Automatic identification of time-series models from long autoregressive models

Identification is the selection of the model type and of the model order by using measured data of a process with unknown characteristics. If the observations themselves are used, it is possible to identify automatically a good time-series model for stochastic data. The selected model is an adequate representation of the statistically significant spectral details in the observed process. Sometimes, identification has to be based on many less than N characteristics of the data. The reduced statistics information is assumed to consist of a long autoregressive (AR) model. That AR model has to be used for the estimation of moving average (MA) and of combined ARMA models and for the selection of the best model orders. The accuracy of ARMA models is improved by using four different types of initial estimates in a first stage. After a second stage, it is possible to select automatically which initial estimates were most favorable in the present case by using the fit of the estimated ARMA models to the given long AR model. The same principle is used to select the best type of the time-series models and the best model order. No spectral information is lost in using only the long AR representation instead of all data. The quality of the model identified from a long AR model is comparable to that of the best time-series model that can be computed if all observations are available.