A Note on AIC and TIC for Model Selection

Yong Li, Zhou Wu, Jun Yu and Tao Zeng
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Yong Li: Renmin University of China
Zhou Wu: Zhejiang University
Tao Zeng: Zhejiang University

No 202420, Working Papers from University of Macau, Faculty of Business Administration

Abstract: This note gives a rigorous justification to Akaike information criterion (AIC) and Takeuchi information criterion (TIC). The existing literature has shown that, when the candidate model is a good approximation of the true data generating process (DGP), AIC is an asymptotic unbiased estimator of the expected Kullback-Leibler divergence between the DGP and the plug-in predictive distribution. When the candidate model is misspecified, TIC can be regraded as a robust version of AIC with its justification following a similar line of argument. However, the justifications in current literature are predominantly confined to the iid scenario. In this note, we establish the asymptotic unbiasedness of AIC and TIC under certain regular conditions. These conditions are applicable in various scenarios, encompassing weakly dependent data.

Keywords: AIC; TIC; Expected loss function; Kullback-Leibler divergence; Model selection; Plug-in predictive distribution; weakly dependent data. (search for similar items in EconPapers)
JEL-codes: C11 C22 C25 C32 C52 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2024-11
New Economics Papers: this item is included in nep-ecm and nep-ets
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