Reflected variance estimators for simulation

We study reflected standardized time series (STS) estimators for the asymptotic variance parameter of a stationary stochastic process. These estimators are based on the concept of data re-use and allow us to obtain more information about the process with no additional sampling effort. Reflected STS estimators are computed from “reflections” of the original sample path. We show that it is possible to construct linear combinations of reflected estimators with smaller variance than the variance of each constituent estimator, often at no cost in bias. We provide Monte Carlo examples to show that the estimators perform as well in practice as advertised by the theory.