2. Car Sales Analysis of monthly sales of light weight vehicles. Laura Pomella Karen Chang Heidi Braunger David Parker Derek Shum Mike Hu

3. Car Sales Overview Slight trend in mean and variance.

4. Car Sales Overview (2) Histogram of Car Sales

5. Trend? Dependent Variable: CARSALES Method: Least Squares Date: 06/01/06 Time: 19:23 Sample: 1976:01 2006:04 Included observations: 364 VariableCoefficientStd. Errort-StatisticProb. TREND0.0127350.00080415.833360.0000 C12.297470.16937872.603490.0000 R-squared0.409168 Mean dependent var14.62159 Adjusted R-squared0.407536 S.D. dependent var2.094847 S.E. of regression1.612439 Akaike info criterion3.798853 Sum squared resid941.1859 Schwarz criterion3.820266 Log likelihood-689.3912 F-statistic250.6953 Durbin-Watson stat0.449535 Prob(F-statistic)0.000000

6. Correlogram of CARSALES Large spike in autocorrelation function at lag one equal to 0.864. Slow decay in ACF suggesting stationary series. Looked to Unit-Root Test for confirmation.

7. Unit-Root Test (2 Lags)

8. Unit-Root Test (3 Lags)

9. Pre-Whitened Series

10. Heteroscedasticity?

11. Histogram of DCARSALES Single-peaked and very kurtotic suggesting conditional heteroscedasticity.

12. Correlogram of DCARSALES

13. Unit-Root Test (1 Lag)

14. First-Differenced Log Did nothing to help with any trend in the variance.

15. DCARSALES as ARMA(2,1)

16. ARMA(2,1) Residuals

17. ARMA(2,1) Residuals (2)

18. ARMA(2,1) Residuals (3) Single-peaked, non-normal and very kurtotic suggesting conditional heteroscedasticity.

19. Breusch-Godfrey Test

20. Competing Model - ARMA(2,2)

21. ARMA(2,2) Residuals

22. ARMA(2,2) Residuals (2)

23. ARMA(2,2) Residuals (3) Single-peaked and very kurtotic suggesting conditional heteroscedasticity.

24. Breusch-Godfrey Test – ARMA(2,2)

25. ARCH Test ARCH Test: F-statistic15.90085 Probability0.000081 Obs*R-squared15.30969 Probability0.000091 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 06/01/06 Time: 19:47 Sample(adjusted): 1976:05 2006:04 Included observations: 360 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. C0.6840560.1500444.5590230.0000 RESID^2(-1)0.2062200.0517153.9875870.0001 R-squared0.042527 Mean dependent var0.861758 Adjusted R-squared0.039852 S.D. dependent var2.774273 S.E. of regression2.718431 Akaike info criterion4.843526 Sum squared resid2645.572 Schwarz criterion4.865116 Log likelihood-869.8348 F-statistic15.90085 Durbin-Watson stat1.993423 Prob(F-statistic)0.000081

26. GARCH(1,1) with ARMA(2,2)

27. GARCH(1,1) Residuals

28. GARCH(1,1) Residuals (2)

29. GARCH(1,1) Residuals (3) Single-peaked but slightly skewed, non-normal and very kurtotic.

30. GARCH(1,1) Residuals Squared

31. ARCH Test

32. In-Sample Forecast DATEForecastdcarsalesSEFH(t) 5/1/2005 -0.54-0.053540.6218580.386707 6/1/2005 1.18-0.069590.8185470.568173 7/1/2005 2.86-0.006810.9380830.706278 8/1/2005 -3.930.0444271.0162740.811383 9/1/2005 -0.410.0606871.0730350.891373 10/1/2005 -1.640.0553081.1146090.95225 11/1/2005 10.0459071.1451150.99858 12/1/2005 1.450.0408561.1677931.03384 1/1/2006 0.430.0403341.1847781.060674 2/1/2006 -1.030.0416541.1975431.081096 3/1/2006 -0.010.0427931.2071661.096639 4/1/2006 0.150.043181.2144381.108468

33. In-Sample Forecast Plots Forecast and confidence interval for months June 2005 to April 2006.

34. In-Sample Forecast Plots (2)

35. Forecast Through April 2007

36. Forecast Through April 2007 (2)

37. Recolored!

38. G o t C a r ?