Explosive Temperatures
Authors: Gronwald Marc 
Published: March 2024

Introduction
&#160;
Extreme price episodes are a common feature in many financial as well as commodity markets: the Nasdaq index reached its historical high early in Year 2000, crude oil prices peaked in Summer 2008, and Bitcoin prices hit a record high end of 2017. These episodes have in common that the price behavior can be captured using the statistical concept of (temporary) explosiveness: Phillips et al. (2011, International Economic Review) who also propose a new empirical testing procedure, find evidence of this feature in the Nasdaq prices. The remaining two of the above-mentioned markets have been analysed by the author of this paper: Gronwald (2016, Energy Economics) deals with crude oil markets; Gronwald (2021, Finance Research Letters) analyses cryptocurrency markets.
&#160;
This paper analyses if the feature of explosiveness can also be found in global as well as hemispheric temperature data.
&#160;
The literature this analysis contributes to finds its origin in the debate whether temperatures are characterised by deterministic (Estrada et al. 2013, Nature Geoscience) or stochastic (Kaufmann et al. 2013, Climatic Change) trends. A direct motivation for this paper are recent contributions such as Chang et al. (2020) and Holt and Terasvirta (2020, both Journal of Econometrics). Both papers point to differences in the time series behaviour in the Northern and Southern hemispheres. Chang et al (2020) find evidence of two stochastic trends in Northern hemispheric data, but only one in the Southern Hemisphere; Holt and Terasvirta (2020) find that shifts in the mean of the Northern series can be adequately characterised by three logistic function components, two are sufficient for the case of the Southern one.
&#160;
Data
&#160;
Data is taken from the HadCRUT5 data set provided by the Met Office Hadley Centre.
&#160;
Finding
&#160;
The key finding of this paper is that global temperature anomalies are characterised by (temporary) explosiveness. This finding indicates that temperatures, given the extended period without systematic change, increase fast and the witnessed increase is large. What is more, clear evidence of explosiveness is only found in Northern hemispheric data; in the South, this is considerably less pronounced.
&#160;
Conclusions
&#160;
What this paper finds is also relevant for the analysis of the relationship between carbon emissions and warming. Among the questions addressed in that literature is whether or not temperatures and radiative forcings from greenhouse gases share the same common trend; in other words, if a cointegration relationship exists. Of particular interest in this context is if that relationship is stable. Papers such as Agliardi et al. (2019, EAERE) as well as Eroglu et al. 2021, Econometric Reviews) epitomise these research efforts. Despite the above-mentioned dispute about the behaviour of the individual series, the conventional view is that there is a stable linear cointegration relationship. This view is based on climate science studies such as Matthews et al. (2009, Nature). The findings of this paper challenge this notion. In addition, this paper shares concerns expressed in Rantanen et al. (2022, CEE) about an underestimation of temperature increases in the Arctic by climate models.