Sephton (2020) demonstrated that nearly all national and relative CO2 emissions in a group of 33 nations were mean-reverting after making allowance for non-linear deterministics and first-order autocorrelation. This suggested that a permanent reduction in emissions could only be accomplished through structural changes that alter trends. This paper extends the analysis in two directions. The first is to test whether the AR1 specification is preferred to an unrestricted general dynamic model through the application of common factor tests. The second is to non-nested hypothesis tests to determine which specification is best supported by the data. In many cases emissions are mean-reverting, but for some countries, none of the models appear to adequately capture the temporal behaviour of national or relative CO2 emissions. In a majority of nations, policies that fundamentally change behaviour and induce structural change are required to achieve a permanent reduction in emissions.