Séminaire MODAL'X : Jean Marc Freyermuth (I2M)

Résumé : Harmonizable time series extend the concept of stationary time series by allowing a spectral decomposition in which the components are correlated. As a result, the covariance function of a harmonizable time series is bivariate and admits a two dimensional Fourier decomposition, known as the Lo`eve spectrum. In this talk, we introduce a parametric form for harmonizable processes, specifically Harmonizable Vector AutoRegressive and Moving Average models (HVARMA). We present a method for generating finite time sample realizations of HVARMA with known Loève spectrum. Finally, after discussing a nonparametric approach to estimate the spectral characteristics of spatiotemporal processes that exhibit local time harmonizability, we illustrate how harmonizable processes can aid in analyzing functional connectivity in EEG data.