Multivariate Local Polynomial Regression for Time Series:uniform Strong Consistency and Rates

Abstract. Local high‐order polynomial fitting is employed for the estimation of the multivariate regression function m (x 1, … x d) = E φ (Y d) φ X 1 = x 1, …, X d = x d, and of its partial derivatives, for stationary random processes Y i, X i. The function φ 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.