Multivariate student versus multivariate Gaussian regression models with application to finance

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Journal of Risk and Financial Management ; ISSN: 1911-8074 ; Volume: 12 ; Year: 2019 ; Issue: 1 ; Pages: 1-21 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: multivariate regression models ; heavy-tailed data ; Mahalanobis distances ; maximum likelihood estimator ; independent multivariate Student distribution ; uncorrelated multivariate Student distribution

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Thi Huong An Nguyen ; Ruiz-Gazen, Anne ; Thomas-Agnan, Christine ; Laurent, Thibault
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2019

Further information

• DOI: doi:10.3390/jrfm12010028
• Handle: http://hdl.handle.net/10419/239029
• Last update: 10.03.2025, 11:45 AM CET