Local polynomial estimation of regression functions for mixing processes

Local polynomial fitting has many exciting statistical properties which where established under i.i.d. setting. However, the need for non-linear time series modeling, constructing predictive intervals, understanding divergence of non-linear time series requires the development of the theory of local polynomial fitting for dependent data. In this paper, we study the problem of estimating conditional mean functions and their derivatives via a local polynomial fit. The functions include conditional moments, conditional distribution as well as conditional density functions. Joint asymptotic normality for derivative estimation is established for both strongly mixing and ρ-mixing processes.