A novel method for time series prediction based on error decomposition and nonlinear combination of forecasters

Abstract

For time series prediction, hybrid systems that combine linear and nonlinear models can provide more accurate performance than a single model. However, the irregularity of the error series and the unknown nature of combinations of different forecasters may strongly impact the performance of hybrid systems. Therefore, in this paper, we propose a novel method for time series prediction, in which error decomposition and a nonlinear combination of forecasters are introduced. The proposed method performs the following: (i) linear modeling to obtain the error series, (ii) error decomposition by using variational mode decomposition (VMD), (iii) nonlinear modeling and a phase fix procedure for the error subseries, and (iv) a combination of forecasters through an appropriate combination function generated by a nonlinear model. By using the proposed method, this paper constructs two hybrid systems, in which the autoregressive integrated moving average (ARIMA) is used for linear modeling, and two artificial intelligence (AI) models, namely, the multilayer perceptron (MLP) and support vector regression (SVR), are used for nonlinear modeling and combination, respectively. Finally, four time series data sets, six evaluation metrics, two single models and thirteen hybrid systems are used to assess the effectiveness of the proposed method. The empirical results show that hybrid systems based on error decomposition and a nonlinear combination of forecasters can achieve better performance than some existing systems and models.