On the relationship between batch means, overlapping means and spectral estimation

Abstract

The conventional method of batch means and the overlapping batch means approach of Meketon and Schmeiser are related to spectral estimation via the time averaging of subsequence periodograms. It is shown that most of the reduction in the variance of the variance estimate can be achieved with modest amounts of overlapping. This may have practical implications because of the large number of batches required for the statistical test of lack of correlation. and the usual practice of rebatching the data after this test is passed.