Phase Space Reconstruction Of Time Series Research Articles

Chaotic Features of Decomposed Time Series from Tidal River Water Level

This study assessed the characteristics of water-level time series of a tidal river by decomposing it into tide, wave, rainfall-runoff, and noise components. Especially, the analysis for chaotic behavior of each component was done by estimating the correlation dimension with phase-space reconstruction of time series and by using a close returns plot (CRP). Among the time series, the tide component showed chaotic characteristics to have a correlation dimension of 1.3. It was found out that the water level has stochastic characteristics showing the increasing trend of the correlation exponent in the embedding dimension. Other components also showed the stochastic characteristics. Then, the CRP was used to examine the characteristics of each component. The tide component showed the chaotic characteristics in its CRP. The CRP of water level showed an aperiodic characteristic which slightly strayed away from its periodicity, and this might be related to the tide component. This study showed that a low water level is mainly affected by a chaotic tide component through entropy information. Even though the water level did not show chaotic characteristics in the correlation dimension, it showed stochastic chaos characteristics in the CRP. Other components showed stochastic characteristics in the CRP. It was confirmed that the water level showed chaotic characteristics when it was not affected by rainfall and stochastic characteristics deviating from the bounded trajectory when water level rises due to rainfall. Therefore, we have shown that the water level related to the chaotic tide component can also have chaotic properties because water level is influenced by chaotic tide and rainfall shock, thus it showed stochastic chaos characteristics.

Stock price prediction based on deep neural networks

Understanding the pattern of financial activities and predicting their development and changes are research hotspots in academic and financial circles. Because financial data contain complex, incomplete and fuzzy information, predicting their development trends is an extremely difficult challenge. Fluctuations in financial data depend on a myriad of correlated constantly changing factors. Therefore, predicting and analysing financial data are a nonlinear, time-dependent problem. Deep neural networks (DNNs) combine the advantages of deep learning (DL) and neural networks and can be used to solve nonlinear problems more satisfactorily compared to conventional machine learning algorithms. In this paper, financial product price data are treated as a one-dimensional series generated by the projection of a chaotic system composed of multiple factors into the time dimension, and the price series is reconstructed using the time series phase-space reconstruction (PSR) method. A DNN-based prediction model is designed based on the PSR method and a long- and short-term memory networks (LSTMs) for DL and used to predict stock prices. The proposed and some other prediction models are used to predict multiple stock indices for different periods. A comparison of the results shows that the proposed prediction model has higher prediction accuracy.

Chaotic Characteristics Identification on Terminal Departing Passenger Traffic Time Series

On the basis of actual survey of departing passengers to reach terminal, chaotic time series prediction theory was adopted for data analysis in this paper. In order to find out the self-similarity of time series, this paper divided passenger traffic into two kinds: holiday traffic and non-holiday traffic by changing interval scale. The optimal delay time and the best embedding dimension had been calculated by using time series phase space reconstruction method. To confirm whether the time series have chaotic characteristics or not, it took the largest Lyapunov exponent as determining criterion.Then the optimal time intervals of passenger traffic time series with chaotic character were determined. The study provides a theoretical basis for the application of chaos theory in passenger traffic forecast.

Chaotic Characteristics of Workface Gas Emission Time-Series Data

The chaotic time series phase space reconstruction theory based in this paper. First, the appropriate embedding dimension and delay time are selected by minimum entropy rate. Followed the chaotic behavior are analyzed by the use of the Poincare section map and Power spectrum of time series from the qualitative point of view. Based on NLSR LLE the quantitative study of the chaotic time series characteristics indicators is proposed. Finally, the gas emission workface of Hebi 10th Mine Coal is studied. The several analytical results of the above methods show that: the gas emission time-series data of this workface has chaotic characteristics.

Multivariate chaotic time series phase space reconstruction based on extending dimension by conditional entropy

For multivariate chaotic time series, a method of conditional entropy extending dimension(CEED) in the reconstructed phase space is proposed. First, the delay time of any variable time series is selected by mutual information method, and then the embedding dimension of phase space is extended by the conditional entropy. This method can ensure the independence of reconstructed coordinates from low space to high space and eliminate the redundancy of phase space, because the largest condition entropy is choosen. The effective input vector for the prediction of multivariate time series is given. Simulations of the Lorenz system and Henon system show that the neural network predictions of multivariate time series are much better than the prediction of univariate and existing multivariate. Therefore, CEED is effective for multivariate chaotic systems.

Chaotic dynamic characteristics of Z component in geomagnetic variation field

对地球变化磁场进行了混沌动力学特性分析，主要进行了以下两个方面的工作：1)运用多种方法对多个地磁台站同一时段变化磁场分量数据（分为磁扰较小和磁扰较大时段）进行了混沌特性分析，主要是为了以更充分的判据来验证地球变化磁场是否具有混沌特性；2)同一地磁台站不同时段变化磁场分量数据的混沌特性分析，主要是验证地球变化磁场是否具有变参数混沌特性.分析结果表明：1)变化磁场时间序列确实具有混沌特性；2)从混沌时间序列相空间重构的角度可初步认为模拟地球变化磁场动力学系统所必须的独立变量应该为6左右；3)变化磁场时间序列不

High-dimensional delay selection for regression models with mutual information and distance-to-diagonal criteria

Delay selection for time series phase space reconstruction may be performed using a mutual information (MI) criterion. However, the delay selection is in that case limited to the estimation of a single delay using MI between two variables only. A high-dimensional estimator of the MI may be used to select more than one delay between more than two variables but this approach is rather time consuming. In this paper, an alternative fast criterion is proposed to optimize all delays for a high-dimensional phase space reconstruction: the distance-to-diagonal (DD) criterion, based on a geometrical heuristic. The use of the distance to diagonal criterion is illustrated and compared to MI on artificial and benchmark time series.