Nonextensive triplets in stock market indices

Abstract

Stock market indices are one of the most investigated complex systems in econophysics.Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover that stock markets follow nonextensive statistics regarding equilibrium, relaxation and sensitivity. We find nonextensive behavior in stock markets for developed countries, but not for developing countries. Distances between nonextensive triplets suggest that some stock markets might share similar nonextensive dynamics, while others are widely different. The current findings strongly indicate that the stock market represents a system whose physics is properly described by nonextensive statistical mechanics. Our results shed light on the complex nature of stock market indices, and establish another formal link with the nonextensive theory.

Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

“…The quantity defined by equation ( 20) is known as the q-distance between two q-triplets and has been used before in financial systems (for example in Stosic, 2019) to describe differences between the extensive statistics of two distinct timeseries.…”

“…In this direction, Stosic et al (Stosic, 2019) studied the non-extensivity of price volatilities for 34 major stock market indices between 2010 and 2019 by the estimation of q-triplet of Tsallis statistics. The distances between q-triplets [2] indicated that some stock markets might share similar non-extensive dynamics, while others are widely different.…”

Discrete q-Exponential Limit Order Cancellation Time Distribution

“…A key innovation of our approach lies in the discovery of a general statistical distribution governing limit order cancellation times. We propose the application of Tsallis statistics, a generalization of Boltzmann-Gibbs statistics [30][31][32], to fit the histograms of limit order cancellation times. Remarkably, the distribution's parameters for various stocks and time periods appear close, suggesting a universal nature of the observed statistical property.…”