Comparing linear and nonlinear forecasts for stock returns

Abstract

We compare the out-of-sample performance of monthly returns forecasts for two indices, namely the Dow Jones (DJ) and the Financial Times (FT) indices. A linear and a nonlinear artificial neural network (ANN) model are used to generate the out-of-sample competing forecasts for monthly returns. Stationary transformations of dividends and trading volume are considered as fundamental explanatory variables in the linear model and the input variables in the ANN model. The comparison of out-of-sample forecasts is done on the basis of forecast accuracy, using the Diebold and Mariano test [J. Bus. Econ. Stat. 13 (1995) 253.], and forecast encompassing, using the Clements and Hendry approach [J. Forecast. 5 (1998) 559.]. The results suggest that the out-of-sample ANN forecasts are significantly more accurate than linear forecasts of both indices. Furthermore, the ANN forecasts can explain the forecast errors of the linear model for both indices, while the linear model cannot explain the forecast errors of the ANN in either of the two indices. Overall, the results indicate that the inclusion of nonlinear terms in the relation between stock returns and fundamentals is important in out-of-sample forecasting. This conclusion is consistent with the view that the relation between stock returns and fundamentals is nonlinear.