Batch size selection for the batch means method

The batch means method is among the most popular confidence interval techniques for the output analysis of a steady-state simulation. The selection of the batch size for the batch means method affects the quality of the confidence interval estimator. Many existing algorithms, however, are ad hoc in nature and lack a rigorous foundation. We explore the relationship between the sample size and the optimal batch size ("optimality" is a sense to be defined in this paper). We focus on steady-state analysis and assume that the underlying process is stationary and strongly mixing. Three drastically different choices of batch sizes for the batch means method are discussed. Several empirical results illustrate our findings.