Estimating linear dependence between nonstationary time series using the locally stationary wavelet model

Large volumes of neuroscience data comprise multiple, nonstationary electrophysiological or neuroimaging time series recorded from different brain regions. Accurately estimating the dependence between such neural time series is critical, since changes in the dependence structure are presumed to reflect functional interactions between neuronal populations. We propose a new dependence measure, derived from a bivariate locally stationary wavelet time series model. Since wavelets are localized in both time and scale, this approach leads to a natural, local and multi-scale estimate of nonstationary dependence. Our methodology is illustrated by application to a simulated example, and to electrophysiological data relating to interactions between the rat hippocampus and prefrontal cortex during working memory and decision making.