Can Multistep Nonparametric Regressions Beat Historical Average in Predicting Excess Stock Returns?

Several economic and financial variables are said to have predictive power over excess stock returns. Empirically there is little consensus among academics, whether these variables have predictive power or not. Results are often sensitive to the econometric model of choice. The econometric models can produce biased results due to the high degree of persistence in predictive variables. Apart from high persistence, the relationship between stock return and the predictive variable may also be misspecified in the model. In order to address possible non-linearities and endogeneity between the residuals and persistent independent variables in predictive regressions, multi-step non-parametric and semiparametric regressions are explored in this paper. In these regressions, the conditional mean and the residuals are estimated separately and then added to obtain the predicted excess stock returns. Goyal and Welch's (2008) predictive variables are used to predict excess S&P 500 returns. The predictive performance of both in-sample and out-of-sample of the two proposed models are compared with the historical average, Ordinary Least Squares (OLS) and non-parametric regressions. The performance of the models is evaluated using Root Mean Squared Errors (RMSEs). The explored models, particularly the two-step nonparametric model, outperform the compared models in-sample. Out-of-sample several variables are found to have predictive ability.