Correlational and Non-extensive Nature of Carbon Dioxide Pricing Market

Abstract

In this paper, at the first time, the analysis of correlational and non-extensive properties of the $$\text {CO}_{2}$$ emission market relying on the carbon emissions futures time series for the period 04.07.2008–10.05.2021 is performed, and the daily data of the power sector from the U.S. Carbon Monitor for the period 01.01.2019–10.05.2021, which consist the data of both individual countries (USA, Germany, China, India, United Kingdom, et al.) and global emissions (World) are investigated using such approach. To demonstrate the applicability of these methods on systems of another nature and complexity, the analysis of the Dow Jones Industrial Average (DJIA) index is presented. The results show that both futures and the DJIA are presented to be non-extensive, and the distribution of their normalized returns can be better described by power-law probability distributions, particularly, by $$q$$ -Gaussian. Tsallis triplet for the entire time series of $$\text {CO}_{2}$$ emissions futures and the DJIA is estimated, and $$q$$ -triplet as an indicator of crisis phenomena is presented, relying on the sliding window algorithm. It can be seen that the triplet behaves characteristically during economic crises. This study shows that the toolkit of the random matrix theory (RMT) allows to investigate the correlational nature of the carbon emissions market and to build appropriate indicators of crisis phenomena, which clearly reflect the collective dynamics of the entire research base during events of this kind.