Bridging AIC and BIC: a new criterion for autoregression
This work addresses model selection in time series analysis, offering a more flexible and robust alternative to classical criteria like AIC and BIC, though it appears incremental as it builds on existing methods.
The authors introduced a new criterion for selecting the order of autoregressive models in time series data, combining benefits of AIC and BIC to adaptively achieve consistency or efficiency based on the true model, with numerical results demonstrating its adaptivity across datasets.
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.