Analytic finite sample criteria for autoregressive-model order selection

Analytic finite sample equivalents for autoregressive-model order selection criteria are introduced. These equivalents are based on approximately analytic formulas and can be used in the case where the estimation method is least-squares-forward. In fact, these criteria are approximately analytic equivalents of existing empirical finite sample criteria. The performance of the finite sample criteria is better than that of their asymptotic equivalents in the finite sample case. In the large sample case, the criteria introduced in this paper converge to the existing criteria.