In this study, we propose a new genetic algorithm that uses a statistical-based chromosome replacement strategy determined by the empirical distribution of the objective function values. The proposed genetic algorithm is further used in the training process of a multiplicative neuron model artificial neural network. The objective function value for the genetic algorithm is the root mean square error of the multiplicative neuron model artificial neural network prediction. This combination of methods is proposed for a particular type of problems, that is, time-series prediction. We use different subsets of three stock exchange time series to test the performance of the proposed method and compare it against similar approaches, and the results prove that the proposed genetic algorithm for the multiplicative neuron model of the artificial neural network works better than many other artificial intelligence optimization methods. The ranks of the proposed method are 1.78 for the Nikkei data sets, 1.55 for the S&P500 data sets and 1.22 for the DOW JONES data sets for data corresponding to different years, according to the root mean square error, respectively. Moreover, the overall mean rank is 1.50 for the proposed method. Also, the proposed method obtains the best performance overall as well as the best performance for all the individual tests. The results certify that our method is robust and efficient for the task investigated.