Adaptation of Partial Mutual Information from Mixed Embedding to Discrete-Valued Time Series

Area of Science:

• Causality analysis
• Time series analysis
• Information theory

Background:

• Causality analysis estimates interactions and connectivity in dynamical systems.
• Partial Mutual Information from Mixed Embedding (PMIME) is effective for continuous-valued time series.
• PMIME uses dimension reduction and conditional mutual information (CMI) to identify causal effects.

Purpose of the Study:

• To adapt PMIME for discrete-valued multivariate time series, creating Discrete PMIME (DPMIME).
• To develop a parametric significance test for CMI in DPMIME.
• To investigate the impact of the global financial crisis on financial market causality networks.

Main Methods:

• Developed DPMIME for discrete time series by estimating discrete probability distributions and CMI.
• Derived the asymptotic distribution of estimated CMI for parametric significance testing.
• Conducted Monte Carlo simulations using discrete time series and applied DPMIME to financial market data.

Main Results:

• DPMIME accurately estimates discrete probability distributions and CMI.
• The parametric significance test in DPMIME favorably compares to resampling tests.
• DPMIME's accuracy in estimating direct causality converges with time series length, matching PMIME's accuracy.

Conclusions:

• DPMIME is a robust method for causality analysis in discrete time series.
• The parametric significance test enhances the reliability of causality detection.
• DPMIME can be applied to real-world complex systems, such as financial markets, to understand causality network changes.