A Nonparametric Additive Model for Stock Returns with

The paper proposes a class of nonlinear additive predictive regression models, which improve the linear predictive regression models when the predictors are highly persistent or nonstationary. We use local-to-unity to describe the persistency of the predictor series. The main novelties of the paper are the estimation and test for the nonparametric additive model within the framework of nearly-integrated predictors. With Monte Carlo simulations, we find that the nonparametric additive model outperforms the linear benchmark model for most of the time. By combining the generalized likelihood ratio test with wild bootstrap, we find evidence for stock return predictabilities of different frequen-cies with persistent predictors as well as nonlinear relationships between the predictor series and the return series. Simulation studies also show that the test has reasonable statistical performance. We apply the nonparametric additive model to S&P 500 Composite Index returns, and we observe that our model captures the variations in the index returns well over 1968 to 2008. In addition, we find that there exists predictability of the S&P index returns as well as nonlinear relationship between the predictors and the index returns