Local Linear Estimation of a Nonparametric Cointegration Model

The nonparametric local linear method has superior properties compared with the local constant method in the independent and weak dependent data setting, see e.g. Fan and Gijbels (1996). Recently, much attention has been drawn to the nonparametric models with nonstationary data. Wang and Phillips (2009a) studied the asymptotic property of a local constant estimator of a nonparametric regression model with a nonstationary I(1) regressor. Sun and Li (2011) show a surprising result that for a semiparamtric varying coefficient model with nonstationary I(1) regressors, the local linear estimator has a faster rate of convergence than the local constant estimator. In this article, we study the asymptotic behavior of the local linear estimator for the same nonparametric regression model as considered by Wang and Phillips (2009a). We focus on the derivation of the joint asymptotic result of both the unknown regression function and its derivative function. We also examine the performance of the local linear estimator with the bandwidth selected by the data driven least squares cross validation (LS-CV) method. Simulation results show that the local linear estimator, coupled with the LS-CV selected bandwidth, enjoys substantial efficiency gains over the local constant estimator.