The estimation of standard errors in Monte Carlo simulation experiments

SUMMARY In using Monte Carlo methods for estimating some constant it often happens that successive observations are not independent. Various methods of estimating the variance of the mean of all the observations are considered. It is shown by numerical examples that in many cases these are strongly biased and the bias is calculated when the serial correlation is of the form ps. If an upper bound for the serial correlation is known, this enables one to choose the length of the simulation and the method of estimating variance which makes the latter small.