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- 1. A Statistical Analysis of Global Warming Gaetan Lion. July 2006
- 2. Global Warming basics <ul><li>The anthropogenic emission of CO2 is increasing CO2 concentration in the atmosphere. </li></ul><ul><li>CO2 increasing level is causing Global temperature to rise. </li></ul>
- 3. Independent Variables to test <ul><li>CO2 emission </li></ul><ul><li>CO2 concentration </li></ul>We test each of these independent variables separately against the dependent variable: Land Air temperature .
- 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.
- 14. Modify the variables <ul><li>For the tested independent variable, we will change it from CO2 emission level to % change in CO2 emission. </li></ul><ul><li>For the dependent variable, instead of looking at temperature level, we’ll take the change in temperature. </li></ul>
- 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.
- 25. Using different variables <ul><li>For the tested independent variable, we will change it from CO2 concentration level to change in CO2 concentration level (% change over previous year). </li></ul><ul><li>For the dependent variable, instead of looking at temperature level, we’ll take the change in temperature (in Celsius) over previous year. </li></ul>
- 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.

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