This is using statistical method to investigate whether CO2 concentration and CO2 emission do cause a rise in global temperature.

1. A Statistical Analysis of Global Warming Gaetan Lion. July 2006

4. Data Sources Time series: Carbon Emission and Air temperature: 1867 – 2004. Carbon Concentration: 1958 – 2004.

5. Testing CO2 Emission

6. The Cause?

7. The Effect?

8. A Perfect Granger Causality set up

9. Models’ preliminary results The tested independent variable is CO2 emission level in mm of tons a year ago. The dependent variable is avg. global temperature in Celsius in current year.

10. Checking for residual serial correlation A Durbin Watson score close to 2.00 indicates there is no residual serial correlation. We confirmed this by also calculating the actual residual serial correlation that was indeed clause to zero.

11. Checking for Heteroskedasticity Land. Residual in Celsius. Heteroskedasticity looks like this. The two larger graphs above indicate that the residuals are not heteroskedastic.

12. How Should we test the Residuals? The Jarque-Berra test calculates the probability a sample (square residuals) comes from a normally distributed population. The probability is close to zero. Thus, we should weigh more on nonparametric test (Mann Whitney). Jarque-Berra test

13. Granger Causality output We observe a large difference in P values between the t test and Mann-Whitney test. Given the Jarque Berra test result, we should rely more on the Mann-Whitney test P values. At end of presentation, we’ll see a way to reconcile between the t test and Mann-Whitney.

15. Models’ preliminary results The tested independent variable is CO2 emission % change a year ago. The dependent variable is avg. global temperature change in Celsius in current year.

16. How Should we test the Residuals? The probability is very close to zero that these two samples would come from a normally distributed population. Thus, we should rely more on nonparametric test (Mann Whitney) test. Jarque-Bera Test

17. Granger Causality output Here the P values from the t test and the Mann-Whitney test are really close. They both tell us that % change in CO2 does not Granger cause change in average global temperature.

18. Scatter Plot1

19. Testing CO2 Concentration

20. CO2 Concentration history

21. Models’ preliminary results The tested independent variable is CO2 concentration level a year ago. The dependent variable is avg. global temperature in Celsius in current year.

22. Checking for residual serial correlation Per Durbin Watson score and actual serial correlation calculation, residual serial correlation is close to zero.

23. How Should we test the Residuals? The probability is very close to zero that samples come from a normally distributed population. Thus, we should weigh much more on nonparametric test (Mann Whitney). Jarque-Bera test

24. Granger Causality output The difference in P value is huge. We will shortly reconcile the difference between the two. Given the result from the Jarque-Berra test, we should definitely weight the result of the Mann-Whitney test more.

26. Models’ preliminary results The tested independent variable is change in CO2 concentration (% change a year ago). The dependent variable is avg. global temperature change in Celsius in current year.

27. How Should we test the Residuals? Probability is very close to zero. Thus, we should weigh much more on nonparametric test (Mann Whitney) in our hypothesis testing. Jarque-Bera test

28. Granger Causality output Here the P values from the t test and the Mann-Whitney test are closer. They both tell us that % change in CO2 concentration does not appear to Granger cause change in average global temperature.

29. Scatter Plot2

30. Granger Causality Summary Two tail P value

31. T test vs Mann-Whitney reconciliation Two tail P value If we recalculate the unpaired t test using Medians instead of Averages, the resulting P values get a lot closer to the ones generated by the Mann-Whitney test.