Forecasting time series with optimal neural networks using multi-objective optimization algorithm based on AICc

In this letter, time series forecasting using optimal neural networks with optimal performance of generalization and stability is studied. After analyzing the reasons for overfitting and instability of neural networks, in order to find the optimal NNs (neural networks) architecture, we consider minimizing three objective index: average training AICc (ATRAICc), average testing AICc (ATEAICc) and testing error variance AICc (VAAICc) based on Akaike information criterion theory. Then we built a multi-objective optimization model and proved the existence and uniqueness theorem of optimal solution. After determining the searching interval, a multi-objective optimization algorithm for optimal neural network architecture based on AICc (ONNAICc) with optimal generalization and stability is constructed to solve above model. Some experiments with simple sample datasets A and B from simple function, complicated stock market time series datasets C and highly nonlinear tungsten price datasets D are taken to verify the validity of the model. And some performances of the presented ONNAICc algorithm are compared with the traditional prediction algorithms, such as AR, ARMA, ordinary BP, SVM, verified the superiority and accuracy of the proposed ONNAICc algorithm. The technical details, proofs and evaluations can be found in the support information.