Estimating the Asymptotic Variance with Batch Means

In this paper it is shown that there does not exist a procedure to consistently estimate the asymptotic variance constant in a stochastic simulation using batch means when the number of batches is held fixed as the run length increases. Thus, if consistency is desired, then the number of batches must increase as the run length increases. To be precise, we must first specify what we mean by an estimation procedure. To be interesting, an estimation procedure should apply to a large family of stochastic processes.