Nonparametric Predictive Regressions for Stock Return Prediction

We propose two new nonparametric predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series. We define estimation methods and establish the large sample properties of these methods in the short horizon and the long horizon case. We apply our methods to stock return prediction using a number of standard predictors such as dividend yield. The empirical results show that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we find that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting. We also propose a trading strategy based on our methodology and show that it beats the buy and hold stategy provided the tuning parameters are well chosen.