Facts and fiction in spectral analysis of stationary stochastic processes

New developments in time series analysis can be used to determine a better spectral representation for unknown data. Any stationary process can be modeled accurately with one of the three model types: AR (autoregressive), MA (moving average) or the combined ARMA model. Generally, the best type is unknown. However, if the three models are estimated with suitable methods, a single time series model can be chosen automatically in practice. The accuracy of the spectrum, computed from this single AR-MA time series model, is compared with the accuracy of many tapered and windowed periodogram estimates. The time series model typically gives a spectrum that is better than the best of all periodogram estimates.