Matrix algebraic selection of ARMA model order

A matrix algebraic method of order selection is proposed for ARMA time series modeling for situations in which both inputs and outputs are observed in additive noise with known variances. Such situations include observational studies in which all observations-those of both inputs and outputs-are erred and controlled experiments in which outputs are observed with error while inputs are observed without error. The proposed method is based on the eigenvalue structure of the covariance matrices associated with the observed data and performs well for short, data records at moderate SNRs.