Moments of the power spectral density estimated from samples of the autocorrelation function (a robust procedure for monitoring changes in the statistical properties of lengthy non-stationary time series such as the EEG.
Accurate estimates of the statistical moments of the power spectral density (PSD) are obtained without computing the Fourier transform of the associated time series. An innovative analytical procedure is derived which reduces the problem to that of summing a small number of weighted samples of the autocorrelation function (ACF). This result significantly reduces the computational requirements for generating meaningful PSD shape descriptors and thus is especially important in biomedical applications where the cost and effort of monitoring lengthy non-stationary time series is a serious practical limitation. In addition the procedure is robust and therefore can be rigorously applied to any stochastic process to estimate its fundamental statistical properties.