Relations between information criteria for model-structure selection Part 3. Strong consistency of the predictive least squares criterion

Abstract

The strong consistency of the predictive least squares (PLS) structure selection criterion is proved for ARMA processes. The advantage of the PLS criterion defined by Rissanen and Wertz (1985) over the BIC, φ or AIC criteria is that it is an online information criterion obtained by simple calculation. The strong consistency is proved for the case of the maximum likelihood estimator, while in simulations the likelihood estimator is substituted by its recursive maximum likelihood estimator approximation. Repeated simulations show the small sample comparison of the PLS and BIC criteria.