Data adaptive ARMA modeling of time series

An algebraic characterization of ARMA random time series is presented. This characterization in turn gives rise to a time series modeling procedure which is a generalization of the so-called high performance method [1]-[14]. This new modeling procedure has been found to possess exceptional modeling capabilities which makes possible the generation of lower order, high quality ARMA spectral estimates from short data lengths. This capability is a consequence of the data smoothing achieved upon making a singular value decomposition of an extended autocorrelation matrix estimate.