Local high-order polynomial fitting is employed for the estimation of the multivariate regression function rn(x1, . . ., xd) = E{v(Yd)lXl = XI, . . ., Xd = x d } . and of its partial derivatives, for stationary random processes { K, T.}. The function may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of Rd, along with rates, are established for the regression function and its partial derivatives for strongly mixing processes.

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Local polynomial ®tting 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 ®tting for dependent data. In this paper, we study the problem of estimating conditional mean functions and their derivatives via a local polynomial ®t. 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 r r-mixing processes.

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