Complexity analysis of multiscale multivariate time series based on entropy plane via vector visibility graph

Nonlinear Dynamics - Vector visibility graph (VVG) is an algorithm that transforms multivariate time series into directed complex networks. However, at present, the researches of VVG mainly focus...     

Weighted multiscale permutation entropy of financial time series

In this paper, we propose the weighted multiscale permutation entropy (WMPE) as a novel measure to quantify the complexity of nonlinear time series containing amplitude-coded information. WMPE is different from multiscale permutation entropy (MPE) in the sense that it suits better signals having considerable amplitude information and also succeed in accounting for the multiple time scales inherent in the financial systems. We first perform the MPE and WMPE methods on synthetic data showing the power of WMPE. Then, we apply the MPE and WMPE methods to the US and Chinese stock markets and make a comparison to discuss their differences and similarities between these different markets. The WMPE of each US and Chinese stock market points out the necessity of applying permutation entropy on multiple scales and reveals amplitude-coded information contained in the signals and immunity to degradation by noise when \(m = 5-7\) . Some new conclusions are gotten by the new characteristics we detected in the comparison. WMPE method can distinguish ShangZheng and ShenCheng from these markets and imply that HSI is more similar to the US markets. WMPE moves the fluctuation range of entropy values of different market down differently reflecting more accurate complexity of different stock markets containing amplitude information. Compared WMPE of ShangZheng and ShenCheng with the WMPE of US markets and HSI, US stock market and HSI may have more amplitude information carried by the signals of stock market. Furthermore, compared with MPE, WMPE can reduce the standard deviation which ensures the results more robust. The conclusion that \(m = 7\) is the best embedding dimension to investigate the WMPE results can be drawn because the WMPE tends to be stable in a certain range and reflects the necessity of investigation on multiscale and advantages of adding different weight, and it can distinguish these markets while reducing the standard deviations of all the markets.     

Modified generalized multiscale sample entropy and surrogate data analysis for financial time series

Nonlinear Dynamics - Complexity in time series is an intriguing feature of living dynamical systems such as financial systems, with potential use for identification of system state. Multiscale...     

Weighted link entropy and multiscale weighted link entropy for complex time series

Nonlinear Dynamics - In the presented paper, an analytical approach based on the Harmonic Balance method is used to evaluate amplitudes of higher-order harmonics generated due to the interaction of...     

A new method for tolerance estimation of multivariate multiscale sample entropy and its application for short-term time series

Multivariate multiscale sample entropy (MMSE) is a robust method to detect the complexity of multivariate system. It is evaluated for a certain value of tolerance parameter r which is mainly calculated from common acknowledged range. This kind of selection of r is not suitable for short-term time series and may lead to the unreliable detection. To reduce the impact of limited range of r, we apply cumulative histogram method to estimate the range of r. It is data-driven and needs no parameters. Moreover, we use secondary statistics, AvgMMSE and SDMMSE rather than the single value of MMSE to detect the complexity of signals and differentiate them. Several time series, either generated from chaotic or stochastic systems, are analyzed to demonstrate the approach. The core achievement of this experiment is the stability and classification for short-term time series. Then we apply this method to financial time series. Empirical results show that the proposed method is vigorous enough to classify different stock indices over different periods.     

Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N = 19,625 elements that must be filled with the given data. A substantial number of practical time series have fewer elements than 19,625. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series of any length 5 ≤ N ≤ 19,625. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short-time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. In addition to external noise, the hyperparameter (bias) used in entropy calculation also plays a critical role. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal-to-Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

     

Complexity analysis of the time series using inverse dispersion entropy

Nonlinear Dynamics - The primary object of this study is to measure the complexity of different types of signals. We undertake the experiment to support the hypothesis of inverse dispersion entropy...     

Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection

Nonlinear Dynamics - This work proposes a novel method to construct weighted dynamic transfer network to map time series to complex networks. Firstly, we map time series into symbolic series by...     

The multiscale large deviation spectrum based on higher moments for financial time series

Nonlinear Dynamics - In this letter, based on large deviations theory, we propose to use higher moments (e.g., skewness, kurtosis) to investigate the multifractal features of large deviations...     

Multiscale cumulative residual distribution entropy and its applications on heart rate time series

Nonlinear Dynamics - Distribution entropy has been proved to reveal stability for short time series and to distinguish different classes of series by complexity. However, there still exists some...     

An analytic and application to state space reconstruction about chaotic time series

The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.     

Analysis of time series in the cumulative residual entropy plane based on oscillation roughness exponent

Nonlinear Dynamics - In this work, we propose the cumulative residual entropy (CRE) plane and CRE curve based on the weighted-multiscale cumulative residual Rényi/Tsallis permutation entropy...     

Separatrices and basins of stability from time series data: an application to biodynamics

An approach is presented for identifying separatrices in state space generated from noisy time series data sets which are representative of those generated from experiments. We demonstrate how these separatrices can be found using Lagrangian coherent structures (LCSs), ridges in the state space distribution of the maximum finite-time Lyapunov exponent. As opposed to the current approach which requires a vector field in the state space at each instant of time, this method can be performed using only trajectories reconstructed from time series. As such, this paper forms a bridge connecting methods for evaluating time series data with methods used to evaluate LCSs in vector fields. The methods are applied to a problem in musculoskeletal biomechanics, considered as an exemplar of a class of experimental systems that contain separatrices. In this case, the separatrix reveals a basin of stability for a balancing task, outside of which is a zone of failure. We demonstrate that LCSs calculated from only trajectory data, which samples only portions of the state space, align well with LCSs found using a known vector field. In general, we believe this method provides a fruitful approach for extracting information from noisy experimental data regarding boundaries between qualitatively different kinds of behavior.     

The application of evolutionary and maximum entropy algorithms to photoelastic spectral analysis

Over the past 10 years, spectral analysis has been shown to have the potential to be a reliable means of automating photoelasticity. However, the four methods of analyzing the spectra that have previously been proposed are slow and, in some cases, inaccurate. This paper describes three new methods for spectral analysis based on the maximum entropy method, a genetic algorithm and a memetic algorithm. Thirty-five spectra for known fringe orders were recorded and used in testing the four existing methods and the three new ones. It was found that the new methods were all considerably faster than the existing methods, although less accurate than the best existing method. By combining the maximum entropy method with either the genetic algorithm or the memetic algorithm, spectra could be analyzed up to 30 times as fast as they could with any of the existing methods and with comparable accuracy.     

The application of graph theory to the limit analysis for torsion of thin-walled bars with complex cross-sections

Graph theory is employed in this paper as a means to establish the topological model of complex thin-walled cross-sections. On this basis, the upper and lower bound theorems of the plastic limit analysis are applied to the analysis of the plastic limit shear flows on the cross-section of thin-walled bars under St. Venant torsion. Corresponding mathematical programming problems are formulated and their duality is shown. After solving the linear programming problem corresponding to the lower bound theorem, the limit torsional moment of a thin-walled cross-section can be calculated according to the shear stress distribution in the limit state. The formula for calculating the limit torsional moment is given. Furthermore, the limit state of thin-walled cross-sections under St. Venant torsion is also discussed and the concept of the limit tree is introduced. A computer program has been developed by the author. Results calculated by the program for typical complex cross-sections are given.     

An advection-based model to increase the temporal resolution of PIV time series

A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor’s hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency domain whereby the spectrum becomes significantly less prone to aliasing error for the super-sampled data series.     

Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal

In this paper, based on the Hirota bilinear method, a kind of lump solutions and two classes of interaction solutions are discussed to the \((2+1)\)-dimensional generalized KdV equation with the aid of symbolic computation system Mathematica. Analyticity is naturally guaranteed by taking special choices of the involved parameters to achieve a positive constant term. Particularly, these solutions with special values of the included parameters are plotted, as illustrative example.     

Multiscale permutation mutual information quantify the information interaction for traffic time series

Pendulums and similar systems, such as links of chains, bodies hanging on ropes, kinematic chains forming working parts of manipulators, and robotic devices, are frequently used in industrial applications. They often cooperate in tubes or working spaces limited by walls or other rigid obstacles. This was the inspiration to carry out this study on the influence of impacts on the behaviour of a chain-like system represented by a double pendulum moving between two vertical walls. The simulations were performed for a specified extent of excitation frequencies. The results indicate a number of bifurcations that change the character of the induced motion to regular, quasi-periodic, and chaotic in the individual frequency subintervals.