An analysis of more than 50 years of monthly data shows that the rate of change of temperature precedes the rate of change of atmospheric CO2 content by 6 months. Both variables are determined as 12 month changes to remove any possible seasonal effects.
If CO2 is responsible for temperature change as is generally claimed, then it is difficult to explain how the effect precedes the cause.
On the much longer time scale of ice ages it has been found that temperature precedes CO2 changes by about 800 years. So it is surprising to find that a moderate correlation exists with just a 6 month lag.
The graphs of the two variables are shown below. Each is treated the same way, by calculating a 12 month change and then smoothed for 12 months together and plotted at the centre of the period. The 6 month lag between temperature rate of change and CO2 rate of change is evident.