Summary: Consider the nonparametric regression model
where is an unknown regression function and assumed to be bounded and real valued on , ’s are known and fixed design points and ’s are assumed to be both dependent and non-identically distributed random variables.
This paper investigates the asymptotic properties of the general nonparametric regression estimator
where the weight function is of the form . The estimator is shown to be weak, mean square error, and universal consistent under very general conditions on the temporal dependence and heterogeneity of ’s. Asymptotic distribution of the estimator is also considered.