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

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.

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• Universal spectral features of different classes of random diffusivity processes
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• Superstatistical analysis of sealevel fluctuations
• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
• Bridging stylized facts in finance and data non-stationarities
• Spatio-temporal complexity of power-grid frequency fluctuations
• Generalization of the Beck-Cohen superstatistics
• Asymmetric Tsallis distributions for modelling financial market dynamics
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• Extreme Value Laws for Superstatistics
• Superstatistical generalisations of Wishart-Laguerre ensembles of random matrices
• First passage time for superstatistical Fokker-Planck models
• Analysis of Realized Volatility for Nikkei Stock Average on the Tokyo Stock Exchange
• A relative information approach to financial time series analysis using binary $N$-grams dictionaries
• Fundamental temperature exclusively determines the validity of superstatistics
• Bayesian inference and superstatistics to describe long memory processes of financial time series
• Skewed superstatistical distributions from a Langevin and Fokker-Planck approach