Accurate design and optimization of short response time solar energy systems with storage are sensitive to the stationary and sequential characteristics of hourly solar radiation. We perform monthly time series analyses of hourly global horizontal solar radiation for a wide range of climatic stations that span temperate and tropical conditions. The stationary statistics for individual hours are found to be very similar to the corresponding results for daily total global horizontal radiation, in keeping with a related fundamental observation of Liu & Jordan. Investigation of sequential properties shows that autocorrelation coefficients are, to a good approximation, independent of time of day and that persistence times are nearly as long as the entire daylight period, mainly due to the effect of very strong correlations at one-hour lag times. The isolated effect of two-hour and longer lag times, via the partial autocorrelation coefficients, is found to be negligible in most, but by no means all, instances. Finally, we find no universal correlation between hourly autocorrelation coefficients and monthly average radiation figures.