Limits of the memory coefficient in measuring correlated bursts

Area of Science:

• Complex systems analysis
• Statistical physics
• Time series analysis

Background:

• Temporal event sequences exhibit inhomogeneities.
• Interevent time correlations (correlated bursts) are poorly understood.
• Memory coefficient and burst size distribution are key measures.

Purpose of the Study:

• To analytically derive the memory coefficient based on interevent time and burst size distributions.
• To explain the observed association between memory coefficient and burst size distribution tail.
• To reconcile inconsistent empirical findings in human activities.

Main Methods:

• Assuming conditional independence of consecutive interevent times.
• Deriving an analytical formula for the memory coefficient.
• Comparing analytical results with empirical data.

Main Results:

• The derived analytical form explains the general tendency of larger memory coefficients with heavier burst size distribution tails.
• The model reconciles apparently contradictory observations in human activity data.
• The memory coefficient's limitations in measuring correlated bursts are identified.

Conclusions:

• The analytical framework provides a deeper understanding of correlated bursts.
• The study resolves inconsistencies in human activity data analysis.
• The memory coefficient's utility is clarified, highlighting its limitations.