Multivariate regression estimation - Local polynomial fitting for time series

We consider the estimation of the multivariate regression function m(x(1), ..., x(d)) = E [Psi(Y-d)\X(1) = x(1), ..., X(d) = x(d)], and its partial derivatives, for stationary random processes {Y-i, X(i)} using local higher-order polynomial fitting. Particular cases of Psi yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and rho-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.