Quantifying the randomness of the stock markets

Area of Science:

• Quantitative Finance
• Complexity Science
• Time Series Analysis

Background:

• Approximate Entropy (ApEn) quantifies randomness in time series.
• Direct comparison of financial data using ApEn is limited due to varying statistical properties.
• A need exists for a standardized measure to compare patterns across different financial markets and time periods.

Purpose of the Study:

• To develop a novel measure for comparing time series patterns using Approximate Entropy.
• To adapt ApEn for cross-series and cross-epoch comparisons in financial data.
• To investigate stock market dynamics in relation to economic situations.

Main Methods:

• Utilized Approximate Entropy (ApEn) as a foundation for pattern quantification.
• Developed a maximum entropy approach to enable comparative analysis of time series.
• Applied the refined methodology to analyze six global stock markets.

Main Results:

• The number of quantifiable patterns varied significantly across the analyzed stock markets.
• Observed changes in pattern counts correlated with prevailing economic conditions.
• Findings support the Adaptive Markets Hypothesis by demonstrating market adaptability.

Conclusions:

• The developed method allows for robust comparison of randomness and patterns in financial time series.
• Market dynamics exhibit significant changes influenced by economic factors.
• This approach offers new insights into market behavior and adaptability.