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

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.