Automatic statistical analysis of bivariate nonstationary time series - Inmemory of Jonathan A. Raz

We propose a new method for analyzing bivariate nonstationary time series. The proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span t o be used to obtain the smoothed estimates of the time-varying spectra and coherence. It is based on the smooth localized complex exponential (SLEX) t ransform, which forms a library of orthogonal complex-valued transforms tha t are simultaneously localized in time and frequency. We show that the smoo thed SLEX periodograms are consistent estimators, report simulation results , and apply the method to a two-channel electroencephalogram dataset record ed during an epileptic seizure.