This paper deals with the analysis of the relationship between CO 2 emissions and temperatures. For this purpose, global CO 2 emissions and four measures of global temperatures (land, land and ocean, northern and southern temperatures) are used. We used techniques based on fractional integration and cointegration. The results indicate first that the orders of integration differ in the two variables. Thus, while emissions are I(1) or I(d) with d higher than 1, temperatures display orders of integration strictly smaller than 1 and thus invalidating the hypothesis of cointegration between the two variables. Due to this, another approach is conducted where we suppose that the emissions are weakly exogenous in relation to the temperatures. The results using this approach show a significantly positive relationship between the two variables with a long memory pattern. K E Y W O R D S fractional integration, global emissions, global temperatures, long memory 1 | INTRODUCTION Concern about global warming and climate change around the world is increasing. According to Nicholls et al. (1996), Jones and Wigley (2010), Folland et al. (2018), among others, the temperature on the Earth's surface has raised significantly over the last 100 years. This has been caused by industrialization and the effect of burning and emissions of fossil fuel, greenhouse gas concentration that affects the atmosphere (Anderegg et al., 2010; Beckage et al., 2018, etc.), but also by the innate variability of the climate system (e.g., solar irradiance) or by the combination of the two. The most noticeable aspect is the strong correspondence between temperature and the concentration of carbon dioxide in the atmosphere (see Zickfeld et al., 2012; McMillan and Wohar, 2013; Zickfeld et al., 2016). According to the National Oceanic and Atmospheric Administration (NOAA), carbon dioxide concentration and temperatures have the same behaviour and they