anne Ruiz-Gazen, 2010. "Fast and robust estimation of the multivariate errors in variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 286-303, August.
    4. Kelejian, Harry H. & Prucha, Ingmar R., 1985. "Independent or uncorrelated disturbances in linear regression : An illustration of the difference," Economics Letters, Elsevier, vol. 19(1), pages 35-38.
    5. Singh, Radhey S., 1988. "Estimation of error variance in linear regression models with errors having multivariate student-t distribution with unknown degrees of freedom," Economics Letters, Elsevier, vol. 27(1), pages 47-53.
    Full references (including those not matched with items on IDEAS)

    More about this item


    multivariate regression models; heavy-tailed data; Mahalanobis distances; maximum likelihood estimator; independent multivariate Student distribution; uncorrelated multivariate Student distribution;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jjrfmx:v:12:y:2019:i:1:p:28-:d:204457. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.