Opinion dynamics in financial markets via random networks

Global motion filtered nonlinear mutual information analysis: Enhancing dynamic portfolio strategies

The complex financial networks, with their nonlinear nature, often exhibit considerable noises, inhibiting the analysis of the market dynamics and portfolio optimization. Existing studies mainly focus on the application of the global motion filtering on the linear matrix to reduce the noise interference. To minimize the noise in complex financial networks and enhance timing strategies, we introduce an advanced methodology employing global motion filtering on nonlinear dynamic networks derived from mutual information. Subsequently, we construct investment portfolios, focusing on peripheral stocks in both the Chinese and American markets. We utilize the growth and decline patterns of the eigenvalue associated with the global motion to identify trends in collective market movement, revealing the distinctive portfolio performance during periods of reinforced and weakened collective movements and further enhancing the strategy performance. Notably, this is the first instance of applying global motion filtering to mutual information networks to construct an investment portfolio focused on peripheral stocks. The comparative analysis demonstrates that portfolios comprising peripheral stocks within global-motion-filtered mutual information networks exhibit higher Sharpe and Sortino ratios compared to those derived from global-motion-filtered Pearson correlation networks, as well as from full mutual information and Pearson correlation matrices. Moreover, the performance of our strategies proves robust across bearish markets, bullish markets, and turbulent market conditions. Beyond enhancing the portfolio optimization, our results provide significant potential implications for diverse research fields such as biological, atmospheric, and neural sciences.

Anomalous diffusion and long-range memory in the scaled voter model

We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We derive analytical expressions for the time evolution of the first and second moments of the scaled voter model. In addition, we have derived an analytical approximation of the first passage time distribution. By numerical simulation, we confirm our analytical results as well as showing that the model exhibits long-range memory indicators despite being a Markov model. The proposed model has steady-state distribution consistent with the bounded fractional Brownian motion, thus we expect it to be a good substitute model for the bounded fractional Brownian motion.

Opinion Dynamics Systems on Barabási-Albert Networks: Biswas-Chatterjee-Sen Model

A discrete version of opinion dynamics systems, based on the Biswas-Chatterjee-Sen (BChS) model, has been studied on Barabási-Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barabási-Albert networks (DBANs), as well as on Erdös-Rènyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities.

Precision Measurement of the Return Distribution Property of the Chinese Stock Market Index

In econophysics, the analysis of the return distribution of a financial asset using statistical physics methods is a long-standing and important issue. This paper systematically conducts an analysis of composite index 1 min datasets over a 17-year period (2005−2021) for both the Shanghai and Shenzhen stock exchanges. To reveal the differences between Chinese and mature stock markets, we precisely measure the property of the return distribution of the composite index over the time scale Δt, which ranges from 1 min to almost 4000 min. The main findings are as follows: (1) The return distribution presents a leptokurtic, fat-tailed, and almost symmetrical shape that is similar to that of mature markets. (2) The central part of the return distribution is described by the symmetrical Lévy α-stable process, with a stability parameter comparable with a value of about 1.4, which was extracted for the U.S. stock market. (3) The return distribution can be described well by Student’s t-distribution within a wider return range than the Lévy α-stable distribution. (4) Distinctively, the stability parameter shows a potential change when Δt increases, and thus a crossover region at 15 <Δt< 60 min is observed. This is different from the finding in the U.S. stock market that a single value of about 1.4 holds over 1 ≤Δt≤ 1000 min. (5) The tail distribution of returns at small Δt decays as an asymptotic power law with an exponent of about 3, which is a widely observed value in mature markets. However, it decays exponentially when Δt≥ 240 min, which is not observed in mature markets. (6) Return distributions gradually converge to a normal distribution as Δt increases. This observation is different from the finding of a critical Δt= 4 days in the U.S. stock market.