The Estimation of Spectral and Bispectral Density Functions

Abstract

As noted previously, if a stationary time series is Gaussian, and therefore linear, the second order spectra contain all the useful information present in the series, including, for example, information about the possible presence of harmonic components. If the series is non-linear the second order spectra will not adequately characterise the series. For instance, for some types of non-linear time series (e.g. bilinear models which will be considered later) one can show that the second order properties are similar to those of a linear time series model. As such, second order spectral analysis will not necessarily show up any features of non-linearity (or non-Gaussianity) present in the series. It may be necessary, therefore, to perform higher order spectral analysis on the series in order to detect departures from linearity and Gaussianity.