Effectiveness of Stochastic Neural Network for Prediction of Fall or Rise of TOPIX

Stochastic neural network is a hierarchical network of stochastic neurons which emit 0 or 1 with the probability determined by the values of inputs. We have developed an efficient training algorithm so as to maximize the likelihood of such a neural network. This algorithm enables us to apply the stochastic neural network to a practical problem like prediction of fall or rise of Tokyo Stock Price Index (TOPIX). We trained it with the data from 1994 to 1996 and predicted the fall or rise of 1 day ahead of TOPIX for the period from 1997 to 2000. The result is quite promising. The accuracy of the prediction of the stochastic network is the 60.28%, although those of non-stochastic neural network, autoregressive model and GARCH model are 50.02, 51.38 and 57.21%, respectively. However, the stochastic neural network is not so advantageous over other networks or models for prediction of the TOPIX used for training. This means that the stochastic neural network is less over fitting to the training data than others, and results in the best prediction. We will demonstrate how the stochastic neural network learns well non-linear structure behind of the data in comparison to other models or networks, including Generalized Linear model (GLM).