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.
"Spline-backfitted kernel smoothing of nonlinear additive autoregression model." Ann. Statist. 35 (6) 2474 - 2503, December 2007. https://doi.org/10.1214/009053607000000488