Weighted Batch Means and Improvements in Coverage

Abstract

Weighted batch means is a procedure for producing a confidence interval for the mean of a covariance- stationary process. Weights placed on the observations within a batch are functions of the parameters of a fitted time-series model. Experiments show that the method works well in terms of achieved coverage when only a comparatively small number of observations is available, even for processes that display strong correlation. In theory the method should provide exact coverage for some processes. However, practice the time-series identification procedure and estimation of the parameters and weights bring in bias. We investigate the sources of bias and suggest how coverage might be improved.