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Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

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  • 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.)

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.

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
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    References listed on IDEAS

    as
    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

    Keywords

    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

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