The influence of the penalty factor in order selection criteria

The quest in autoregressive model order selection is for the model with smallest prediction error. The possibilities of selecting a suboptimal order can be divided in overfitting and underfitting. In order selection criteria based on asymptotical large sample theory as well as in their finite sample counterparts, the penalty factor α can be considered as the balancing factor between overfit and underfit. An optimization of the value for the penalty factor is only effective, after a correction for the statistics of the finite observation length has been carried out, by using the results of the finite sample theory. A theoretical treatment is in asymptotic theory based on the true AR process order. To apply the reasonings to the practical situations, where only a finite number of observations has been measured, the optimal model order is introduced. It is defined as the order with lowest expected prediction error