An Enriched Prediction Intervals Construction Method with Hybrid Intelligent Optimization

Prediction intervals (PIs), within which future observations of time series are expected to fall, are a powerful method for uncertainty modeling and forecasting. This paper presents the construction of optimal PIs using an enriched extreme learning machine (ELM)-based method. While quality evaluation indices for PIs on reliability and sharpness of prediction results have been defined in the literature, this paper proposes a new PIs evaluation index, robustness, which focuses on the forecasting error. Combined with the above three indices, a more comprehensive objective function is then formed for optimal PIs construction. The paper also proposes an efficient hybrid quantum-behaved particle swarm optimization method with bacterial foraging mechanism to optimize the parameters in the ELM model. The effectiveness of the additional robustness index and the proposed improved ELM approach in determining higher quality PIs is demonstrated by applying them to PIs constructions for the cases of prediction in different datasets.