Empirical Confidence Limits for Variance Spectra

Abstract

A method is presented for obtaining empirical confidence limits for variance spectra. It can be applied whenever the distribution of spectral variances is unknown but the stochastic model of the data is known or proposed. For computer-generated white noise the results show that the normalized raw spectral variances do not vary as the theoretical model, ?210/10, predicts due to the appearance of expected negative line variances. Thus, the lower a priori and a posteriori confidence limits are less than their theoretical counterparts. The empirical confidence limits for normalized hanned spectral variances agree with those from the theoretical model, ?227/27.