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Title: Positive-definite wavelet estimation of time-varying spectral density matrices Authors:  Rainer von Sachs - Université catholique de Louvain (Belgium) [presenting]
Joris Chau - Université catholique de Louvain (Belgium)
Abstract: In nonparametric estimation of the spectral density matrix of a multivariate time series it is important to preserve positive-definiteness of the estimator. To this purpose, in previous work the authors have considered multivariate spectral estimation on the Riemannian manifold of Hermitian and positive-definite matrices based on a geometric wavelet approach. Nonlinear wavelet curve denoising on the Riemannian manifold allows one to capture local smoothness behaviour of the spectral matrix across frequency, but also varying degrees of smoothness across components of the spectral matrix. We discuss extensions of this approach to a) non-stationary, i.e. time-varying analyses (the underlying spectral density is allowed to change over time) and b) to situations of replicated multivariate time series as treated in the functional mixed-effects model approach of the authors.