Superstatistical fluctuations in time series: applications to share-price dynamics and turbulence

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036108. doi: 10.1103/PhysRevE.80.036108. Epub 2009 Sep 14.

Abstract

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions. We test the method thoroughly with surrogate data sets. Then the applicability of the superstatistical approach is illustrated using real experimental data. We study two examples, velocity time series measured in turbulent Taylor-Couette flows and time series of log returns of the closing prices of some stock market indices.

MeSH terms

  • Computer Simulation
  • Data Interpretation, Statistical*
  • Models, Econometric*
  • Models, Statistical*
  • Nonlinear Dynamics*
  • Rheology / methods*
  • Time Factors