Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/239029 
Year of Publication: 
2019
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 12 [Issue:] 1 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-21
Publisher: 
MDPI, Basel
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.
Subjects: 
multivariate regression models
heavy-tailed data
Mahalanobis distances
maximum likelihood estimator
independent multivariate Student distribution
uncorrelated multivariate Student distribution
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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