The asymptotic validity of sequential stopping rules for confidence interval construction using standardized time series

ABSTRACTWe establish the asymptotic validity of a class of sequential stopping rules when applying standardized time series (STS) to construct fixed-width confidence intervals (CI). The STS CI construction avoids requiring a consistent variance estimator, which is attractive to a class of steady-state simulation problems in which variance estimation is difficult. We quantify the asymptotic distribution of STS at stopping times as the prescribed half-width of the CI approaches zero. This provides us with the appropriate scaling parameter for the CI in the sequential stopping setting.