SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

This article presents SPSTS, an automated sequential procedure for computing point and Confidence-Interval (CI) estimators for the steady-state mean of a simulation-generated process subject to user-specified requirements for the CI coverage probability and relative half-length. SPSTS is the first sequential method based on Standardized Time Series (STS) area estimators of the steady-state variance parameter (i.e., the sum of covariances at all lags). Whereas its leading competitors rely on the method of batch means to remove bias due to the initial transient, estimate the variance parameter, and compute the CI, SPSTS relies on the signed areas corresponding to two orthonormal STS area variance estimators for these tasks. In successive stages of SPSTS, standard tests for normality and independence are applied to the signed areas to determine (i) the length of the warm-up period, and (ii) a batch size sufficient to ensure adequate convergence of the associated STS area variance estimators to their limiting chi-squared distributions. SPSTS's performance is compared experimentally with that of recent batch-means methods using selected test problems of varying degrees of difficulty. SPSTS performed comparatively well in terms of its average required sample size as well as the coverage and average half-length of the final CIs.