Neural network linear forecasts for stock returns Angelos Kanas, страница 8

This Table reports the estimated coefficients from equations: E_1,t=₀+₁D_t+w_t and E_2,t=d₀+d₁D_t+u_t, where 1=ANN model, 2=linear model, E_i is the forecast error for model i (i=1, 2), and D is the difference of the forecasts from the two models. The values in parentheses are heteroskedasticity-robust t-statistics. * Statistically significant coefficient at the 5% level.

On the basis of the forecast encompassing tests, the nonlinear ANN-based monthly stock return forecasts are preferable to the linear model-based forecasts for both the DJ and the FT indices. This result indicates that the inclusion of nonlinear terms in the linear model, as is done by the ANN model, is important in terms of out-of-sample monthly stock return forecasting, and is consistent with the view that the relation between stock return and fundamental variables is nonlinear and not linear.

5. CONCLUSIONS

The paper compared out-of-sample forecasts of monthly return from both DJ and FT indices generated by two competing models, namely a linear model and a nonlinear ANN model. We consider two fundamental variables as the explanatory variables in the linear model and the input variables in the ANN model, namely the trading volume and the dividend. The comparison of out-of-sample forecasts is carried out on the basis of two approaches: directional accuracy and forecast encompassing. Whilst both models perform badly in terms of predicting the directional change of the two indices, the ANN forecasts can explain the forecast errors of the linear model while the linear model cannot explain the forecast errors of the ANN for both indices. Thus, the ANN forecasts are preferable to linear forecasts, indicating 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 underlying relation between stock returns and fundamentals is nonlinear.

ACKNOWLEDGEMENTS

I wish to thank Giorgos Kouretas, Yue Ma and Laurence Copeland for helpful comments and discussions in preparing this draft. Partial financial assistance from the Research Committee, University of Crete is gratefully acknowledged. The usual disclaimer applies.

NOTES

1.  For a discussion of MLPs, see Campbell et al. (1998).

2.  To simplify the presentation of the MLP in Figure 1, the variable X3 has been omitted. The signals that leave from X3 are exactlythe same as those leaving from X1 and X2.

3.  The algebraic expression of this function is: F(u)=1/[1+exp(−u)].

4.  This is known as ‘supervised’ learning. The contrast, in unsupervised learning there are no target values (i.e. observed values of the output variable), and the training process attempts to distil a subset of the input variables which explain most of the variance of the complete set of input variables. Unsupervised learning is a form of nonlinear principal component analysis.