An Improved Divergence Information Criterion for the Determination of the Order of an AR Process

Abstract

In this article we propose a modification of the recently introduced divergence information criterion (DIC, Mattheou et al., 2009) for the determination of the order of an autoregressive process and show that it is an asymptotically unbiased estimator of the expected overall discrepancy, a nonnegative quantity that measures the distance between the true unknown model and a fitted approximating model. Further, we use Monte Carlo methods and various data generating processes for small, medium, and large sample sizes in order to explore the capabilities of the new criterion in selecting the optimal order in autoregressive processes and in general in a time series context. The new criterion shows remarkably good results by choosing the correct model more frequently than traditional information criteria.

Keywords:

• AR process
• Information criterion
• Measure of divergence
• Model selection

Mathematics Subject Classification:

• 62M10
• 62F07
• 91B84
• 94A15

Acknowledgments

The authors express their appreciation to the editor and an anonymous referee for valuable comments and suggestions that greatly improved both the quality and the presentation of the manuscript. We especially thank the referee whose careful and thorough reading helped in identifying and correcting a typo in our Gauss program that was overlooked.

Notes

*Indicates best performance information criterion.

*Indicates best performance information criterion.

*Indicates best performance information criterion.

*Indicates best performance information criterion.

*Indicates best performance information criterion.

*Indicates best performance information criterion.