Entropic Dynamic Time Warping Kernels for Co-Evolving Financial Time Series Analysis.

Area of Science:

• Quantitative Finance
• Network Science
• Time Series Analysis

Background:

• Financial markets are complex systems with dynamic, time-varying networks.
• Modeling these networks is crucial for understanding co-evolving financial time series like stock prices.

Purpose of the Study:

• To develop a novel framework for computing kernel-based similarity measures between dynamic financial networks.
• To analyze the structural evolution of financial networks over time using kernel machines.
• To bridge the gap between graph kernels and dynamic time warping for financial time series.

Main Methods:

• Constructed weighted adjacency matrices from stock price correlations.
• Computed commute time (CT) matrices to derive enhanced correlation values.
• Identified dominant correlated time series and their probability distributions.
• Represented networks as dominant Shannon entropy time series.
• Developed entropic dynamic time warping kernels for network analysis.

Main Results:

• The CT matrix effectively identifies dominant correlated stocks and their probability distributions.
• Dominant entropy time series capture network structural evolution.
• The proposed entropic dynamic time warping kernel accurately measures similarity between financial networks.
• Experiments on NYSE data validate the method's effectiveness.

Conclusions:

• The novel kernel-based framework provides a robust method for analyzing dynamic financial networks.
• The approach enhances understanding of structural evolution in financial time series.
• This work offers a valuable tool for quantitative finance and network science applications.