Single multiplicative neuron artificial neural networks have different importance than many other artificial neural networks because they do not have complex architecture problem, too many parameters and they need more computation time to use. In single multiplicative neuron artificial neural network, it is assumed that there is a one data generation process for time series. Many time series need an assumption that they have two data generation process or more. Based on this idea, the threshold model structure can be employed in a single multiplicative neuron model artificial neural network for taking into considering data generation processes problem. In this study, a new artificial neural network type is proposed and it is called a threshold single multiplicative neuron artificial neural network. It is assumed that time series have two data generation processes according to the architecture of single multiplicative neuron artificial neural network. Training algorithms are proposed based on harmony search algorithm and particle swarm optimization for threshold single multiplicative neuron artificial neural network. The proposed method is tested by various time series data sets and compared with well-known forecasting methods by considering different error measures. Finally, the performance of the proposed method is evaluated by a simulation study.