Hybridization of the probabilistic neural networks with feed-forward neural networks for forecasting

Feed-forward neural networks (FFNNs) are among the most important neural networks that can be applied to a wide range of forecasting problems with a high degree of accuracy. Several large-scale forecasting competitions with a large number of commonly used time series forecasting models conclude that combining forecasts from more than one model often leads to improved performance, especially when the models in the ensemble are quite different. In the literature, several hybrid models have been proposed by combining different time series models together. In this paper, in contrast of the traditional hybrid models, a novel hybridization of the feed-forward neural networks (FFNNs) is proposed using the probabilistic neural networks (PNNs) in order to yield more accurate results than traditional feed-forward neural networks. In the proposed model, the estimated values of the FFNN models are modified based on the distinguished trend of their residuals and optimum step length, which are respectively yield from a probabilistic neural network and a mathematical programming model. Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than FFNN models. Therefore, it can be applied as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.