Bridging AIC and BIC: a new criterion for autoregression

TL;DR

This paper introduces a new model selection criterion for autoregressive models that adaptively combines the benefits of AIC and BIC, offering robustness and flexibility in practical time series analysis.

Contribution

The proposed criterion adaptively achieves consistency or efficiency depending on the true model, improving robustness over classical methods.

Findings

The new criterion is consistent for finite order autoregressions.

It behaves like AIC when the true order is high or infinite.

Numerical results show improved performance across datasets.

Abstract

We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is 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 prediction 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 robust compared with classical approaches. Numerical results are presented demonstrating the adaptivity of the proposed technique when applied to various datasets.