A Convex Combination Approach for Artificial Neural Network of Interval Data

Abstract

As the conventional models for time series forecasting often use single-valued data (e.g., closing daily price data or the end of the day data), a large amount of information during the day is neglected. Traditionally, the fixed reference points from intervals, such as midpoints, ranges, and lower and upper bounds, are generally considered to build the models. However, as different datasets provide different information in intervals and may exhibit nonlinear behavior, conventional models cannot be effectively implemented and may not be guaranteed to provide accurate results. To address these problems, we propose the artificial neural network with convex combination (ANN-CC) model for interval-valued data. The convex combination method provides a flexible way to explore the best reference points from both input and output variables. These reference points were then used to build the nonlinear ANN model. Both simulation and real application studies are conducted to evaluate the accuracy of the proposed forecasting ANN-CC model. Our model was also compared with traditional linear regression forecasting (information-theoretic method, parametrized approach center and range) and conventional ANN models for interval-valued data prediction (regularized ANN-LU and ANN-Center). The simulation results show that the proposed ANN-CC model is a suitable alternative to interval-valued data forecasting because it provides the lowest forecasting error in both linear and nonlinear relationships between the input and output data. Furthermore, empirical results on two datasets also confirmed that the proposed ANN-CC model outperformed the conventional models.