Deep learning in finance in cross sectional sectional predictions for random forests

$$y_{i,t}={\alpha }_{i,t-1}+{\beta }_i^{\prime }$$

$${\alpha }_{i,t-1}=g_{\alpha ,t}(x_{i,t-1})$$

$$y_{i,t+1}\approx$$

$$aNT=\varphi NT+\eta NT+bNT$$

$$A_s-B_s\approx G_{\beta ,t}(X_{t-1})(f_s-\mathbb{E}{f}_s)$$

$$G_{\beta ,t}$$

$$A_s-B_s\approx G_{\beta ,t}(f_s-\mathbb{E}{f}_s)$$

$$R_t=X_{t,p}^{\prime }{\theta }_p+e_t$$

$$Risk(p)=\frac{1}{25}\sum _{s=1}^{25}(R_{T+s}-X_{T+s,p}^{\prime }$$

CRSP

1965-2018

one peridod head prediction

in sample decomposition- realized returns
$$\kappa$$

$$\mathrm{K}$$

$$R_{\hat{y}}^2$$

$$R_{{\beta }^{\prime }F}^2$$

$$R_{\alpha }^2$$

$$R_{{\beta }^{\prime }(F+\lambda )}$$

$$R_{\hat{y}}^2\approx R_{\beta }$$

$${\hat{r}}_{\alpha ,t}=\frac{1}{N_t}{\widehat{g_{\alpha }}}^{{}^{\prime }}\widehat{y_t}$$

$$K,R_{\hat{y}}^2$$