Artificial neural networks are frequently used to solve many problems and give successful results. Artificial neural networks, which we frequently encounter in solving forecasting problems, attract the attention of researchers with the successful results they provide. Pi-sigma artificial neural network, which is a high-order artificial neural network, draws attention with its use of both additive and multiplicative combining functions in its architectural structure. This artificial neural network model offers successful forecasting results thanks to its high-order structures. In this study, the pi-sigma artificial neural network was preferred due to its superior performance properties, and the particle swarm optimization algorithm was used for training the pi-sigma artificial neural network. To evaluate the performance of this preferred artificial neural network, monthly ready-made manufacturer sale shelled hazelnut quantities in Giresun province was used and a comparison was made with many artificial neural network models available in the literature. It has been observed that this tested method has the best performance among other compared methods.