Estimation of semi-parametric additive coefficient model

In the multivariate regression setting, we propose a flexible varying coefficient model in which the regression coefficients of some predictors are additive functions of other predictors. Marginal integration estimators of the coefficients are developed and their asymptotic properties investigated. Under ββ-mixing, it is found that the estimators of the parameters in the regression coefficients have rate of convergence 1/n, and the nonparametric additive components are estimated at the same rate of convergence as in univariate smoothing. A data-driven bandwidth selection method is developed based on asymptotic considerations. Its effectiveness is confirmed in a Monte-Carlo study. The procedure is applied to the real German GNP and Wolf's Sunspot data, where the semi-parametric additive coefficient model demonstrates superior performance in terms of out-of-sample forecasts.