Dynamic heteroscedasticity of time series interpreted as complex networks

Area of Science:

• Time Series Analysis
• Complex Networks
• Econometrics

Background:

• Heteroscedasticity in time series is crucial for understanding nonlinearity and complexity.
• Existing research primarily focuses on long-term heteroscedasticity, neglecting nonlinear dynamics.

Purpose of the Study:

• To propose a new complex network model for analyzing short-term time series heteroscedasticity.
• To investigate the dynamic evolution of heteroscedasticity from a nonlinear perspective.
• To provide tools for predicting fluctuation patterns and understanding their roles.

Main Methods:

• Converting time series data into complex networks.
• Symbolizing heteroscedastic features using the autoregressive generalized autoregressive conditional heteroscedasticity (ARCH) model.
• Analyzing network properties like node out-strength and betweenness centrality.
• Applying clustering effects analysis.

Main Results:

• The model successfully analyzes short-term heteroscedasticity and its dynamic evolution.
• Network analysis reveals the importance of pattern diversity in determining short-term period length.
• Node centrality metrics help understand the roles of different fluctuation patterns.

Conclusions:

• The proposed complex network model offers a novel approach to studying short-term time series heteroscedasticity.
• Understanding the dynamic evolution of fluctuation patterns enhances insights for researchers and investors.
• The method facilitates prediction of probable future patterns and detection of cluster-specific behaviors.