CO2 and global temp: Can you model relation between two measures if one is monotonic? In 1998 the "hockey stick" paper was published in Nature (Mann Bradley Hughes Nature April 1998 v392 pp 779-787). This was supposedly mainly Mann;s dissertation work, so I will say "Mann."
Mann basically took a bunch of predictors and used PCA to form grand predictors, and examined the degree that they correlated with global temps.
In that article is Figure 5b, "the hockey stick" that launched a thousand ships.
One predictor was atmospheric CO2. Here is a problem I see with this analysis. In the decades of recent well-recorded temp and CO2 data, CO2 has been monotonic: it has risen steadily. So, how can we use statistical approaches to figure out what correlates with rise and fall of CO2 if CO2 never falls, but rises in a predictable, steady fashion? Statistically, any measured variable that has either a positive or negative trend will have a notable "correlation," mathematically, with CO2, and so will be in the set of possible causes.
Would it not be necessary for any modeling of a linear relation, for the purposes of considering causal relations, to have both measures vary both up and down across time? If so, then how can we statistically test whether any suspected cause contributes to the monotonically rising CO2 levels of the recent 100 years?