Nonextensive statistical features of the Polish stock market fluctuations

TL;DR

This study analyzes the statistical features of Polish stock market returns across various time scales, revealing nonextensive behavior modeled by q-Gaussians and a systematic decrease of the nonextensivity parameter with longer time lags.

Contribution

It demonstrates that return distributions of the Polish stock market can be effectively described by q-Gaussians across multiple time scales, highlighting nonextensive statistical features.

Findings

Return distribution tails follow inverse cubic power-law at short time scales.

Distributions deviate towards Gaussian at longer time scales.

The nonextensivity parameter q decreases with increasing time lag.

Abstract

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging from one minute up to one hour. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power-law, as identified previously for majority of the mature markets. Within the time scales studied a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single $q$-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter $q$ is found to systematically decrease when increasing the time scales.