# Bridging AIC and BIC: A New Criterion for Autoregression

@article{Ding2018BridgingAA, title={Bridging AIC and BIC: A New Criterion for Autoregression}, author={Jie Ding and Vahid Tarokh and Yuhong Yang}, journal={IEEE Transactions on Information Theory}, year={2018}, volume={64}, pages={4024-4043} }

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…

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## References

SHOWING 1-10 OF 44 REFERENCES

### Order selection for same-realization predictions in autoregressive processes

- Computer Science
- 2005

This paper presents the first theoretical verification that AIC and its variants are still asymptotically elficient (in the sense defined in Section 4) for same-realization predictions, and shows that A IC also yields a satisfactory saute- realization prediction in finite samples.

### Parametric or nonparametric? A parametricness index for model selection

- Mathematics, Computer Science
- 2011

A measure, parametricness index (PI), is developed to assess whether a model selected by a potentially consistent procedure can be practically treated as the true model, which also hints on AIC or BIC is better suited for the data for the goal of estimating the regression function.

### PREDICTION/ESTIMATION WITH SIMPLE LINEAR MODELS: IS IT REALLY THAT SIMPLE?

- Computer ScienceEconometric Theory
- 2006

It turns out that it is not possible to share the pointwise adaptationproperty of BIC and the minimax-rate adaptation property of AIC by any model selection method, and when model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.

### PREDICTION‐FOCUSED MODEL SELECTION FOR AUTOREGRESSIVE MODELS

- Computer Science
- 2007

This work proposes an extension of the focused information criterion (FIC) for model‐order selection, with emphasis on a high predictive accuracy (i.e. the mean squared forecast error is low) and illustrates the possibility of using the FIC for purposes other than forecasting, and explores its use in an extended model.

### Finite sample criteria for autoregressive order selection

- MathematicsIEEE Trans. Signal Process.
- 2000

The special finite sample information criterion and combined information criterion are necessary because of the increase of the variance of the residual energy for higher model orders that has not been accounted for in other criteria.

### Catching up faster by switching sooner: a predictive approach to adaptive estimation with an application to the AIC–BIC dilemma

- Computer Science
- 2012

The catch‐up phenomenon is identified as a novel explanation for the slow convergence of Bayesian methods, which inspires a modification of the Bayesian predictive distribution, called the switch distribution, which solves the AIC–BIC dilemma for cumulative risk.

### Regression and time series model selection in small samples

- Mathematics
- 1989

SUMMARY A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small,…

### The Focused Information Criterion

- Mathematics
- 2003

A variety of model selection criteria have been developed, of general and specific types. Most of these aim at selecting a single model with good overall properties, for example, formulated via…

### Can the Strengths of AIC and BIC Be Shared

- Computer Science
- 2003

It is shown that in a rigorous sense, even in the setting that the true model is included in the candidates, the above mentioned main strengths of AIC and BIC cannot be shared.

### Some recent advances in time series modeling

- Mathematics
- 1974

The aim of this paper is to describe some of the important concepts and techniques which seem to help provide a solution of the stationary time series problem (prediction and model identification).…