A Form of Optimum Weighing System for Spectrum Estimates

摘要

A previous paper has demonstrated some weaknesses of the usual class of estimates of the spectrum of a stationary time series, where the weights are dependent solely on a 'lag window generator' and choice of truncation point. To pursue this matter further, we here calculate an expression for the optimum weights according to the criterion of minimum average mean square error (although a fairly natural choice, some bad aspects of this criterion are demonstrated). This expression, which depends on the spectrum being estimated, is rather complicated, and two approximations to it are devised and examined. Finally the optimum weights in certain autoregression situations are computed and compared with the weights in the standard types of spectrum estimate. (Author)