Intrinsic Multi-Scale Dynamic Behaviors of Complex Financial Systems

Area of Science:

• Financial econometrics
• Complex systems analysis
• Time series analysis

Background:

• Financial markets exhibit complex dynamics across various time scales.
• Understanding multi-scale behaviors is crucial for accurate financial modeling.
• Traditional methods may not fully capture the intricacies of financial time series.

Purpose of the Study:

• To analyze the intrinsic multi-scale dynamic behaviors of complex financial systems.
• To investigate the time scale dependency of financial characteristics.
• To identify dominant modes governing market structures and effects.

Main Methods:

• Application of Empirical Mode Decomposition (EMD) to stock price return time series.
• Decomposition into intrinsic mode functions (IMFs) representing different frequencies.
• Grouping IMFs into fast, medium, and slow modes for analysis.

Main Results:

• Probability distribution of returns and auto-correlation of volatilities are robust across time scales for fast and medium modes.
• Cross-correlation between stocks and return-volatility correlation are time scale dependent.
• Business sector structure is governed by the fast mode (short sampling) and medium mode (long sampling).
• Leverage and anti-leverage effects are predominantly driven by the medium mode.

Conclusions:

• Financial system dynamics are multi-scale, with different modes dominating distinct phenomena.
• The robustness of certain statistical properties contrasts with the time scale dependency of others.
• EMD provides a valuable framework for dissecting complex financial behaviors across frequencies.