Spectrum inference for replicated spatial locally time-harmonizable time series

In this paper, we develop tools for statistical inference on repli-cated realizations of spatiotemporal processes that are locally time-harmonizable. Our method estimates both the rescaled spatial time-varying Loeve-spectrum and the spatial time-varying dual-frequency coherence function under re-alistic modeling assumptions. We construct confidence intervals for these parameters of interest using the Circular Block Bootstrap method and prove its consistency. We illustrate the application of our methodology on a dataset arising from an experiment in neuropsychology. From EEG recordings, our method allows studying the dynamic functional connectiv-ity within the brain associated to visual working memory performance.