A Hybrid Model Based on a Two-Layer Decomposition Approach and an Optimized Neural Network for Chaotic Time Series Prediction

Xinghan Xu,Weijie Ren

doi:10.3390/sym11050610

Abstract

The prediction of chaotic time series has been a popular research field in recent years. Due to the strong non-stationary and high complexity of the chaotic time series, it is difficult to directly analyze and predict depending on a single model, so the hybrid prediction model has become a promising and favorable alternative. In this paper, we put forward a novel hybrid model based on a two-layer decomposition approach and an optimized back propagation neural network (BPNN). The two-layer decomposition approach is proposed to obtain comprehensive information of the chaotic time series, which is composed of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD). The VMD algorithm is used for further decomposition of the high frequency subsequences obtained by CEEMDAN, after which the prediction performance is significantly improved. We then use the BPNN optimized by a firefly algorithm (FA) for prediction. The experimental results indicate that the two-layer decomposition approach is superior to other competing approaches in terms of four evaluation indexes in one-step and multi-step ahead predictions. The proposed hybrid model has a good prospect in the prediction of chaotic time series.

Highlights

Chaotic time series exist in a wide range of areas, such as nature, the economy, society, and industry
The evaluation criteria are selected as root-mean-squared error (RMSE), normalized root-mean-square error (NRMSE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE)
According to the results presented in the tables, the proposed model has a minimum prediction error in multiple prediction experiments, which indicates that the hybrid model of CEEMDAN–variational mode decomposition (VMD)–FABP has the best prediction performance

Summary

Introduction

Chaotic time series exist in a wide range of areas, such as nature, the economy, society, and industry. They contain many important and valuable information, useful for complex system modeling and prediction. Han et al [3] proposed an improved extreme learning machine combined with a hybrid variable selection algorithm for the prediction of multivariate chaotic time series, which can achieve high predictive accuracy and reliable performance. Chandra [4] put forward a competitive cooperative coevolution algorithm to train recurrent neural networks (RNNs) for chaotic time series prediction. Chen [6] proposed a prediction model of a radial basis function (RBF) neural network optimized by an artificial bee colony algorithm for prediction of traffic flow time series. A multilayered echo state machine with the addition of multiple layers of reservoirs was introduced in [7], and it could be more robust than the echo state network with a conventional reservoir in dealing with chaotic time series prediction

Methods

Results

Conclusion