Statistical Error Due to Finite Time Averaging in Computer Experiments

In using a computer experiment to calculate the time correlation function of some dynamical variable, the ensemble average over an equilibrium distribution in phase space often is replaced by a time average over a finite interval T. It is shown here that the statistical uncertainty due to this kind of average is of the order of 1{T^1{2}}. The coefficient of the square root is related to a characteristic relaxation time of the correlation function. If only time averaging is performed, the resulting statistical uncertainty in typical computer experiments may be of the order of 20%.