Bridging AIC and BIC: A New Criterion for Autoregression

2017/06/20 by Jie Ding, Vahid Tarokh, Yuhong Yang · 98 citations
Engineering · Computer Science · Mathematics · #Control Systems and Identification #Blind Source Separation Techniques #Neural Networks and Applications #Akaike information criterion #Bayesian information criterion #Model selection #Information Criteria #Autoregressive model #Mathematics #Minimum description length #Deviance information criterion #Selection (genetic algorithm) #Series (stratigraphy) #Bayesian probability #Mathematical optimization #Algorithm #Computer science #Applied mathematics #Bayesian inference #Statistics #Artificial intelligence

paper · doi:10.1109/tit.2017.2717599

published in IEEE Transactions on Information Theory 64(6), 4024-4043 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2017/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

To address order selection for an autoregressive model fitted to time series data, we propose a new information criterion. It has the benefits of the two well-known model selection techniques: the Akaike information criterion and the Bayesian information criterion. When the data are generated from a finite-order autoregression, the Bayesian information criterion is known to be consistent, and so is the new criterion. When the true order is infinity or suitably high with respect to the sample size, the Akaike information criterion is known to be efficient in the sense that its predictive performance is asymptotically equivalent to the best offered by the candidate models; in this case, the new criterion behaves in a similar manner. Different from the two classical criteria, the proposed criterion adaptively achieves either consistency or efficiency depending on the underlying true model. In practice, where the observed time series is given without any prior information about the model specification, the proposed order selection criterion is more flexible and reliable compared with classical approaches. Numerical results are presented, demonstrating the adaptivity of the proposed technique when applied to various data sets.

Citations

• Regression and time series model selection in small samples
• Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
• Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series
• The Focused Information Criterion
• Order selection for same-realization predictions in autoregressive processes
• Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach
• Almost the Best of Three Worlds: Risk, Consistency and Optional Stopping for the Switch Criterion in Nested Model Selection

Cited by

• Regression model selection via log‐likelihood ratio and constrained minimum criterion
• Akaike information criterion [wikipedia]
• Model selection [wikipedia]

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• Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series