Selection of NARX models estimated using weighted least squares method via GIC-based method and l₁-norm regularization methods

We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike's information criterion, Schwarz's Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l₁-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875-890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwisemethod with Subsampling; (b) in the latter two methods, we employ the l₁-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.