Identification of Nonlinear Additive Autoregressive Models

Jianhua Z. Huang and Lijian Yang

Abstract:

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 their 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.