Since many of predictive financial variables are highly persistent and non-stationary, it is challenging econometrically to explore the predictability of asset returns. Predictability issues are generally addressed in parametric regressions [1,2] in which rates of asset returns are regressed against the lagged values of stochastic explanatory variables, but three limitations stand ahead [3-5]. This paper studies a predictive functional regression model for asset returns, which takes account of endogeneity and integrated or nearly integrated explanatory variables. The regression function is expressed in terms of distribution of the vector of the observable variables. Estimators are nonlinear functionals of a kernel estimator for the distribution of the observable variables [6]. We find that the estimators for the distribution of the unobservable random terms and the nonparametric function are consistent and asymptotically normal. This paper obtains the similar results in many literatures, for example [1-5], but in different method.