An Automatic Precise Estimation of Stationary Power Spectra by Multi-Step Fittings of AR Model

Abstract

A practical method of power spectral estimation is proposed, that can automatically provide the precise estimates of stationary random signals.
First, by reviewing the conventional automatic estimation by AR model fitting, the necessity of some means for the order determination under the assured whiteness of residue error series is stressed, even when the whiteness, assumed by most of the criterions such as AIC, is violated by the conventional.
Secondly, based on the fact that the residue series include much information about the original series in the above cases, yet, the automatic precise estimation by multistep fittings of AR model is presented, that iterates the model fitting until the whiteness of residue series is ascertained.
Finally, the fundamental characteristic and effectiveness of the proposed method are made clear through automatic power spectral estimation of time series, generated numerically for both cases with and without fitting to the AR model.