In the literature, the multiplicative neuron model artificial neural networks are trained by gradient-based or some artificial intelligence optimization algorithms. It is well known that the hybrid algorithms give successful results than classical algorithms in the literature and the use of hybrid systems increase day by day. From this point of view, different from other studies contribute to multiplicative neuron model artificial neural networks, the properties of an artificial intelligence optimization technique, artificial bat algorithm, and a gradient-based algorithm, backpropagation learning algorithm, is used together firstly by using the proposed method in this study. Thus, both a derivative and a heuristic algorithm were used together firstly for multiplicative neuron model artificial neural networks. The proposed method is applied to three well-known different real-world time series data. The performance of the proposed method is both compared with gradient-based optimization algorithms, some artificial optimization algorithms used for the training of artificial neural networks and some popular analyze methods. The analysis results show that the proposed hybrid method has superior performance than other methods.