Order Selection of Autoregressive Processes Using Bridge Criterion

A new criterion is introduced for determining the order of an autoregressive model fit to time series data. The proposed technique is shown to give a consistent and asymptotically efficient order estimation. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the true order of the autoregression is relatively large compared with the sample size, the Akaike information criterion is known to be efficient, and the new criterion behaves in a similar manner. When the true order is finite and small compared with the sample size, the Bayesian information criterion is known to be consistent, and so is the new criterion. Thus the new criterion builds a bridge between the two classical criteria automatically. In practice, where the observed time series is given without any prior information about the autoregression, the proposed order selection criterion is more flexible and robust compared with classical approaches. Numerical results are presented demonstrating the robustness of the proposed technique when applied to various datasets.