1. Dow Jones and Oil Prices ECON 240C Take Home 2 Members: Jessica Aguirre Edward Han Masatoshi Hirokawa Han Liu Lu Mao Christian Mundo Yuejing Wu

2. Contents Part A: Introduction Part B: The 1973-1974 oil crisis Part C: Pre-whitening oil price (oilp) Part D: Transforming first differenced Dow Jones Average (ddji) to W Part E: Fitting a distributed lag model Part F: Forecasting the Dow Jones Industrial Average

3. Introduction The impact of oil prices on the stock market is inversely proportional. An increase in oil prices leads to a decrease in the stock market. On the contrary, a decrease in oil price on average leads to a higher stock market return. We assume that the effect of oil prices can be predictable in the stock market. We used following monthly data from January 1946 to April 2011. 1.The Spot Oil Price: West Texas Intermediate (adjusted to real oil price) 2.The Dow Jones Industrial Average.

4. 1973-74 Oil Crisis Part 1 In October of 1973 Middle-eastern OPEC nations stopped oil exports to the US and other western nations. They meant to punish the western nations that supported Israel. Prices of gasoline quadrupled, rising from just 25 cents to over a dollar per gallon in just a few months. The American Automobile Association recorded that up to twenty percent of the country ’ s gas stations had no fuel one week during the crisis and drivers were forced to wait in line for 2-3 hours to get gas.

5. 1973-74 Oil Crisis Part 2 The total consumption of oil in the U.S. dropped twenty percent due to the effort of the public to conserve oil and money. The embargo ended in 1974 and Arabs began to ship oil to Western nations again, but at inflated prices. Therefore, there is a huge gap with oil price in 1973.

6. Oil Prices Oil prices for 1946 to 2010 (taken monthly) Notice the change in habit around 1973-1974 Before 1973 Oil prices remained extremely stable

7. Normality (OILP) Using a histogram we can show that OILP is not Normal Jaque-Bera: 177.94 Probability: 0.0000 This breaks an assumption of the OLS Model

8. Correlation (OILP) Autocorrelation shows signs of an evolutionary model This may be the result of a unit root

9. ADF Test (OILP) The ADF test shows that the unit root null hypothesis can not be rejected

10. First Difference of Oil Prices In an attempt to remove the unit root we take the first difference of OILP The resulting graph looks much less evolutionary

11. Normality (DOILP) Jarque Bera: 108202 Probability: 0.0000 Kurtosis: 60.08 Skewness: 3.8088

12. Correlation (DOILP) Partial Correlation significant lags are: 4 6 12 15 16 This translates into: AR(4) AR(6)

13. Unit Test (DOILP) ADF Test Statistic -26.369 1% Level:-3.44 5% Level:-2.87 10% Level:-2.57 No Unit root

14. Estimation (DOILP) Estimated Equation: DOILP = AR(4) + AR(6) + C DOILP(t)=-0.0968*DOILP(t-4)- 0.0626*DOILP(t-6)+N(t) N(t) = (1+0.0968*Z4+ 0.0626*Z6)*DOILP(t)

15. Testing Residuals The correlelogram shows a satisfactory form Slight structure at lag 15, but nothing to be concerned of

16. Testing for ARCH Residuals When testing for the Residuals squared we can see that there is no significant lags

17. Distributed Lag Model for DJI(t) dji(t) = h(z) oilp(t) + residdji(t) Take first difference ddji(t) = h(z) doilp(t) + dresiddji(t) Multiply by our estimated model (1+0.0968*Z4+0.0626*Z6)*doilp(t)=Ndoilp(t) W(t) = h(z) Ndoilp (t) + residw(t) Where W(t) = (1+0.0968*Z4+0.0626*Z6) ddji(t) residw(t) = (1+0.0968*Z4+0.0626*Z6) dresiddji(t)

18. Part C: Transforming DDJI to W(t) DJI, unlike oil prices does not spikes and change in volatility in 1973 – 1974

19. Normality (DJI) Jarque Bera: 208 Probability: 0.000 Kurtosis: 3.00 Skewness: 1.264 Non-normal distribution

20. Correlation DJI Autocorrelation shows signs of evolutionary data

21. ADF Test (DJI) T-statistic: 0.57 1% Level:-3.43 5% Level:-2.87 10% Level:-2.5 Shows signs that there exists a unit root

22. First Difference DDJI To remove the evolutionary aspects of DJI we take the first difference

23. Normality (DDJI) Jarque Bera: 15024 Probability: 0.000 Kurtosis: 24.10 Skewness: -1.96

24. ADF Test (DDJI) T-statistic -10.42 1% Level-3.44 5% Level-2.87 10% Level -2.57 Reject unit root

25. Fit DDJI to W W(t) = (1 + 0.0968*Z^4 + 0.0626*Z^6) DDJI(t)

26. Normality (W(t)) Jarque Bera: 15233.9 Skewness: -1.953 Kurtosis: 24.34

27. ADF Test (W) T-statistic:-10.02 1% Level-3.44 5% Level-2.87 10% Level -2.57

28. Part E : Fitting a distributed lag model

29. Part E : fitting a distributed lag model DOILP CAUSES DDJI

30. Part E : fitting a distributed lag model Lags 3,11, 13, 29 are significant

32. Part E : fitting a distributed lag model

38. Normality

40. Part E : fitting a distributed lag model

41. Heteroskedasticity

44. Part F: Forecasting Forecasting: 2011m05 2011m06

45. Forecasting (continued) 150.1134+/- 2*180.2 (-210.3~510.5) 143.4469+/- 2*180.2 (-216.9~503.8) The value for April 2011 is 12434.88 dji(2011.5)=12434.88+150.1134=12584.9934, about 12585 (12224.58~12945.38) Real value for 2011.05 12587.81 only 2.81 points difference! Forecasting for June 2011: Dji(2011.6)= 12587.81+143.4469=12731.2569 (12370.86~13091.61)