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The burst-tree decomposition method reveals complex temporal correlations in event sequences. Different burst-merging kernels significantly impact burst-size distributions and autocorrelation functions, offering insights into time series dynamics.

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Area of Science:

  • Complex Systems
  • Data Analysis
  • Statistical Physics

Background:

  • Temporal correlations are vital for accurate time series modeling in various scientific fields.
  • The burst-tree decomposition method uncovers hierarchical structures in event sequences, revealing correlations beyond simple interevent times.

Purpose of the Study:

  • To investigate the influence of different burst-merging kernels on higher-order temporal correlations.
  • To analyze the effects of kernels on burst-size distributions, memory coefficients, and autocorrelation functions.

Main Methods:

  • Utilized the burst-tree decomposition method to analyze event sequences.
  • Employed various burst-merging kernels, including constant, sum, product, diagonal, and empirically inspired kernels.
  • Analyzed burst-size distributions, memory coefficients, and autocorrelation functions.

Main Results:

  • Kernels promoting preferential merging result in heavy-tailed burst-size distributions.
  • Assortative merging kernels lead to positive correlations between burst sizes.
  • Autocorrelation function decay depends on both the kernel and the interevent time distribution's power-law exponent.

Conclusions:

  • Burst-merging kernels play a crucial role in shaping higher-order temporal correlations within time series.
  • Analytical solutions for burst-size distributions were derived for certain kernels by drawing analogies to coagulation processes.
  • Findings provide insights into the underlying mechanisms governing temporal correlations in complex systems.