Robust Statistical Detection of Power-Law Cross-Correlation

Area of Science:

• Complex systems analysis
• Statistical physics
• Neuroscience

Background:

• Widely used statistical physics methods may incorrectly identify power-law cross-correlations between unrelated time series.
• Existing methodologies struggle to reliably discard spurious cross-correlations, posing risks in complex system analysis.
• Distinguishing genuine from spurious cross-correlations requires robust statistical estimation.

Purpose of the Study:

• To develop a rigorous and robust method for testing power-law cross-correlations.
• To differentiate between genuine and spurious cross-correlations in complex physical systems.
• To establish meaningful relationships between unrelated processes.

Main Methods:

• Proposed a new theory and statistical test (PLCC-test) for power-law cross-correlations.
• Applied the PLCC-test to analyze financial stock market data and human brain activity.
• Focused on cross-correlations between amplitudes of alpha and beta frequency ranges in electroencephalogram (EEG) data.

Main Results:

• Demonstrated that common statistical physics approaches can yield incorrect power-law cross-correlations.
• The proposed PLCC-test method reliably detects genuine and discards spurious cross-correlations.
• Identified, for the first time, power-law cross-correlations between alpha and beta frequency ranges of human EEG.

Conclusions:

• The PLCC-test provides a reliable tool for assessing power-law cross-correlations in complex systems.
• The findings challenge previous assumptions about cross-correlations between financial markets and brain activity.
• The study establishes a novel, statistically validated connection within human brain activity (EEG frequency ranges).