Next Article in Journal
The Determinants of Sovereign Risk Premium in African Countries
Next Article in Special Issue
The Importance of the Financial Derivatives Markets to Economic Development in the World’s Four Major Economies
Previous Article in Journal
Contribution to the Valuation of BRVM’s Assets: A Conditional CAPM Approach
Previous Article in Special Issue
Does the Misery Index Influence a U.S. President’s Political Re-Election Prospects?
Article Menu

Export Article

Open AccessArticle
J. Risk Financial Manag. 2019, 12(1), 28; https://doi.org/10.3390/jrfm12010028

Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

1
Toulouse School of Economics, University of Toulouse Capitole, 21 allée de Brienne, 31000 Toulouse, France
2
Department of Economics, DaNang Architecture University, Da Nang 550000, Vietnam
3
Toulouse School of Economics, CNRS, University of Toulouse Capitole, 31000 Toulouse, France
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 29 December 2018 / Revised: 24 January 2019 / Accepted: 31 January 2019 / Published: 9 February 2019
(This article belongs to the Special Issue Applied Econometrics)
Full-Text   |   PDF [670 KB, uploaded 5 March 2019]   |  

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. View Full-Text
Keywords: multivariate regression models; heavy-tailed data; Mahalanobis distances; maximum likelihood estimator; independent multivariate Student distribution; uncorrelated multivariate Student distribution multivariate regression models; heavy-tailed data; Mahalanobis distances; maximum likelihood estimator; independent multivariate Student distribution; uncorrelated multivariate Student distribution
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Supplementary material

SciFeed

Share & Cite This Article

MDPI and ACS Style

Nguyen, T.H.A.; Ruiz-Gazen, A.; Thomas-Agnan, C.; Laurent, T. Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance. J. Risk Financial Manag. 2019, 12, 28.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
J. Risk Financial Manag. EISSN 1911-8074 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top