From solar flare time series to fractional dynamics

Krzysztof Burnecki*, Joseph Klafter, Marcin Magdziarz, Aleksander Weron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We demonstrate that continuous-time FARIMA processes with α-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of α-stability and self-similarity are implemented for empirical time series describing the energy of solar flares. Based on observed physical time series we solve the challenging problem of how to detect long-range dependence from real data and how to model it via fractional dynamics (Langevin or Fokker-Planck). We employ here codifference as a proper measure for long-range dependence. It is applicable to empirical data from the distribution lacking the second moment.

Original languageEnglish
Pages (from-to)1077-1087
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Issue number5-6
StatePublished - 15 Feb 2008


  • Fractional dynamics
  • Long-range dependence
  • Self-similarity
  • Solar flares
  • Stable noise


Dive into the research topics of 'From solar flare time series to fractional dynamics'. Together they form a unique fingerprint.

Cite this