On the Coefficient of Coherence for Weakly Stationary Stochastic Processes

Abstract

The coefficient of coherence is defined for bivariate weakly stationary stochastic processes which have spectral distributions dominated by a fixed Lebesgue-Stieltjes measure. This quantity is shown to possess two of the important properties which make the ordinary correlation coefficient a desirable measure of linear regression for pairs of random variables. This provides a justification for the already common use of the coefficient of coherence as a measure of linear-regression for pairs of stationarily correlated, weakly stationary time series.