The mean and variance of an estimate V(τ) of autocorrelation φ(τ) are calculated. Tho estimate is derived from a single sample, of finite length, of the time-series which is assumed to be stationary and ergodic. It is found that, for values of τ which make φ(τ) appreciable, tho variance depends markedly on the magnitude of the 4th moment of the first distribution of the time-series. On the other hand, for values of τ which make φ(τ) negligible, the variance in nearly all cases falls off linearly with τ, reaching zero when τ equals the sample length. A simple explanation is also given of the well-known fact that the Fourier transform of V(τ) cloos not yield a good estimate of the spectral density.