Estimation of Spectral Characteristics for a Class of Non-Stationary Time Series

摘要

This paper deals with time series which are stationary in the mean but which have a nonstationary convariance function which is described by a certain parametric model. The non-stationarity results from changes over time of the parameters in the model. The first part of this paper discusses the concepts of stationarity, covariance, and the spectrum. The concept of temporal spectrum is introduced and applied to the analysis of the nonstationary time series. The second part deals with the parametric model. Statistics related to the rate of zero-axis crossings and the rate of relative maxima and minima of the time series are used to estimate the parameters in the model. These estimates are easy to compute from discrete observations of the time series. Expressions for the variances of these estimators are given as a function of the parameters and the sampling period. (Author)