Local Volterra multivariable chaotic time series multi-step prediction based on phase points clustering

To solve the multivariable multi-step prediction problem in chaotic complex systems, this paper proposes a local Volterra model based on phase points clustering. Firstly, reconstruct the phase space of the data and calculate the similarity of the evolution trajectories. According to the similarity, the initial clustering center of the observation point is calculated and the clustering is carried out by means of K mean. We find the cluster class nearest to the prediction phase, compare the predicted phase point with the evolutionary trajectory similarity of all the observed points in the cluster, select the optimal neighboring phase point, and the optimal neighboring phase point is used for training and multi-step prediction of the multivariable local Volterra model. The proposed model method can greatly reduce the time of multi-step prediction and improve the efficiency of prediction. Finally, by experimenting with the data of Beijing PM2.5 acquired from UCI machine learning database, the experimental results show that this model method has better predictive performance.