Estimating The Spectrum

Several alternative methods for constructing reasonable estimators of the spectral density have been proposed and investigated over the years. We will highlight just a few of them that have gained the most acceptance in light of present-day computing power. So-called nonparametric estimation of the spectral density (that is, smoothing of the sample spectral density) assumes very little about the shape of the “true” spectral density. Parametric estimation assumes that an autoregressive model—perhaps of high order—provides an adequate fit to the time series. The estimated spectral density is then based on the theoretical spectral density of the fitted AR model. Some other methods are touched on briefly.