Correlational and Non-extensive Nature of Carbon Dioxide Pricing Market

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