Estimations of the time-average variance for meteorological time series play a central role in climatic studies. They depend on the finite sample length and the correlation structure of the climatic time series. A general equation for these estimations is derived theoretically for autoregressive integrated moving average (ARIMA) process. Comparisons with a first-order Markov, moving average and independent processes are presented with charts for determining equivalent independent process effective number by considering a certain level of relative error percentage. Illustrative examples are given for the application of time-average variance in detecting possible climatic trends. (C) 1998 Royal Meteorological Society.