gioia.vincenzo@spes.uniud.it
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(Supervisor: Prof. Nicola Torelli - Co-supervisors: Prof. Ruggero Bellio and Dr. Matteo Fasiolo)

Title: Additive covariance matrix models with applications to energy demand modelling

Abstract:
The work aims to extend the multivariate Gaussian additive models, allowing the covariance matrix to vary as a function of the covariates in a semi-parametric way. Covariance regression models are a useful class of statistical models, able to capture the potentially dynamic nature of the variance and dependence parameters. However, the intrinsic difficulties involved in their adoption limit the spread of such models in applications. The main challenges are to ensure the positive-definiteness of the covariance matrix and to guarantee computational scalability in moderate dimensional settings. The unconstrained parametrisation approaches resulting from the modified Cholesky decomposition of the precision matrix and the logarithmic transformation of the covariance matrix are adapted within a well-established inferential framework. Motivated by the need to support energy system operations, some applications to electricity demand modelling are taken into account. In addition to the methodological and software contribution, the proposed modelling framework is promising for future applications aiming at model temporal, spatial, spatio-temporal, or more general dependency structures, which are pervasive in several domains, such as economics, finance, engineering, and life sciences.