A hybrid model of stacked autoencoder and modified particle swarm optimization for multivariate chaotic time series forecasting

Abstract

Phase space reconstruction (PSR) is an effective method for chaotic system modeling, which can reveal the implicit evolution information in a complex system. However, the reconstructed time series tend to have a high dimension and contain some redundant information. It is difficult for a traditional simple model to directly forecast the reconstructed time series. In this paper, we propose a hybrid model of stacked autoencoder (SAE) and modified particle swarm optimization (MPSO) for multivariate chaotic time series forecasting. We utilize SAE to extract the reconstructed time series and adopt feedforward neural network (FNN) to forecast time series. In the proposed hybrid model, the SAE is followed by FNN, and we make the MPSO to train the output weights of the model, which is a large-scale optimization problem. To enhance the generalization ability and prevent over-fitting, we add a regularization item to the objective function when MPSO trains the weights of the model. Experimental results show that MPSO algorithm has advantages in the exploration and exploitation in large-scale optimization problems. Then, experiments on Lorenz time series and two real-world time series datasets verify the effectiveness of the hybrid model in multivariate chaotic time series forecasting.