Public Thesis Defense of Gabriel Bailly - LIDAM

Estimation and Distributional Properties of Time-Varying Covariance Matrices by Gabriel Bailly -

Vendredi 6 novembre 2026 à 16h00 - Auditoire MORE 53 - Place Montesquieu, 2 - 1348 Louvain-la-Neuve -

Covariance analysis of multivariate time series aims at describing the joint variability and dependence between several variables evolving over time. In this context, the aim of this thesis is to address distributional approximation and nonparametric estimation problems for covariance matrices arising from multivariate stationary and nonstationary time series.

For stationary Gaussian time series, we study the distribution of the sample covariance matrix under serial dependence and develop univariate and multivariate Satterthwaite approximations based on moment-matched Gamma and Wishart distributions. Stein's method is used to quantify the accuracy of these approximations through explicit finite-sample bounds, leading in particular to a feasible Wishart approximation based on a nearest Kronecker product representation of the dependence structure.

For nonstationary time series, we consider the estimation of time-varying covariance matrices as curves in the space of symmetric positive definite matrices. Exploiting the log-Euclidean geometry of this space, we develop an intrinsic wavelet framework that provides flexible nonparametric estimators while naturally preserving positive definiteness. The resulting methodology combines matrix-valued wavelet thresholding, theoretical consistency results, and bias correction under temporal dependence.

Jury members :

Prof. Rainer VON SACHS (UCLouvain) (Supervisor)
Prof. Christian HAFNER (UCLouvain) (Supervisor)
Prof. Eugen PIRCALABELU (UCLouvain) (President)
Prof. Anna KIRILIOUK (UCLouvain) (Secretary)
Prof. Yvik SWAN (ULB) 
Dr. Joris CHAU (OpenAnalytics)

Pay attention : the public defense of Gabriel Bailly will also take place in the form of a videoconference (Numéro de réunion : 323 761 366 984 019 3 - Mot de passe : tF2sF9PG)