1. Ian Newcombe CO 2 LEVEL RISE OVER 26 YEARS

2. DATASET Quarterly Mauna Loa, HI CO 2 Record Quarterly US gasoline sales Quarterly US car and light truck sales Quarterly US GDP Quarterly US electricity usage http://doktorspinn.com/wp- content/uploads/2012/10/Electric-lines.jpg http://globe-views.com/dcim/dreams/gasoline/gasoline- 05.jpg http://upload.wikimedia.org/wikipedia/commons/3/3e/I- 80_Eastshore_Fwy.jpg http://disc.sci.gsfc.nasa.gov/featured- items/images/fig1_keeling_curve.jpg http://www.moroccoworldnews.com/wp- content/uploads/2014/02/economy.jpg

3. REGRESSION The overall model is significant P-values < 0.05 The gas and cars variables appear to be insignificant The GDP and elec variables are both significant

4. All variables show high significance with each other All p-values < 0.05 VARIABLE ANALYSIS

5. If I remove the gas and cars variables, the model improves, slightly Root MSE goes from 1.827 to 1.815 Adjusted R-Squared goes from 0.9517 to 0.9817 MODIFIED REGRESSION

6. Normality Assumption of normally distributed residuals is violated Visually, the residuals do not appear normal Looking at the Shapiro-Wilk test for normality it is confirmed that the residuals are not normal P-value is < 0.05 RESIDUAL ANALYSIS

7. Constant Variance This assumption is confirmed The White’s test for heteroscedasticty shows that there is no heteroscedasticty P-value > 0.05 RESIDUAL ANALYSIS

8. No Auto-correlation The assumption that residuals will not be auto-correlated is violated The residuals are not white noise P-values < 0.05 RESIDUAL ANALYSIS

9. Including squared and interaction variables, this is the best model according to SAS C(p) of 4.59 Root MSE = 1.592 Gd = interaction variable of gasoline sales and GDP Gde= interaction between GDP and electricity SELECTED REGRESSION MODEL

10. Normal Regression GDP, elec 0.98% MAPE Selected Regression Gas, GDP, elec, gas2, GDP2, gd, gde 0.93% MAPE REGRESSION PREDICTIONS ActualPredicted 396.81 399.13 399.58 397.36 401.15 400.46 395.26 397.97 398.78 410.44 ActualPredicted 396.81 398.34 399.58 397.07 401.15 400.14 395.26 398.67 398.78 408.91

12. The three indicator variables are the quarters 1-3 Quarter 4 is the reference period When all other variables are 0, CO2 will equal 337.75 INDICATOR VARIABLE MODEL

14. By removing orders 1 and 5, I can achieve a significant model It appears that all orders are insignificant POLYNOMIAL MODELS Order 5 ModelCorrected Model

16. CYCLICAL MODEL

17. F-test shows that sin52 needs to stay All included variables have high significance CYCLICAL MODEL

19. 0.45% MAPE 0.11% MAPE PREDICTIONS Indicator Variable ModelPolynomial Model ActualPredicted 396.81 397.56 399.58 399.55 401.15 401.36 395.26 396.23 398.78 399.08 ActualPredicted 396.81 396.92 399.58 397.47 401.15 398.03 395.26 398.59 398.78 399.16

20. 0.40% MAPE PREDICTIONS Cyclical Model ActualPredicted 396.81 395.23 399.58 398.24 401.15 399.48 395.26 393.84 398.78 396.85

21. MA MODEL Took 4th difference of the variable ACF cuts after lag 2 PACF decays I will fit a MA(3) model

22. All lags appear to be significant Residuals are white noise MA MODEL

23. Data is quarterly and there is an very obvious seasonal component I fit and ARIMA(0,1,1)x (0,1,1) 4 model Residuals are white noise SARIMA MODEL

24. Residuals from regression are not white noise I took a 1, 4 seasonal difference ARIMA(1,1,4) x (1,1,4) 4 SARIMA WITH RESIDUALS

26. SARIMA VS MA RESIDUAL SARIMASARIMA with Residuals

27. MAPE = 0.06% MAPE = 0.10% MODEL COMPARISONS MA(3)SARIMA ActualPredicted 396.81 396.41 399.58 399.24 401.15 400.50 395.26 395.41 398.78 398.31 ActualPredicted 396.81 396.53 399.58 399.48 401.15 400.77 395.26 395.69 398.78 398.72

28. MAPE = 0.08% MODEL COMPARISONS ARIMA Residual ActualPredicted 396.81 396.47 399.58 399.55 401.15 400.83 395.26 396.16 398.78 398.79

29. OVERALL COMPARISON The best regression model was the backward selected model Root MSE = 1.59 vs. 1.82 The best deterministic time series model was the cyclical model Root MSE = 0.001 vs. 0.97 vs 2.30 The best time series model was the SARIMA model STD error = 0.37 vs 0.39 (MA) vs 0.91(ARIMA RES) The best overall therefore is the cyclical model

30. PREDICTIONS COMPARISON The best predictions were made with the SARIMA model MAPE = 0.06% ActualPredicted 396.81 396.53 399.58 399.48 401.15 400.77 395.26 395.69 398.78 398.72

31. CONCLUSIONS CO 2 levels can be predicted very well if you know how much gasoline was bought, cars sold, US GDP, and electricity usage CO 2 levels follow a seasonal pattern Summer/Winter in Northern Hemisphere 2014 GDP

32. QUESTIONS?