SPECTRAL ANALYSIS OF A STATIONARY BIVARIATE POINT PROCESS WITH APPLICATIONS TO NEUROPHYSIOLOGICAL PROBLEMS

Abstract. In this paper we discuss the spectral analysis of a stationary bivariate point process applied to the study of a complex physiological system. An estimate of the cross-spectral density can be obtained by smoothing the modified cross-periodogram statistic. The smoothed estimate is calculated by dividing the whole length of the data into a number of disjoint subrecords. Estimates of the coherence function and the cross-intensity function follow directly from the estimate of the cross-spectral density. It is shown that the asymptotic properties of the estimate of the cross-intensity function can be improved by inserting a convergence factor in it. Examples of the estimates are illustrated by using two data sets from neurophysiological experiments and their importance is emphasized by examining the behaviour of the complex physiological system under study.