Model identification using the Efficient Determination Criterion

TL;DR

This paper extends the Efficient Determination Criterion (EDC) to partially nested models, providing a unified approach for model order identification and establishing strong consistency results, including for BEKK GARCH models.

Contribution

It generalizes the EDC to a broader class of models, offering a unified framework for consistent order estimation across various complex models.

Findings

EDC is generalized to partially nested models.

Strong consistency of BIC-based order estimator is proven for BEKK GARCH.

Framework unifies model order identification methods.

Abstract

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.