  In the realm of the model selection context, Akaike's and Schwarz's
information criteria, AIC and BIC, have been applied successfully for decades
for model order identification. The Efficient Determination Criterion (EDC) is
a generalization of these criteria, proposed originally to define a strongly
consistent class of estimators for the dependency order of a multiple Markov
chain. In this work, the EDC is generalized to partially nested models, which
encompass many other order identification problems. Based on some assumptions,
a class of strongly consistent estimators is established in this general
environment. This framework is applied to BEKK multivariate GARCH models and,
in particular, the strong consistency of the order estimator based on BIC is
established for these models.
