Advantages of direct input-to-output connections in neural networks: The Elman network for stock index forecasting

Abstract

The Elman neural network (ElmanNN) is well-known for its capability of processing dynamic information, which has led to successful applications in stock forecasting. In this paper, we introduce direct input-to-output connections (DIOCs) into the ElmanNN and show that the proposed Elman neural network with DIOCs (Elman-DIOCs) significantly out-performs the original ElmanNN without such DIOCs. Four different global stock indices, i.e., the Shanghai Stock Exchange (SSE) Composite Index, the Korea Stock Price Index (KOSPI), the Nikkei 225 Index (Nikkei225), and the Standard & Poor’s 500 Index (SPX), are used to demonstrate the affecacy of the Elman-DIOCs in time-series prediction. We systematically evaluate 8 models, depending whether or not there are hidden layer biases, whether or not there are output layer biases, and whether or not there are DIOCs. The experimental results show that DIOCs lead to much better prediction accuracy, while requiring fewer than a half of the hidden neurons. Take the SPX index, for example - the root mean squared error (RMSE) and the mean absolute error (MAE) of the Elman-DIOCs are improved by 44.2% and 41.1%, respectively, compared to the ElmanNN, and 65.6% and 60.8%, respectively, compared to the multi-layer perceptron (MLP). We argue that (1) DIOCs can always help to improve accuracy, while reducing network complexity and computational burden, as long as the problem at hand (either regression or classification) has linear components, and (2) most real-world applications contain linear components. Therefore DIOCs will be almost always beneficial in any types of neural networks for classification or regression. We also point out that in rare cases where the problem at hand is entirely nonlinear, DIOCs should not be used.