Automatic Spectral Estimation with Time Series Models

Abstract

Automatic spectral estimation gives random data a language to communicate the information it contains. This tutorial treats the recently developed automatic identification of a single time series model for measured random data. One model is selected, with statistical rules, from hundreds of candidates. That model provides an accurate parametric representation of the power spectral density and of the autocorrelation function of the stochastic data. The accuracy of this autocorrelation function is always better than the usual autocorrelation estimate obtained with lagged products of the random observations. Likewise, the accuracy of the spectral density is always better than the accuracy of tapered and windowed periodograms. Let the data themselves decide about their best representation, they can! Three types of time series models can be distinguished: autoregressive (AR), moving average (MA) and combined ARMA. The recent ability to identify an appropriate time series model for measured stochastic data has three causes: increased computational speed, finite sample order selection criteria, and developments in the reliability of time series algorithms. Time series models are excellent for random data, if the best model type and the best model order are known. With the new ARMAsel toolbox, that a priori information is no longer required. For unknown data characteristics, a large number of candidate models are computed. The ARMAsel Matlab® computer program automatically selects the best model order for each of the three model types and also the best model type.