Chaotic Time Series Prediction Method Research Articles

Point and interval prediction of crude oil futures prices based on chaos theory and multiobjective slime mold algorithm.

Crude oil is the most important energy source in the world, and fluctuations in oil prices can significantly influence investors, companies, and governments. However, crude oil prices have numerous characteristics, including randomness, sudden structural changes, intrinsic nonlinearity, volatility, and chaotic nature. This makes the accurate forecasting of crude oil prices a difficult and challenging task. In this paper, a hybrid prediction model for crude oil futures prices is proposed, the accuracy and robustness of which are demonstrated via controlled experiments and sensitivity analysis. This study uses a new data denoising method for data processing to improve the accuracy and stability of the predictions of crude oil prices. Furthermore, the chaotic time-series prediction method, shallow neural networks, linear model prediction methods, and deep learning methods are adopted as submodels. The results of interval forecasts with narrow widths and high prediction accuracies are derived by introducing a confidence interval adjustment coefficient. The results of the simulation experiments indicate that the proposed hybrid prediction model exhibits higher accuracy and efficiency, as well as better robustness of the forecasting than the control models. In summary, the proposed forecasting framework can derive accurate point and interval forecasts and provide a valuable reference for the price forecasting of crude oil futures.

Application research on PM2.5 concentration prediction of multivariate chaotic time series

PM2.5 is affected by complex factors such as meteorological elements in the air system and other pollutants in the air. So PM2.5 has chaotic property, which makes the prediction of PM2.5 concentration extremely difficult. In order to improve the prediction accuracy of PM2.5 concentration, this paper introduces the chaotic time series prediction method to establish multivariate time for PM2.5 concentration. The sequence prediction model achieves short-term predictions based on the hour concentration of PM2.5 in Beijing. Firstly, the chaotic time series phase space of the relevant unit is expanded into the multi-time sequence phase space, and the multi-time sequence phase space matrix of PM2.5 concentration is constructed. Then the RBF neural network is used to predict the state point in the multi-phase space system. The phase space points of the PM2.5 concentration sequence is separated for prediction. Finally, the comparison between the prediction model and the traditional prediction model is carried out. The results show that the root mean square error of the predicted PM2.5 concentration in the multivariate chaotic time series prediction model based on the phase space reconstruction is 4.92% in the next 5 hours. The average absolute error is 2.40%, which is more effective than the commonly used statistical prediction method.

Hidden Phase Space Reconstruction: A Novel Chaotic Time Series Prediction Method for Speech Signals

Speech signals are nonlinear chaotic time series. This paper proposes a novel speech signal nonlinear prediction model with the hidden phase space reconstruction method. The parameters, embedding dimension m, time delay τ and model structure are solved simultaneously, breaking the restriction of phase space, which needs to be reconstructed before modeling for the existing prediction method. Subsequently, an explicit speech signal prediction model is generated. Meanwhile, the introduction of the frame length parameter k effiectively extends the prediction length. Experimental results show that the values of m and τ solved by the proposed method are consistent with the values addressed by the Cao method and mutual information method, respectively. In addition, the optimal value of k is further discussed. The prediction results obtained using the proposed model are more accurate than those of linear prediction coding, the radial basis function neural network model and the long short-term memory network.

Support Vector Echo-State Machine for Chaotic Time-Series Prediction

A novel chaotic time-series prediction method based on support vector machines (SVMs) and echo-state mechanisms is proposed. The basic idea is replacing "kernel trick" with "reservoir trick" in dealing with nonlinearity, that is, performing linear support vector regression (SVR) in the high-dimension "reservoir" state space, and the solution benefits from the advantages from structural risk minimization principle, and we call it support vector echo-state machines (SVESMs). SVESMs belong to a special kind of recurrent neural networks (RNNs) with convex objective function, and their solution is global, optimal, and unique. SVESMs are especially efficient in dealing with real life nonlinear time series, and its generalization ability and robustness are obtained by regularization operator and robust loss function. The method is tested on the benchmark prediction problem of Mackey-Glass time series and applied to some real life time series such as monthly sunspots time series and runoff time series of the Yellow River, and the prediction results are promising.

Time series prediction using Lyapunov exponents in embedding phase space

This paper describes a novel method of chaotic time series prediction, which is based on the fundamental characteristic of chaotic behavior that sensitive dependence upon initial conditions (SDUIC), and Lyapunov exponents (LEs) is a measure of the SDUIC in chaotic systems. Because LEs of chaotic time series data provide a quantitative analysis of system dynamics in different embedding dimension after embedding a chaotic time series in different embedding dimension phase spaces, a novel multi-dimension chaotic time series prediction method using LEs is proposed in this paper. This is done by first reconstructing a phase space using chaotic time series, then using LEs as a quantitative parameter to predict an unknown phase space point, after transferring the phase space point to time domain, the predicted chaotic time series data can be obtained. The computer simulation result of simulation showed that the proposed method is simple, practical and effective.