Bandwidth Selection for Zero Lugsail Estimators

Test statistics, confidence intervals, and p-values all typically rely on an estimate for variance.  For data sets that are not independent and identically distributed (iid) caution must be used when selecting a variance estimator. If the dependence structure is unknown but stationary, a robust long run variance (LRV) estimator can be used which can handle a wide variety of scenarios. Estimation of the LRV is of interest in various fields such as time series, econometrics, spectral analysis, and Markov chain Monte Carlo simulations. Spectral variance (SV) estimators are one of the most common LRV estimation methods, but they suffer from a negative bias in the presence of positive correlation. An alternative zero lugsail estimator has been proposed to combat this issue which has a zero asymptotic bias regardless of correlation. In addition, further advancements have been made regarding nonstandard limiting distributions that better incorporate the variability of LRV estimators. Both SV and zero lugsail estimators rely on a bandwidth parameter, a critical component for the estimation process. Currently no guidelines exist for selecting a bandwidth for the zero lugsail estimator.  We propose an optimal bandwidth rule for zero lugsail estimators when relying on nonstandard limiting distributions. With this procedure we can greatly improve bias, account for variability, and obtain an estimator optimized for inference.