On Spectral Analysis of Stationary Time Series

Abstract

The present statistical theory of analysis of stationary time series (e.g., extrapolation) has assumed complete knowledge of the covariance sequence or equivalently of the spectrum of the process. It is, therefore, of great importance to be able to estimate one of these. However, knowledge of the spectrum seems to yield greater immediate insight into the structure of the process. This seems to have first been noted in a fundamental paper by Bartlett.1 An unpublished paper by Tukey2 deals with some aspects of the problem of estimating the spectrum.