The cross-correlations of stock markets based on DCCA and time-delay DCCA

In this paper, the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) are used to investigate the stock markets. The DFA method is a widely-used method for the determination and detection of long-range correlations in stock time series. DCCA is a recently developed method to quantify the cross-correlations of two non-stationary time series. We report the results of correlation and cross-correlation behaviors in US and Chinese stock markets by using the DFA and DCCA methods, respectively. The DCCA shows that there exists some crossovers in the cross-correlation fluctuation function versus time scale of stock absolute returns. The cross-correlations in Chinese stock markets are stronger than those between Chinese and US stock markets. After documenting the equal-time cross-correlations using DCCA method, we study the dynamics of cross-correlations of stock series based on a time-delay. The time-dependence of the underlying cross-correlations is monitored using a time window by step of 1 day. An interesting finding is that the cross-correlation exponents and crossovers demonstrate periodical uncertainty changing with the time-delay.     

Nonlinear stochastic exclusion financial dynamics modeling and complexity behaviors

In attempt to reproduce and investigate nonlinear dynamics of financial markets, a new random agent-based financial price dynamics is developed and investigated by stochastic exclusion process. The exclusion process, one of Markov interacting processes, is firstly introduced to imitate the trading interactions among the investing agents in this work and to explain various statistical facts found in financial data. To better understand the fluctuation complexity properties of the proposed model, the complex analyses of random logarithmic price return series are preformed, including power-law distribution, Lempel–Ziv complexity, correlation dimension analysis, maximum Lyapunov exponent, mean Lyapunov exponents and Kolmogorov–Sinai entropy density. In order to verify the rationality of the model, the corresponding analyses of real return series are also studied for comparison. The empirical research reveals that this financial model can reproduce similar statistical behaviors, power-law distribution of returns, complexity and chaotic features of returns for real stock markets.     

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.     

Cross-correlations between the CSI 300 spot and futures markets

Financial markets are complex dynamical systems. One of the important features of market dynamics is the existence of cross-correlations between financial variables. Based on the high-frequency transaction prices (every 5 min) data, in this study, we investigate the cross-correlations between China Securities Index 300 (CSI 300) spot and futures markets. Qualitatively, employing a statistical test in analogy to the Ljung-Box test, we find that the cross-correlations are significant at the 1 % level. Quantitatively, using the multifractal detrending moving-average cross-correlation analysis (MF-XDMA) method, we find that the cross-correlations are strongly multifractal. An interesting finding is that the cross-correlation exponent is larger than the averaged generalized scaling exponent for different q, which is different from the general conclusion. Using the method of rolling windows, we find that the cross-correlations are positive over time, which suggests that China’s securities markets are not mature and efficient markets at present.     

An outlier-robust kernel RLS algorithm for nonlinear system identification

In this paper, we propose multivariate multiscale permutation entropy (MMPE) and multivariate weighted multiscale permutation entropy (MWMPE) to explore the complexity of the multivariate time series over multiple different time scales. First, we apply these methods to the simulated trivariate time series which is compose of white noise and 1/f noise to test the validity of multivariate methods. The standard deviations of weighted methods are bigger because of containing more amplitude information, while the standard deviations of multivariate method are smaller than the method for single channel. Hence, it can be found that MWMPE shows a better distinguish capacity, while it is able to measure the complexity of the multichannel data accurately and reflect more information about the multivariate time series as well as holds a better robustness. Then MMPE and MWMPE methods are employed to the financial time series: closing prices and trade volume, from different area. It can be verified that the methods for multichannel data analyze the properties of multivariate time series comprehensively. The entropy values taking the weight into account for both the multichannel and single channel amplify the local fluctuation and reflect more amplitude information. The MWMPE maintain the fluctuation characteristic of SCWMPE of both price and volume. The MWMPE results of these stock markets can be divided into three groups: (1) S&P500, FTSE, and HSI, (2) KOSPI, and (3) ShangZheng. The weighted contingency also shows the difference of inhomogenity of the distributions of ordinal patterns between these groups. Thus, MWMPE method is capable of differentiating these stock markets, detecting their multiscale structure and reflects more information containing in the financial time series.     

Identifying economic periods and crisis with the multidimensional scaling

This paper applied MDS and Fourier transform to analyze different periods of the business cycle. With such purpose, four important stock market indexes (Dow Jones, Nasdaq, NYSE, S&P500) were studied over time. The analysis under the lens of the Fourier transform showed that the indexes have characteristics similar to those of fractional noise. By the other side, the analysis under the MDS lens identified patterns in the stock markets specific to each economic expansion period. Although the identification of patterns characteristic to each expansion period is interesting to practitioners (even if only in a posteriori fashion), further research should explore the meaning of such regularities and target to find a method to estimate future crisis.     

Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the shortrange viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation ( LES ) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.     

A time-domain nonlinear system identification method based on multiscale dynamic partitions

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.     

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.     

复杂系统和涌现:理论如何与现实结合

复杂系统所表现出的涌现行为吸引了人类极长时间的关注. 然而只是在近几十年来, 大量的工作才对这些行为进行了定量的研究, 并发展出许多重要的理论和方法, 比如混沌理论, 随机分形理论以及多尺度分析. 本文旨在对这个广阔研究领域内最好的研究和实践进行介绍, 并着重强调了理论如何与实际问题相结合. 作为说明的例子, 对网络安全、经济危机、河流动力学以及世界范围内的政治冲突进行了简要讨论. 也列举了未来几个重要研究方向.     

Co-Movements and Asymmetric Volatility in the Portuguese and U.S. Stock Markets

It has been widely recognised by economists that economic relationships are typically non-linear. This is so that, for example, C. W. J. Granger and T. Ter?svirta [Modelling Nonlinear Economic Relationships, Oxford University Press, New York, 1993], inter alia, have dedicated a whole book to the subject of modelling non-linear economic relationships. Non-linear relationships are present in many aspects of the economic activity, and particularly so in the context of financial markets. Examples of this include the attitude of investors towards the risk and the process of generating financial variables such as stock returns, dividends, interest rates, and so on. On the other hand, the performance of an economy also presents strong signs of a non-linear behaviour: e.g. business cycles, production functions, growth rates, unemployment, etc. Although the shape of non-linearity in these relationships may be rather complex, there are cases where one may admit some sort of linear relationship between the relevant variables within certain regimes. This is the case when one aims to study the co-movements of stock returns volatility and some relevant macroeconomic factors. One obvious question that we may pose in this context is whether the magnitude of positive and negative responses differs for similar positive and negative variations in the predictors, in which case we can say that the underlying variables display asymmetric adjustment. Markets characterised by higher elasticity of supply are likely to show less asymmetry than their counterparts due to increased security of supply. Models of financial markets have incorporated asymmetry using GARCH-type methodologies. An alternative way to deal with these cases is to use threshold autoregressive (TAR) and momentum threshold autoregressive (M-TAR) models to address the problem of multivariate asymmetry. These methodologies are essential when the asymmetric variables are non-stationary (but not only), because of the low power of unit roots and cointegration tests in such cases. In a non-stationary framework, asymmetric cointegration tests were developed by [W. Enders, and P. Siklos, Journal of Business & Economic Statistics 19(2), 2001, 166–176] using a modified error correction model derived from the original EG testing procedure. We apply this methodology to the Portuguese and U.S. stock markets using monthly observations from January 1993 to December 2003.     

Overconfident agents and evolving financial networks

In this paper, we investigate the impact of agent personality on the complex dynamics taking place in financial markets. Leveraging recent findings, we model the artificial financial market as a complex evolving network: we consider discrete dynamics for the node state variables, which are updated at each trading session, while the edge state variables, which define a network of mutual influence, evolve continuously with time. This evolution depends on the way the agents rank their trading abilities in the network. By means of extensive numerical simulations in selected scenarios, we shed light on the role of overconfident agents in shaping the emerging network topology, thus impacting on the overall market dynamics.     

Everybody else is: Networks, power laws and peer contagion in the aggressive recess behavior of elementary school boys

This paper develops a simple random network model of peer contagion in aggressive behavior among inner-city elementary school boys during recess periods. The model predicts a distribution of aggressive behaviors per recess period with a power law tail beginning at two aggressive behaviors and having a slope of approximately -1.5. Comparison of these values with values derived from observations of aggressive behaviors during recess at an inner-city elementary school provides empirical support for the model. These results suggest that fluctuations in aggressive behaviors during recess arise from the interactions between students, rather than from variations in the behavior of individual students. The results therefore support those interventions that aim to change the pattern of interaction between students.     

Do nonlinear dynamics in economics amount to a Kuhnian paradigm shift?

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies "free enterprise" with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it.     

基于EMD改进算法的爆破振动信号去噪

为了解决振动信号经验模态分解(empirical mode decomposition, EMD)滤波去噪效果不佳的问题,提出一种自适应性正交经验模态分解(principal empirical mode decomposition, PEMD)的信号去噪方法。该算法融合了EMD分解的自适应性和主成分分析(principal component analysis,PCA)的完全正交性特点,对信号EMD分解过程中产生的模态混叠现象进行消除,得到了最佳的去噪效果。分析表明：PEMD在仿真模拟试验中相比于传统EMD算法和集总经验模态分解(ensemble empirical mode decomposition, EEMD) 算法,信噪比分别提高了1.15 dB和0.38 dB,且均方根误差最小;频域上PEMD对仿真信号频率(30 Hz)识别的灵敏度最高,30 Hz之外的噪声滤除效果最好。在爆破振动试验中,PEMD和EEMD去除噪声毛刺的效果较为理想,且PEMD在0～300 Hz的中低频振动信号保存效果最好,300 Hz以上的高频噪声滤除效果最好。

     

Measuring the asymmetric contributions of individual subsystems

Information on the structure of a complex system can be obtained by measuring at what rate the individual subsystems exchange information among each other and to what extent they contribute to the information production. In this paper, we use relative transfer entropy to analyze the contributions of asymmetric information flow from one subsystem to another. We also propose information-theoretic tools to estimate the contributions of individual subsystems to the information production of system over time. On one hand, we analyze the artificial processes, including unidirectionally coupled linear processes, unidirectionally coupled Rössler systems, and bidirectionally coupled Hénon maps that reveal the information flows between variables and the contributions to the information production of each variable. On the other hand, we apply these measures to real-world systems, the stock markets that uncover the interactions between high-frequency stock price and trading volume.     

Multiscale coupling of molecular dynamics and peridynamics

We propose a multiscale computational model to couple molecular dynamics and peridynamics. The multiscale coupling model is based on a previously developed multiscale micromorphic molecular dynamics (MMMD) theory, which has three dynamics equations at three different scales, namely, microscale, mesoscale, and macroscale. In the proposed multiscale coupling approach, we divide the simulation domain into atomistic region and macroscale region. Molecular dynamics is used to simulate atom motions in atomistic region, and peridynamics is used to simulate macroscale material point motions in macroscale region, and both methods are nonlocal particle methods. A transition zone is introduced as a messenger to pass the information between the two regions or scales. We employ the “supercell” developed in the MMMD theory as the transition element, which is named as the adaptive multiscale element due to its ability of passing information from different scales, because the adaptive multiscale element can realize both top-down and bottom-up communications. We introduce the Cauchy–Born rule based stress evaluation into state-based peridynamics formulation to formulate atomistic-enriched constitutive relations. To mitigate the issue of wave reflection on the interface, a filter is constructed by switching on and off the MMMD dynamic equations at different scales. Benchmark tests of one-dimensional (1-D) and two-dimensional (2-D) wave propagations from atomistic region to macro region are presented. The mechanical wave can transit through the interface smoothly without spurious wave deflections, and the filtering process is proven to be efficient.     

Analysis of financial stock markets through multidimensional scaling based on information measures

In this paper, a novel multidimensional scaling (MDS) based on information measures method is proposed to analyze financial stock markets. In order to examine the effectiveness of this method, we applied it to the classification of two types of artificial series, the logistic map model and the cubic map model, as well as stock time series. Moreover, the traditional MDS using Euclidean dissimilarity is also provided as a reference for comparisons. The results show that the MDS based on information measures can give us more detailed, exact and clearer information on the classification of simulation series and stock time series than the MDS using Euclidean dissimilarity. In addition, the proposed graphical method may also assist in the construction of multivariate econometric models.     

Multiscale time irreversibility analysis of financial time series based on segmentation

Time irreversibility is a subject of increasing interest in an unbalanced system of various time series. Taking into account dynamic basic concepts, we provide multiscale time irreversibility analysis of financial time series based on segmentation which quantifies the time asymmetry in multiscales and is applied to several different forms of financial time series. Specifically, we adopt four distinct time irreversibility indices—Porta’s, Guzik’s and Ehler’s indices (P%, G% and E) and \(\gamma _{2,1} (k)\), respectively, derived from data segments on various timescales. We investigate the performance of our statistical tests for local financial time series from segmented series system with known time reversal properties and find out that it can help classify the partially representative financial markets finally. Particularly, the smaller the scale factor L is the better the ability to distinguish data. Statistical analysis shows a close relationship between G% and E. On the contrary, the connection between P% and G% or P% and E is not proven. In addition, we define a new metric \(\gamma _{2,1} (k)\) to measure the degree of time irreversibility. By further observing the results of the proposed method for computing the degree of irreversibility of the time series, we confirm that the asymmetry is an inherent property of the financial time series, which can be extended to a wide range of scales. Finally, we apply this method to the recurrence plot and multiscale recurrence quantification analysis, to compare effectiveness of the segmentation method.