Estimation in Partial Linear Models under Long-Range Dependence

We consider estimation of the linear component of a partial linear model when errors and regressors have long-range dependence. Assuming that errors and the stochastic component of regressors are linear processes with i.i.d. innovations, we closely examine the asymptotic properties of the OLS estimator calculated from nonparametric regression residuals. Especially we derive the asymptotic distribution when the combined long-range dependence of errors and the stochastic component of regressors exceeds a level. The case is not considered in any previous works on partial linear models. We also improve the existing results when the combined long-range dependence is less than the level.