A Weighted Sieve Estimator for Nonparametric Time Series Models With Nonstationary Variables

A novel and unified approach is proposed in sieve estimation to tackle the issue of unbounded support of variables in nonparametric regression models. The model em- braces time trend and both stationary and nonstationary variables that are allowed to be correlated. This approach is introduced via weighted least squares, and it im- proves the existing methodology and alleviates the requirement of related moments. As a byproduct, the requirement on the α-mixing coefficients for stationary process is reduced to the least in comparison with the literature. Central limit theorems are established for the sieve estimator and other related quantities. Monte Carlo simulation confirms the theoretical results and an empirical study is provided