70 Relative Performance of Neural Networks on Standard and Poor's 500 Index Prediction of Aggregate Sales

This paper explains the out-of-sample performance of neural networks relative to regression forecasts of aggregate sales based on the independent input Standard and Poor's (S&P) 500 composite price index. In a typical regression problem the goal is to find model parameters that yield the best linear approximation of the input output pairs. A neural network is typically a nonlinear fault tolerant parallel system that makes use of adjustable and highly redundant model parameters. The dynamic neural network models used were trained with the Levenburg-Marquardt backpropagation through time algorithm under supervised learning. Aggregate sales differences were found to be positively related to and lagged the S&P 500 differences by six months. The neural network models out-performed regression models on the out-of-sample forecasts of aggregate sales differences with the single model forecasts yielding the better results. The performance statistics used were correlation, root mean square, mean absolute error, and Theil inequality coefficient.