Abstract
We consider in this article a class of nonlinear additive autoregressive models with exogenous variables for nonlinear time series analysis and propose two modeling procedures for building such models. The procedures proposed use two backfitting techniques (the ACE and BRUTO algorithms) to identify the nonlinear functions involved and use the methods of best subset regression and variable selection in regression analysis to determine the final model. Simulated and real examples are used to illustrate the analysis.