Modeling Complex and Composite Behaviors of Stock Market Entropy Fluctuations Using Statistical Physics
Keywords:
Complex Behaviors, Stock Market Entropy Fluctuations, Statistical Physics, Uncertainty, Standard Deviation MotionAbstract
Objective: This study aims to analyze and model the complex and composite behaviors of stock market entropy fluctuations in Iran using statistical physics, integrating Brownian motion, Poisson, Lévy, and Lévy–Khintchine processes.
Methods and Materials: This quantitative study employed a predictive modeling approach using monthly data from Iran’s stock market indices from 2012 to 2024. Random contact processes, jump-diffusion mechanisms, and composite probability distributions were applied under a statistical physics framework. The study utilized Brownian, Poisson, and Lévy–Khintchine processes to simulate random and jump fluctuations. Data analysis was performed with R, Python, and MATLAB software using correlation tests, multivariate regression, AR and GARCH models, and a multivariate exponentially weighted moving average (EWMA) model to examine the dynamic interdependence among variables.
Findings: Results revealed that stock market entropy was significantly influenced by oil price volatility, exchange rate fluctuations, global gold prices, market risk premiums, and cryptocurrency prices. Sudden shocks in oil and cryptocurrency markets sharply increased market entropy and complexity, whereas smaller fluctuations had gradual effects. The Lévy–Khintchine and jump-diffusion models effectively captured nonlinear dynamics and inter-variable interactions. Engel–Sheppard and Tsay tests confirmed that correlations among variables were time-varying, and the EWMA model outperformed the conditional heteroskedasticity model in dynamic estimation.
Conclusion: The study concludes that statistical physics models, particularly the Lévy–Khintchine process, provide a robust framework for understanding and forecasting nonlinear and complex behaviors in Iran’s stock market. These models enhance the precision of volatility and entropy estimation and can guide risk management and investment strategies.
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Copyright (c) 2025 Mahsa Rahavi, Gholamreza Zomorodian, Bahman Banimahd (Author)
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