Statistical Spectral Analysis of Time Series Arising from Stationary Stochastic Processes

Abstract

We consider time series which are realizations of a stochastic process. From the time series we construct various estimates of the spectral distribution function of the process (Section 3) and we study the sampling distributions of some functionals of these estimates (Sections 4-7). We then obtain confidence regions for the spectral distribution function and various tests of hypotheses in the normal case (Sections 8-10).