Multivariate regression estimation local polynomial fitting for time series

We consider the estimation of the multivariate regression function m(x1, …, xd) = E[ψ(Yd)|X1 = x1, …, Xd = xd], and its partial derivatives, for stationary random processes Yi, Xi using local higher-order polynomial fitting. Particular cases of ψ 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 ϱ-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.