Local Prediction of Chaotic Time Series Based on Support Vector Machine

Based on phase space delay-coordinate reconstruction of a chaotic dynamics system, we propose a local prediction of chaotic time series using a support vector machine （SVM） to overcome the shortcomings of traditional local prediction methods. The simulation results show that the performance of this proposed predictor for making onestep and multi-step prediction is superior to that of the traditional local linear prediction method and global SVM method. In addition, it is significant that its prediction performance is insensitive to the selection of embedding dimension and the number of nearest neighbours, so the satisfying results can be achieved even if we do not know the optimal embedding dimension and how to select the number of nearest neighbours.     

Multi-Scale Gaussian Processes： a Novel Model for Chaotic Time Series Prediction

Based on the classical Gaussian process （GP） model, we propose a multi-scale Gaussian process （MGP） model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine. Moreover, the scaling function with its different dilations and translations can form a set of complete bases, resulting in the fact that the MGP can acquire better prediction performance than the GP. The experiments can lead to the following conclusions： （i） The MGP gives a relatively better prediction performance in comparison with the classical GP model. （ii） The prediction performance of the MGP is competitive with support vector machine （SVM）. They give better performance as compared to the radial basis function networks.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is thatit can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. Atime-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the timeevolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate thelocal dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is testedfor the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this predictiontechnique can improve the prediction of chaotic time series.     

Nonlinear Time Series Prediction Using Chaotic Neural Networks

A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network,the network becomes a chaotic one.For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting,we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation.By selecting the suitable feedback term,the system can escape from the local minima and converge to the global minimum or its approximate solutions,and the forecasting results are better than those of backpropagation algorithm.     

Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.     

Multimodality Prediction of Chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model

The contribution of this work is twofold:(1) a multimodality prediction method of chaotic time series with the Gaussian process mixture(GPM) model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series.(2) An effective sparse hard-cut expectation maximization(SHC-EM) learning algorithm for the GPM model is proposed to improve the prediction performance. SHC-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval. SHC-EM outperforms the traditional variational learning in terms of both prediction accuracy and speed. In addition,SHC-EM is more robust and insusceptible to noise than variational learning.     

Online Tracking of Maneuvering Target Trajectory Based on Chaotic Time Series Prediction

Online prediction of maneuvering target trajectory is one of the most popular research directions at present. Specifically, the primary factors balancing, between prediction accuracy and response time, will give the research substance. This paper presents an online trajectory prediction algorithm based on small sample chaotic time series (OTP-SSCT). First, we optimize in terms of data breadth. The dynamic split window is built according to the motion characteristics of the maneuvering target, thus realizing trajectory segmentation and constructing a small sample chaotic time series prediction set. Second, since fully considering the motion patterns of maneuvering targets, we introduce the spatiotemporal features into the particle swarm optimization (PSO) model identification algorithm, which improves the identification sensitivity of key trajectory data points. Furthermore, we propose a feedback optimization strategy of residual compensation to correct the trajectory prediction values to improve the prediction accuracy. For the initial value sensitivity problem of the PSO model identification algorithm, we propose a new initial population strategy, which improves the effectiveness of initial parameters on model identification. Through simulation experiment analysis, it is verified that the proposed OTP-SSCT algorithm achieves better prediction accuracy and faster response time.     

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of chaotic time series. The effectiveness of the method is demonstrated by applying it to the Hénon map. This study also compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.     

A Novel Adaptive Predictor for Chaotic Time Series

Many chaotic time series show non-Gaussian distribution, and non-Gaussianity can be characterized not only by higher-order cumulants but also by negative entropy. Since negative entropy can be accurately approximated by some special non-polynomial functions, which also can form an orthogonal system, these functions are used to construct an adaptive predictor to replace higher-order cumulants. Simulation shows the algorithm performs well for different chaotic systems.     

Analyses of Optimal Embedding Dimension and Delay for Local Linear Prediction Model

In the reconstructed phase space, a novel local linear prediction model is proposed to predict chaotic time series. The parameters of the proposed model take the values that are different from those of the phase space reconstruction. We propose a criterion based on prediction error to determine the optimal parameters of the proposed model. The simulation results show that the proposed model can effectively make one-step and multistep prediction for chaotic time series, and the one-step and multi-step prediction accuracy of the proposed model is superior to that of the traditional local linear prediction.     

Entanglement-Structured LSTM Boosts Chaotic Time Series Forecasting

Traditional machine-learning methods are inefficient in capturing chaos in nonlinear dynamical systems, especially when the time difference Δt between consecutive steps is so large that the extracted time series looks apparently random. Here, we introduce a new long-short-term-memory (LSTM)-based recurrent architecture by tensorizing the cell-state-to-state propagation therein, maintaining the long-term memory feature of LSTM, while simultaneously enhancing the learning of short-term nonlinear complexity. We stress that the global minima of training can be most efficiently reached by our tensor structure where all nonlinear terms, up to some polynomial order, are treated explicitly and weighted equally. The efficiency and generality of our architecture are systematically investigated and tested through theoretical analysis and experimental examinations. In our design, we have explicitly used two different many-body entanglement structures—matrix product states (MPS) and the multiscale entanglement renormalization ansatz (MERA)—as physics-inspired tensor decomposition techniques, from which we find that MERA generally performs better than MPS, hence conjecturing that the learnability of chaos is determined not only by the number of free parameters but also the tensor complexity—recognized as how entanglement entropy scales with varying matricization of the tensor.     

Stock Index Prediction Based on Time Series Decomposition and Hybrid Model

The stock index is an important indicator to measure stock market fluctuation, with a guiding role for investors’ decision-making, thus being the object of much research. However, the stock market is affected by uncertainty and volatility, making accurate prediction a challenging task. We propose a new stock index forecasting model based on time series decomposition and a hybrid model. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the stock index into a series of Intrinsic Mode Functions (IMFs) with different feature scales and trend term. The Augmented Dickey Fuller (ADF) method judges the stability of each IMFs and trend term. The Autoregressive Moving Average (ARMA) model is used on stationary time series, and a Long Short-Term Memory (LSTM) model extracts abstract features of unstable time series. The predicted results of each time sequence are reconstructed to obtain the final predicted value. Experiments are conducted on four stock index time series, and the results show that the prediction of the proposed model is closer to the real value than that of seven reference models, and has a good quantitative investment reference value.     

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

This paper considers the problem of separating the trend and the chaotic component of chaotic time series in the absence of information on the characteristics of the chaotic component. Such a problem arises in nuclear physics, biomedicine, and many other applied fields. The scheme has two stages. At the first stage, smoothing linear splines with different values of smoothing parameter are used to separate the “trend component.” At the second stage, the method of least squares is used to find the unknown variance σ² of the noise component.     

Complex Networks from Chaotic Time Series on Riemannian Manifold

Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities.In this work we propose a reliable method for constructing complex networks from chaotic time series.We first estimate the covariance matrices,then a geodesic-based distance between the covariance matrices is introduced.Consequently the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and geodesic-based distance,respectively.The proposed method provides us with an intrinsic geometry viewpoint to understand the time series.     

Deep Prediction Model Based on Dual Decomposition with Entropy and Frequency Statistics for Nonstationary Time Series

The prediction of time series is of great significance for rational planning and risk prevention. However, time series data in various natural and artificial systems are nonstationary and complex, which makes them difficult to predict. An improved deep prediction method is proposed herein based on the dual variational mode decomposition of a nonstationary time series. First, criteria were determined based on information entropy and frequency statistics to determine the quantity of components in the variational mode decomposition, including the number of subsequences and the conditions for dual decomposition. Second, a deep prediction model was built for the subsequences obtained after the dual decomposition. Third, a general framework was proposed to integrate the data decomposition and deep prediction models. The method was verified on practical time series data with some contrast methods. The results show that it performed better than single deep network and traditional decomposition methods. The proposed method can effectively extract the characteristics of a nonstationary time series and obtain reliable prediction results.     

基于加权改进的AR模型的负载预测研究

负载预测在故障管理中有着十分重要的作用,通过对CPU负载以及内存使用率的预测可以对系统进行实时监控,预知未来时间段资源的可用性,发出异常告警;文中提出一种加权改进的自回归模型,通过对最小二乘法求出的参数进行加权处理,结合时间序列分析理论,建立一个负载预测模型,用于CPU负载和内存使用率的预测;实验证明,对AR模型的参数进行加权的方法优化了参数估计,预测误差减小了60%~80%。     

基于时间序列预测的电子稳像算法研究

块匹配电子稳像算法是一种稳定性好、准确度高的电子稳像算法.块匹配算法在目标区域中从起始点到匹配点进行搜索时,需要对图像块进行反复匹配,计算量大、实时性差成为限制其应用的主要问题.本文从缩小块匹配算法搜索范围的思想出发,提出了一种利用时间序列预测来确定最优搜索起始点的电子稳像算法.根据图像序列全局运动矢量的内部统计特性,选择合适的时间序列模型;采用AIC准则和Durbin-Levinson递推算法估计模型的阶次和参量,并通过残差检验对模型进行检验和更新.利用建立的时间序列模型和历史数据对当前时刻全局运动矢量进行最优预测,并将其作为搜索起点来进行下一步精确搜索.实验结果证明,时间序列预测方法有效缩小了块匹配算法的搜索范围,使计算速度得到较大幅度的提高,并可直接推广到其它电子稳像算法中.     

Functional Time Series Prediction Using Process Neural Network

Time series prediction methods based on conventional neural networks do not take into account the functional relations between the discrete observed values in the time series. This usually causes a low prediction accuracy. To solve this problem, a functional time series prediction model based on a process neural network is proposed in this paper. A Levenberg-Marquardt learning algorithm based on the expansion of the orthonormal basis functions is developed to train the proposed functional time series prediction model. The efficiency of the proposed functional time series prediction model and the corresponding learning algorithm is verified by the prediction of the monthly mean sunspot numbers. The comparative test results indicate that process neural network is a promising tool for functional time series prediction.