Artificial neural networks (ANNs) have been frequently used in forecasting problems in recent years. One of the most popular types of ANNs in these days is Pi-Sigma artificial neural networks (PS-ANNs). PS-ANNs have a high order ANN structure and they use both multiplicative and additive neuron models in their architecture. PS-ANNs produce superior forecasting performance because of their high order structure. PS-ANNs are affected negatively by an outlier or outliers in a data set because of having a multiplicative neuron model in their architecture. In this study, a new robust learning algorithm based on particle swarm optimization and Huber's loss function for PS-ANNs is proposed. To evaluate the performance of the proposed method, Dow Jones stock exchange and Australian beer consumption data sets are analyzed and the obtained results are compared with many ANNs types proposed in the literature. Besides, the performance of the proposed method in outlier cases is also investigated by injecting outliers into these data sets. It is seen that the proposed learning algorithm has a satisfying performance both the data have an outlier or outliers' case and original case.
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