Order selection for ARMA parametric spectrum estimation

Conventional criteria of order selection have concentrated on so called "consistency" of selecting the "true" order. However, the "consistent" order model, in general, differs from the optimal model that produces the best application effect. In an effort towards an optimal order selection for the ARMA parametric spectrum estimation, the model spectral distance (MSD) is proposed to measure the difference of two concerned models. The distinction between the consistent and the optimal orders is illustrated by simulation examples in terms of the MSD. The parameter estimation error is evaluated through the MSD. The MSD from the lower to the higher order model is utilized as a measurement of possible accuracy improvement and the difference between the higher model associated parameter estimation error and the lower model associated parameter estimation error is used as a measure of possible accuracy loss, when the order increases. Thus, a novel order selection criterion, namely the model spectral distance criterion (MSDC) is proposed based on a comparison between this possible improvement and loss. Theoretical work has shown that the orders selected by this criterion are optimal or suboptimal. Its excellent performance has also been shown by extensive simulations.