ASAP2: an improved batch means procedure for simulation output analysis

Abstract

We introduce ASAP2, an improved variant of the batch-means algorithm ASAP for steady-state simulation output analysis. ASAP2 operates as follows: the batch size is progressively increased until the batch means pass the Shapiro-Wilk test for multivariate normality; and then ASAP2 delivers a correlation-adjusted confidence interval. The latter adjustment is based on an inverted Cornish-Fisher expansion for the classical batch means t-ratio, where the terms of the expansion are estimated via a first-order autoregressive time series model of the batch means. ASAP2 is a sequential procedure designed to deliver a confidence interval that satisfies a prespecified absolute or relative precision requirement. When used in this way, ASAP2 compares favorably to ASAP and the well-known procedures ABATCH and LBATCH with respect to close conformance to the precision requirement as well as coverage probability and mean and variance of the half-length of the final confidence interval.