Facts and fiction in spectral analysis

This analysis is limited to the spectral density of unknown stationary stochastic processes. The main estimation methods are parametric with time series, or non-parametric with a Fourier transform of the data. A single time series model is chosen automatically from the three selected models: the best autoregressive, AR, the best moving average, MA and the best combined ARMA. The accuracy of the spectrum, computed from this single ARMA time series model, is compared with the accuracy of windowed periodogram estimates. The time series model generally gives a spectrum that is better than the best periodogram. It is a fact that a single time series model can be selected automatically for unknown statistical data. It is fiction to believe that objective choices between windowed periodograms can be made.