The model adequacy and input significance tests have not been proposed as features for the specification of a single multiplicative neuron model artificial neural networks in the literature. Moreover, there is no systematic approach based on hypothesis tests for using single multiplicative neuron model artificial neural networks for forecasting purposes like classical time series forecasting methods. In this study, new methods are proposed to solve these problems. The performance of the proposed test procedures is investigated in a simulation study. According to simulation results, the proposed tests have very good performance. Moreover, the test procedures are illustrated by using two real-world examples. The second contribution of the paper is that an automatic forecasting method is proposed based on input significance and model adequacy tests and the particle swarm optimization-based learning algorithm. The proposed automatic forecasting method is applied to M4 competition hourly data sets, and it is the best pure machine learning method among others in the competition. The proposed automatic forecasting method is more accurate than all benchmarks, such as MLP, RNN, and ETS, which were proposed by the competition organizers.