Abstract — Time series prediction is a crucial task in many areas but the development of effective modeling and simulation methods to understand or predict the behavior of time dependent phenomena remains particularly difficult. In this paper we propose to use a Genetic Programming (GP) approach as a robust method for coping with problems in which finding a solution and its representation is difficult but evaluating the performance of a candidate solution is reasonably simple. A new methodology is applied in synergy with the GP process. The original time series is transformed in a multidimensional input space where a variable is assigned to each distinct time delay. Then, the method deals with scalar functions of N variables and subdivides the input space of N dimensions in two input spaces. This subdivision is realized by a new algorithm called Hyper-Volume Error Separation (HVES), able to divide the original input space according to the errors made by the best individual found in the early steps of the GP process. Our results show that coupling HVES with GP is an effective approach for this task and could be part of the toolbox of many analysts. Moreover the formulas obtained with the GP process could give better insights on time dependent phenomena. I.
