For the purpose of our analysis we compute the moving decadal mean OF annual emissions with the end year of the decades running from 1859 to 2014. We compute the correlation between warming and emissions at a decadal time scale in a moving decadal window that moves through the time series one year at a time. We find that both series show an upward drift in the moving average sample period 1859-2014 and test their relationship at the decadal time scale. Both series are detrended by subtracting the observed values from the OLS trend lines. We now look for a correlation between the two detrended series at different values of lag. Each value of lag represents the number of years after the first year of the moving emissions decade that the moving warming decade begins.

The results of the hypothesis tests are summarized in the last chart above where two two longer time scales (15 years and 20 years) are also considered. We are unable to reject the null hypothesis of no correlation in any column and therefore conclude that the data do not show evidence of a correlation between detrended emissions and detrended rate of warming at these finite time scales.

CONCLUSION: The movement to reduce fossil fuel emissions as a way of attenuating the rate of global warming subsumes a causal relationship between the rate of fossil fuel emissions and the rate of warming. This work is an attempt to detect the TCRE causal relationship between the rate of emissions and the rate of warming at finite time scales of 10 to 20 years instead of the full span of the data used in the TCRE. Three different lengths of the moving average window from one to two decades long are considered each with four different intervals for the years by which emissions lag warming. We find that none of the twelve scenarios show a statistically significant correlation between the rate of emissions and the rate of warming. The data do not show evidence of a causal relationship between emissions and warming in the decadal frequency response range. The results are inconsistent with the TCRE measure that relates the rate of warming directly to rate of emissions.

A further inconsistency in the TCRE is demonstrated in a related post where a parody shows that the TCRE methodology that relates warming to emissions also relates warming to any variable with positive values such as UFO sightings. Like fossil fuel emissions, UFO sightings are also always positive.

LINK: https://tambonthongchai.com/2018/12/03/tcruparody/