Estimation of the accuracy of mean and variance of correlated data

Monte Carlo simulations are an important tool in computational physics or statistical mechanics. Physical constants or properties are found as the mean or the variance of successive states of simulated systems. A new method to determine the statistical accuracy of the estimated means and variances is described. It uses the parameters of an automatically selected time series model. That time series model gives an optimal description of the spectral density and of the correlation structure of correlated data which are considered as stationary or in equilibrium. The resulting accuracy estimates are close to the Cramer-Rao bound for data where the correlation is determined by a single time constant.