For more than a century now astronomers have used the O - C (Observed
minus Calculated) method to detect the presence of systematic changes
in the periods of variable stars. The method is based on an analysis o
f residuals from a linear fit to the observed epochs. A rather common
error in applications of the method is a failure to make provision for
autocorrelation which exists in the data. In this paper we consider a
model that accounts for the presence of autocorrelation and develop a
n alternative to the O - C method of analysis. The proposed method foc
uses on the frequency domain characteristics of observed periods. Its
use is illustrated by application to data from the variable stars X Au
rigae and RY Sagittarii.