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 _nd 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 compare our methods with the linear regression and historical mean methods according to an economic metric. In particular, we show how our methods can be used to deliver a trading strategy that beats the buy and hold strategy (and linear regression based alternatives) over our sample period.