Fitting models of nonstationary time series: An application to EEG data

A computationally efficient algorithm is presented for fitting models to a nonstationary time series with an evolutionary (time-varying) spectral representation. We formally define time-varying memory process and prove that this process satisfies local stationarity definition. Our procedure segments the EEG nonstationary time series into stationary or approximately stationary blocks, with and without overlapping, and then estimates the time varying parameters using the local stationarity concept. Our estimation procedure does not make any assumptions about the distribution of innovations (data generating process). We also present a systematic procedure to separate the short memory part from the nonstationary long memory part of the test example time series using a simple frequency domain procedure. Our method is simple and efficient compared to the currently available procedures to analyze the EEG data. Using our procedure, we present a thorough analysis of the sleep EEG data of fullterm and preterm neonates. Several extensions of our method to multivariate time series are also proposed.