With the levels of confidence and system complexity, interval forecasts and entropy analysis can deliver more information than point forecasts. In this paper, we take receivers’ demands as our starting point, use the trade-off model between accuracy and informativeness as the criterion to construct the optimal confidence interval, derive the theoretical formula of the optimal confidence interval and propose a practical and efficient algorithm based on entropy theory and complexity theory. In order to improve the estimation precision of the error distribution, the point prediction errors are STRATIFIED according to prices and the complexity of the system; the corresponding prediction error samples are obtained by the prices stratification; and the error distributions are estimated by the kernel function method and the stability of the system. In a stable and orderly environment for price forecasting, we obtain point prediction error samples by the weighted local region and RBF (Radial basis function) neural network methods, forecast the intervals of the soybean meal and non-GMO (Genetically Modified Organism) soybean continuous futures closing prices and implement unconditional coverage, independence and conditional coverage tests for the simulation results. The empirical results are compared from various interval evaluation indicators, different levels of noise, several target confidence levels and different point prediction methods. The analysis shows that the optimal interval construction method is better than the equal probability method and the shortest interval method and has good anti-noise ability with the reduction of system entropy; the hierarchical estimation error method can obtain higher accuracy and better interval estimation than the non-hierarchical method in a stable system.
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