Selection of order and type of time series models estimated from reduced statistics

Time series modeling is a parametric solution for spectral analysis. If a time series of N observations is given, it is possible to select automatically the type and order of a time series model. That selected model is an adequate representation of the statistically significant spectral details in the observed process. If N is very large, reduced statistics estimators, computed from much less than N characteristics of the data are computationally attractive. The reduced statistics information can consist either of a number of covariance estimates or of a long AR (autoregressive) model. Estimated ARMA (autoregressive moving average) models, however, can have a poor statistical accuracy. A first improvement is found by defining the best dimension for the reduced statistic to be used in the actual computations. The accuracy is also improved by using four different types of initial ARMA estimates. Afterwards, it is possible to select automatically which initial estimates were most favorable in the present case. The fit of estimated models to a very long autoregressive model is used for the selection of the type of initial ARMA estimates. The same principle is used to select the best model type, AR, MA or ARMA and the best model order.