Multi-objective learning of neural network time series prediction intervals

In this paper, we address multi-step ahead time series Prediction Intervals (PI). We extend two Neural Network (NN) methods, Lower Upper Bound Estimation (LUBE) and Multi-objective Evolutionary Algorithm (MOEA) LUBE (MLUBE), for multi-step PI. Furthermore, we propose two new MOEA methods based on a 2-phase gradient and MOEA based learning: M2LUBET1 and M2LUBET2. Also, we present a robust evaluation procedure to compare PI methods. Using four distinct seasonal time series, we compared all four PI methods. Overall, competitive results were achieved by the 2-phase learning methods, in terms of both predictive performance and computational effort.This work was supported by COMPETE: POCI-01-0145FEDER-007043 and FCT Fundação para a Ciência e Tecnologia within the Project Scope: UID/CEC/00319/2013, and project: NORTE-01-0247-FEDER-017497.