Quantum Bohmian-Inspired Potential to Model Non-Gaussian Time Series and Its Application in Financial Markets

Area of Science:

• Quantum mechanics
• Time series analysis
• Financial modeling

Background:

• Gaussian statistics underestimate rare events in time series.
• Strong coupling between events leads to non-Gaussian probability densities.
• Understanding rare events is crucial for accurate time series analysis.

Purpose of the Study:

• Investigate the impact of rare events on time series probability densities using quantum measurements.
• Model non-Gaussian time series behavior and its quantum mechanical implications.
• Apply quantum potential analysis to financial markets.

Main Methods:

• Implemented quantum modeling based on Bohmian mechanics.
• Utilized the multifractal random walk (MRW) approach to model non-Gaussian time series.
• Analyzed the role of the MRW parameter λ in derived quantum potentials.
• Computed quantum potentials for S&P financial market time series.

Main Results:

• Rare events in time series can generate a potential barrier in the high-frequency region of the quantum potential.
• Bohmian quantum analysis showed the quantum potential's behavior is significantly influenced by the degree of non-Gaussianity (λ).
• The derived quantum potential exhibits distinct characteristics for rare events, deviating from Gaussian assumptions.
• Quantum potentials were successfully computed for S&P financial market data, confirming the presence of rare events.

Conclusions:

• Bohmian mechanics and quantum potentials offer a robust framework for analyzing time series with rare events.
• The multifractal random walk parameter λ is key in determining the quantum potential's structure and the impact of rare events.
• Quantum potential analysis provides insights into financial market dynamics, highlighting deviations from Gaussian behavior due to rare events.