Financial factor influence on scaling and memory of trading volume in stock market

Multifractal analysis of financial markets: a review

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

Application of an Improved Correlation Method in Electrostatic Gait Recognition of Hemiparetic Patients

Hemiparesis is one of the common sequelae of neurological diseases such as strokes, which can significantly change the gait behavior of patients and restrict their activities in daily life. The results of gait characteristic analysis can provide a reference for disease diagnosis and rehabilitation; however, gait correlation as a gait characteristic is less utilized currently. In this study, a new non-contact electrostatic field sensing method was used to obtain the electrostatic gait signals of hemiplegic patients and healthy control subjects, and an improved Detrended Cross-Correlation Analysis cross-correlation coefficient method was proposed to analyze the obtained electrostatic gait signals. The results show that the improved method can better obtain the dynamic changes of the scaling index under the multi-scale structure, which makes up for the shortcomings of the traditional Detrended Cross-Correlation Analysis cross-correlation coefficient method when calculating the electrostatic gait signal of the same kind of subjects, such as random and incomplete similarity in the trend of the scaling index spectrum change. At the same time, it can effectively quantify the correlation of electrostatic gait signals in subjects. The proposed method has the potential to be a powerful tool for extracting the gait correlation features and identifying the electrostatic gait of hemiplegic patients.

Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features

Employing Random Matrix Theory and Principal Component Analysis techniques, we enlarge our work on the individual and cross-sectional intraday statistical properties of trading volume in financial markets to the study of collective intraday features of that financial observable. Our data consist of the trading volume of the Dow Jones Industrial Average Index components spanning the years between 2003 and 2014. Computing the intraday time dependent correlation matrices and their spectrum of eigenvalues, we show there is a mode ruling the collective behaviour of the trading volume of these stocks whereas the remaining eigenvalues are within the bounds established by random matrix theory, except the second largest eigenvalue which is robustly above the upper bound limit at the opening and slightly above it during the morning-afternoon transition. Taking into account that for price fluctuations it was reported the existence of at least seven significant eigenvalues-and that its autocorrelation function is close to white noise for highly liquid stocks whereas for the trading volume it lasts significantly for more than 2 hours -, our finding goes against any expectation based on those features, even when we take into account the Epps effect. In addition, the weight of the trading volume collective mode is intraday dependent; its value increases as the trading session advances with its eigenversor approaching the uniform vector as well, which corresponds to a soar in the behavioural homogeneity. With respect to the nonstationarity of the collective features of the trading volume we observe that after the financial crisis of 2008 the coherence function shows the emergence of an upset profile with large fluctuations from that year on, a property that concurs with the modification of the average trading volume profile we noted in our previous individual analysis.

Understanding Financial Market States Using an Artificial Double Auction Market

The ultimate value of theories describing the fundamental mechanisms behind asset prices in financial systems is reflected in the capacity of such theories to understand these systems. Although the models that explain the various states of financial markets offer substantial evidence from the fields of finance, mathematics, and even physics, previous theories that attempt to address the complexities of financial markets in full have been inadequate. We propose an artificial double auction market as an agent-based model to study the origin of complex states in financial markets by characterizing important parameters with an investment strategy that can cover the dynamics of the financial market. The investment strategies of chartist traders in response to new market information should reduce market stability based on the price fluctuations of risky assets. However, fundamentalist traders strategically submit orders based on fundamental value and, thereby stabilize the market. We construct a continuous double auction market and find that the market is controlled by the proportion of chartists, P_c. We show that mimicking the real state of financial markets, which emerges in real financial systems, is given within the range P_c = 0.40 to P_c = 0.85; however, we show that mimicking the efficient market hypothesis state can be generated with values less than P_c = 0.40. In particular, we observe that mimicking a market collapse state is created with values greater than P_c = 0.85, at which point a liquidity shortage occurs, and the phase transition behavior is described at P_c = 0.85.

Structure of local interactions in complex financial dynamics

With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Further, we explore the time evolution of the interaction structure of the business sectors, and observe that the local interaction structure changes dramatically during a financial bubble or crisis.