Chapter 2 - Models for Spectral Analysis—The Univariate Case

Abstract

This chapter deals with the analysis of the univariate case and the models for spectral. The introduction of models for time series that admit a spectral decomposition followed two lines of development. This chapter outlines the spectral analysis for functions with finite power. The second line of development began with a series of papers in 1932–1934 by the Russian mathematician Khintchine who introduced both stationary and weakly stationary stochastic processes, and developed the correlation theory for weakly stationary processes. The development proved important as one of the pioneering works in the modern theory of stochastic processes. This chapter illustrates that the more recent work in time series analysis, both in the study of problems of a purely probabilistic nature and in the development of the statistical theory, has been based on the stationary models. Finally, Wiener model provides some peace of mind to the experimenter who is concerned about the validity of his model, because it applies equally well to a large class of nonstochastic as well as stochastic time series.