In recent years, demand for energy, the main source of carbon emissions, has continued to increase against the background of GDP production growth. Ensuring a global transition to a low-carbon economy can be achieved by increasing the consumption of environmentally friendly energy. Crises have a noticeable impact on the development of the global energy system, slowing down economic growth and transforming the structure of consumed energy sources. Russia has been affected by several crises over the past two decades, which have led to disruptions in supply chains, volatility in energy prices, fluctuations in GDP growth and carbon emissions. The classical approach to the study of relationships suggests replacing empirical data with smoothed ones, abstracting from taking into account fluctuations caused by crises. The article examines the changes in the correlation between GDP growth trends and carbon emissions in Russia, which occur under the influence of crises. The article proposes a new method for studying relationships in economics, which refuses regression smoothing of data. Its conceptual basis is the interpolation of data by a cubic spline, which preserves all changes in the dynamics of processes without distortion. Correlations are searched for between trends -fluctuations in the rate of GDP growth and carbon emissions. The method is based on a natural mathematical method of analytical description of velocity – differentiation of spline models of GDP growth dynamics and carbon emissions. Fluctuations in the growth rate reveal the evolution of the parameters of the relationship between trends in the rate of GDP growth and carbon emissions under the influence of crises.
