Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming

Abstract

Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid.We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality.

Anthropogenic greenhouse gas concentrations and global temperature: a smooth transition analysis

“…where temp t , x t and Δz t are defined as in (1) and growth t refers to world GDP growth at time t/n (the time is rescaled by the sample size to make the results comparable across different sample sizes). 8 Since the abnormal climate change is assumed to be affected by both the enhanced greenhouse effect and the depletion of the ozone layer, the GDP growth is used as a proxy of economic/industrial activity where industrial emissions play a crucial role in both processes. As noted by Babiy et al [2], the enhanced greenhouse effect is caused by the emissions of carbon dioxide, methane, nitrous oxide and fluorine-containing compounds, and substances, which contribute indirectly to the greenhouse effect (such as nitrogen oxides, carbon monoxide and volatile organic compounds), while atmospheric emissions of acidifying substances such as sulphur dioxide (SO2) and nitrogen oxides (NOx), mainly from the burning of fossil fuels contribute to the formation of ozone at low level.…”

Is radiative forcing cointegrated with temperature? A further examination using a structural time series approach

“…As our preceding discussion suggests, there is considerable and ongoing debate with regard to choice of econometric models and use of an appropriate empirical strategy in order to study our main relationships of interest (e.g. Chevillon (2017), Lai and Yoon (2018), Stern and Kaufmann (2014), Gallegati (2018) and McMillana and Wohar (2013)). Based on our consideration of the empirical literature we believe that our results make a contribution to the literature due to our use of a theoretically motivated framework in which a number of plausible alternatives are considered in detail, as opposed to simply employing a basic cointegration framework, as outlined in detail below.…”

“…Another example of an econometric development applied to this topic is Chevillon (2017) who employs a procedure that offers a robust test for the rank of cointegration within a vector autoregressive (VAR) that may have misspecified local linear trends. Using this approach, it is reported that temperature and greenhouse gases appear to be cointegrated.…”