We study asymptotic properties of estimators of parameter and non-parameter in a partially linear model in which errors are dependent. Using a difference-based and ordinary least square (DOLS) method, the estimator of an unknown parametric component is given and the asymptotic normality of the DOLS estimator is obtained. Meanwhile, the estimator of a nonparametric component is derived by the wavelet method, and asymptotic normality and the weak convergence rate of the wavelet estimator are discussed. Finally, the performance of the proposed estimator is evaluated by a simulation study.
Keywords: Asymptotic normality; Finite difference; Least square; NSD random variables; Partially linear model.