Abstract: After a brief review of several information-based and prediction-based model selection criteria, we extend Rissanen's accumulated prediction error criterion and Wei's Fisher information criterion (FIC) from linear to general stochastic regression models, which include ARMA models and nonlinear ARX models in time series analysis as special cases. Strong consistency of these model selection criteria is established under certain conditions and the FIC is also shown to be an asymptotic approximation to some Bayes procedure. The special case of ARMA models is then studied in detail, and theoretical analysis and simulation results show that the FIC compares favorably with other procedures in the literature.
Key words and phrases: Accumulated prediction error criterion, BIC, Fisher information criterion, FPE, Kullback-Leibler information.