Neural Network for Partially Linear Time Series Models

This paper proposes an iterative neural network estimate (INNE) for the partially linear (PL) time series models. It is shown that the parametric coefficients of INNE are √n consistent and asymptotically normal, and the convergence rate of nonparametric function is O(n ^−α), where α is a constant independent of the dimension of the nonparametric part. To obtain the INNE, an initial estimator of the parametric coefficients is proved to be asymptotically normal. Our estimation procedure circumvents “curse of dimensionality” incurred by the traditional nonparametric smoothing approach. A simulation study is carried out to assess the performance of the INNE in the finite samples. It is shown that our INNE outperforms the traditional nonparametric smoothing approach according to several criteria used in this paper. One real example is used to illustrate our approach.