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June, 1964 On the Coefficient of Coherence for Weakly Stationary Stochastic Processes
L. H. Koopmans
Ann. Math. Statist. 35(2): 532-549 (June, 1964). DOI: 10.1214/aoms/1177703553


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.


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L. H. Koopmans. "On the Coefficient of Coherence for Weakly Stationary Stochastic Processes." Ann. Math. Statist. 35 (2) 532 - 549, June, 1964.


Published: June, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0125.08206
MathSciNet: MR161404
Digital Object Identifier: 10.1214/aoms/1177703553

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 2 • June, 1964
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