Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System

Nonlinear continuous fluctuation intensity financial dynamics and complexity behavior

The exploration of return volatility dynamics is of great significance to evaluate investment risk, avoid stock market crisis, and purchase stock portfolio. In this paper, we propose a novel concept to characterize the fluctuation duration of stock markets, which is continuous fluctuation intensity (CFI). The CFI represents the duration for continuous increasing or decreasing return volatilities (or normalized absolute returns) above or below a previous day's value. Distinguished from previous studies, the CFI does not need to set a threshold in advance but to select the sequence of return volatilities that are continuously growing or falling in the series. So, the research on continuous fluctuation intensity is a new approach in return volatility study. For investigating the nonlinear properties of CFI, probability distribution, autocorrelation analysis, and scatterplot analysis are utilized for the empirical data from China and USA stock markets. Besides, fractional sample entropy and fuzzy entropy are employed to explore the complexity of CFI series. Then, some meaningful results of CFI series are acquired, which manifest that the study of the proposed concept is feasible and valuable. Moreover, we do the same investigations for return volatility series to explore the similarities and differences between CFI series and volatility series.

Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

This paper investigates the complex behaviors and entropy properties for a novel random complex interacting stock price dynamics, which is established by the combination of stochastic contact process and compound Poisson process, concerning with stock return fluctuations caused by the spread of investors’ attitudes and random jump fluctuations caused by the macroeconomic environment, respectively. To better understand the fluctuation complex behaviors of the proposed price dynamics, the entropy analyses of random logarithmic price returns and corresponding absolute returns of simulation dataset with different parameter set are preformed, including permutation entropy, fractional permutation entropy, sample entropy and fractional sample entropy. We found that a larger λ or γ leads to more complex dynamics, and the absolute return series exhibit lower complex dynamics than the return series. To verify the rationality of the proposed compound price model, the corresponding analyses of actual market datasets are also comparatively preformed. The empirical results verify that the proposed price model can reproduce some important complex dynamics of actual stock markets to some extent.

Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks

Measurement of time series complexity and predictability is sometimes the cornerstone for proposing solutions to topology and congestion control problems in sensor networks. As a method of measuring time series complexity and predictability, multiscale entropy (MSE) has been widely applied in many fields. However, sample entropy, which is the fundamental component of MSE, measures the similarity of two subsequences of a time series with either zero or one, but without in-between values, which causes sudden changes of entropy values even if the time series embraces small changes. This problem becomes especially severe when the length of time series is getting short. For solving such the problem, we propose flexible multiscale entropy (FMSE), which introduces a novel similarity function measuring the similarity of two subsequences with full-range values from zero to one, and thus increases the reliability and stability of measuring time series complexity. The proposed method is evaluated on both synthetic and real time series, including white noise, 1/f noise and real vibration signals. The evaluation results demonstrate that FMSE has a significant improvement in reliability and stability of measuring complexity of time series, especially when the length of time series is short, compared to MSE and composite multiscale entropy (CMSE). The proposed method FMSE is capable of improving the performance of time series analysis based topology and traffic congestion control techniques.

New approach of financial volatility duration dynamics by stochastic finite-range interacting voter system

We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.