Potential predictability of a meteorological time series can be estimated from the ratio of the actual interannual variability to the natural variability associated with climatic noise. The extent to which this ratio is larger than one is taken as a measure of the climatic signal-to-noise variance ratio. However, there are major problems in separating out the signal from the noise which are compounded by persistence in the time series, the presence of an annual cycle and the effects of finite sample size. An F test may be used to deduce that a signal is present by rejecting the null hypothesis of no signal. However, it is shown that, generally, the null hypothesis should not be accepted just because it cannot be rejected. Confidence limits can be very large when a signal is present in a finite sample since the signal will be fictitiously correlated with the noise due to sampling in a manner that is unknown. Although the correlation coefficient is statistically not significant, there is a large im... Abstract Potential predictability of a meteorological time series can be estimated from the ratio of the actual interannual variability to the natural variability associated with climatic noise. The extent to which this ratio is larger than one is taken as a measure of the climatic signal-to-noise variance ratio. However, there are major problems in separating out the signal from the noise which are compounded by persistence in the time series, the presence of an annual cycle and the effects of finite sample size. An F test may be used to deduce that a signal is present by rejecting the null hypothesis of no signal. However, it is shown that, generally, the null hypothesis should not be accepted just because it cannot be rejected. Confidence limits can be very large when a signal is present in a finite sample since the signal will be fictitiously correlated with the noise due to sampling in a manner that is unknown. Although the correlation coefficient is statistically not significant, there is a large im...