OBM confidence intervals: Something for nothing?

Since the 1950s, nonoverlapping batch means (NBM) has been a basis for confidence-interval procedures (CIPs) for the mean of a steady-state time series. In 1985, overlapping batch means (OBM) was introduced as an alternative to NBM for estimating the standard error of the sample mean. Despite OBM's inherent efficiency, because the OBM statistic does not approach normality via the chi-squared distribution, no OBM CIP was introduced. We define two fixed-sample-size OBM CIPs. OBM1 is based on the result that asymptotically OBM has half again as many degrees of freedom as NBM. OBM2 does the same, but increases degrees of freedom. We argue that OBM's sampling distribution has skewness and kurtosis closer to normal than the chi-squared distribution. We show experimentally that for AR(1) processes the OBM CIPs perform better than NBM CIPs in terms of classic criteria and the VAMP1RE criterion. Finally, we introduce the concept of VAMP1RE-optimal batch sizes.