MULTIVARIATE LOCAL POLYNOMIAL REGRESSION FOR TIME SERIES: UNIFORM STRONG CONSISTENCY AND RATES by

Local high-order polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and of its partial derivatives, for stationary random processes {Yi , Xi}. The function ψ may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of R d , along with rates, are established for the regression function and its partial derivatives for strongly mixing processes. Short Title: Multivariate Regression Estimation.