Asymptotics for partly linear regression with dependent samples and ARCH errors: consistency with rates

Partly linear regression model is useful in practice, but little is investi gated in the literature to adapt it to the real data which are dependent an d conditionally heteroscedastic. In this paper, the estimators of the regre ssion components are constructed via local polynomial fitting and the large sample properties are explored. Under certain mild regularities, the condi tions are obtained to ensure that the estimators of the nonparametric compo nent and its derivatives are consistent up to the convergence rates which a re optimal in the i.i.d. case, and the estimator of the parametric componen t is root- n consistent with the same rate as for parametric model. The tec hnique adopted in the proof differs from that used and corrects the errors in the reference by Hamilton and Truong under i.i.d. samples.