Combination of Biased Artificial Neural Network Forecasters

Abstract

Artificial neural networks (ANN) have been paramount for modeling and forecasting time series phenomena. In this way it has been usual to suppose that each ANN model generates a white noise as prediction error. However, mostly because of disturbances not captured by each model, it is yet possible that such supposition is violated. On the other hand, to adopt a single ANN model may lead to statistical bias and underestimation of uncertainty. The present paper introduces a two-step maximum likelihood method for correcting and combining ANN models. Applications involving single ANN models for Dow Jones Industrial Average Index and S&P500 series illustrate the usefulness of the proposed framework.