Abstract

Harmonizable time series are natural extensions of stationary time series with a spectral decomposition whose components are correlated. Thus, the covariance function of a harmonizable time series is bivariate and admits a two-dimensional Fourier decomposition (Loeve spectrum). They form a broad class of nonstationary processes that has been a subject of investigation for a long time. In this talk, we introduce a parametric form for these harmonizable processes, namely Harmonizable Vector AutoRegressive and Moving Average models (HVARMA), and we give tools to generate finite time sample realizations of HVARMA with known Loeve spectrum. Then, we discuss nonparametric estimation of spectral characteristics of spatiotemporal processes that are locally time-harmonizable, and illustrate its application in EEG data analysis.