The variance of a time average of a stationary time series depends on the spectral density near frequency zero rather than on the variance of the process. Equations are given for estimating the variance of a time average by fitting a low-order autoregression to the data. Details are given for selecting the order of the autoregression. An example is presented which uses an analysis of variance approach for testing for climatic trends, allowing for diurnal and annual variability and serial correlation. Abstract The variance of a time average of a stationary time series depends on the spectral density near frequency zero rather than on the variance of the process. Equations are given for estimating the variance of a time average by fitting a low-order autoregression to the data. Details are given for selecting the order of the autoregression. An example is presented which uses an analysis of variance approach for testing for climatic trends, allowing for diurnal and annual variability and serial correlation.