Linear combinations of overlapping variance estimators for simulations

We examine properties of linear combinations of overlapping standardized time series area estimators for the variance parameter of a stationary stochastic process. We find that the linear combination estimators have lower bias and variance than their overlapping constituents and nonoverlapping counterparts; in fact, the new estimators also perform particularly well against the benchmark batch means estimator. We illustrate our findings with analytical and Monte Carlo examples.