A stepwise testing procedure using Lagrangian multiplier tests is developed to determine the order of an ARMA-process. The strong consistency of this procedure under slightly weaker assumptions than in Hannan (1980) (proof of the consistency of the order estimators obtained via BIC) is proved.
"Order Estimation in ARMA-Models by Lagrangian Multiplier Tests." Ann. Statist. 11 (3) 872 - 885, September, 1983. https://doi.org/10.1214/aos/1176346253