Particle swarm optimization for construction of neural network-based prediction intervals

Point forecasts suffer from unreliable and uninformative problems when the uncertainty level increases in data. Prediction intervals (PIs) have been proposed in the literature to quantify uncertainties associated with point forecasts. In this paper, a newly introduced method called Lower Upper Bound Estimation (LUBE) (Khosravi et al., 2011, [1]) is applied and extended for construction of PIs. The LUBE method adopts a neural network (NN) with two outputs to directly generate the upper and lower bounds of PIs without making any assumption about the data distribution. A new width evaluation index that is suitable for NN training is proposed. Further a new cost function is developed for the comprehensive evaluation of PIs based on their width and coverage probability. The width index is replaced by the new one and PSO with mutation operator is used for minimizing the cost function and adjusting NN parameters in the LUBE method. By introducing these two changes we observe dramatic improvements in the quality of results and speed. Demonstrated results for six synthetic and real-world case studies indicate that the proposed PSO-based LUBE method is very efficient in constructing high quality PIs in a short time.