Improved model order determination by information theoretic criteria

An approach for using minimum description length (MDL) criterion for autoregressive moving-average (ARMA) models and autoregressive models with exogenous input (ARX) is formulated in terms of the minimum eigenvalue of a covariance matrix. It is shown that as the number of observation data points increases without bound, the MDL criterion reduces to a simple monotonic nonlinear transformation of this minimum eigenvalue. Consequently, it is shown that in the asymptotic case the minimum-eigenvalue provides exactly the same information as the original MDL formulation. Additionally, the approach does not require prior estimation of the model parameters, and thus has the potential for significantly reduced computation compared to other MDL-based model order determination schemes. The approach´s application to the selection of ARMA and ARX model orders is discussed, and several numerical examples are presented