1. The model error for AR and ARMA processes, and 2. The ‘little bootstrap’ method for autoregressive model selection

There are two consecutive papers, concerning one subject. First, the model error for the regression problem defined by Breiman is considered. The paper introduces the definition of the model error for AR and ARMA processes. The true model error for AR and ARMA processes is unknown being a random variable. Then, in the second paper the application of little bootstrap method is shown for the autoregressive model selection. The definition of the model for autoregressive process, introduced in the previous paper, is used to perform model selection. Because the true model error is unknown, the use of this criterion must be based on model error estimates. We use the little bootstrap method to estimate the model error. Simulation results are considered in the paper. We compare the little bootstrap method with two other model selection procedures. Comparison is made with the method based on AICC statistic and the Durbin–Levinson algorithm.