<p>Due to their flexible model structures and their success in nonlinear modelling, artificial neural networks provide good alternatives for solving the forecasting problem. It is seen that different artificial neuron models can positively affect the forecasting performance and pave the way for the creation of new artificial neural network models. In this study, a new artificial neural network with an architecture based on multiplicative and additive neuron models and using the feedback logic in exponential smoothing methods is presented. The training algorithm of the proposed neural network is based on particle swarm optimization using a dynamic fitness function that gives more weight to recent observations. The performance of the proposed new neural network is investigated with the help of statistical hypothesis tests in comparison with established methods in the literature on Nasdaq stock exchange time series. As a result of the study, it is empirically observed that the proposed neural network has a successful forecasting performance.</p>