Three time series of varves from the Eocene Green River Formation in Colorado, consisting of 1469, 1869, and 4158 annual thickness measurements, were analyzed by a variety of statistical techniques to characterize climate variations. The analysis reveal that the time series are lognormal after adjustment for a trend. Moreover, the analyses suggest that the time series are generally nonstationary and are noiselike in structure. Fourier spectra and maximum entropy spectra of the time series are ''reddish,'' indicating the importance of nonoscillatory changes in varve thickness at time scales ranging from tens to hundreds of years. There are no statistically significant peaks in Fourier spectra for the entire time series; however, one segment of one of the three time series displays statistically significant peaks corresponding to periods of 10.8 and 5.4 years. Overall, the time series are suggestive of a nonperiodic and weakly predictive climate during the time periods corresponding to deposition of the varves.