Spline-backfitted kernel smoothing of nonlinear additive autoregression model

Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the ``curse of dimensionality.'' Under rather weak conditions, we propose spline-backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high-dimensional time series, and theoretically reliable so inference can be made on the component functions with confidence. Simulation experiments have provided strong evidence that corroborates the asymptotic theory.Comment: Published in at http://dx.doi.org/10.1214/009053607000000488 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org