Currently, as a typical problem in data mining, Times Series Analysis and Prediction are facing continuously more applications on a wide variety of domains. Huge data collections are generated or updated from science, military, financial and environmental applications. Prediction of the future trends based on previous and existing values is of a high importance and various machine learning algorithms have been proposed. In this paper we discuss results of a new approach based on the moving average of the n ^th -order difference of limited range margin series terms. Based on our original approach, a new algorithm has been developed: performances on measurement records of sunspots for more than 200 years are reported and discussed. Finally, Artificial Neural Networks (ANN) are added for improving the precision of prediction by addressing the error of prediction in the initial approach.