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

TL;DR

This paper introduces a method to analyze complex time series using superstatistics, extracting key parameters and validating the model with both surrogate and real data, including turbulence and stock market indices.

Contribution

It presents a general technique for applying superstatistics to time series, enabling the extraction and validation of superstatistical parameters from experimental data.

Findings

Successful extraction of superstatistical parameters from data

Validation of superstatistics model with surrogate data

Application to turbulence and stock market data

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.