Identification of Nonlinear Additive Autoregressive Mod- els

We propose a lag selection method for nonlinear additive autoregressive models based on spline estimation and the BIC criterion. The additive structure of the autoregression function is used to overcome the “curse of dimensionality”, while the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the proposed method. Comprehensive Monte Carlo study demonstrates good performance of the proposed method and substantial computational advantage over existing local polynomial based methods. Consistency of the BIC based lag selection method is established under the assumption that the observations are from a stochastic process that is strictly stationary and strongly mixing, which provides the first theoretical result of this kind for spline smoothing of weakly dependent data.