Dow Jones and Oil PricesECON 240C Take Home 2Members:Jessica AguirreEdward HanMasatoshi HirokawaHan LiuLu MaoChristian MundoYuejing Wu

ContentsPart A: IntroductionPart B: The 1973-1974 oil crisisPart C: Pre-whitening oil price (oilp)Part D: Transforming first differenced Dow Jones Average (ddji) to WPart E: Fitting a distributed lag modelPart F: Forecasting the Dow Jones Industrial Average

IntroductionThe 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. The Spot Oil Price: West Texas Intermediate (adjusted to real oil price)The Dow Jones Industrial Average.

1973-74 Oil Crisis Part 1In 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 countrys 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.

1973-74 Oil Crisis Part 2The 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.

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

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

Correlation (OILP)Autocorrelation shows signs of an evolutionary modelThis may be the result of a unit root

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

First Difference of Oil PricesIn an attempt to remove the unit root we take the first difference of OILPThe resulting graph looks much less evolutionary

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

Correlation (DOILP)Partial Correlation significant lags are:46121516This translates into:AR(4)AR(6)

Unit Test (DOILP)ADF Test Statistic-26.3691% Level:-3.445% Level:-2.8710% Level:-2.57No Unit root

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

Testing ResidualsThe correlelogram shows a satisfactory formSlight structure at lag 15, but nothing to be concerned of

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

Distributed Lag Model for DJI(t)dji(t) = h(z) oilp(t) + residdji(t) Take first differenceddji(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) WhereW(t) = (1+0.0968*Z4+0.0626*Z6) ddji(t) residw(t) = (1+0.0968*Z4+0.0626*Z6) dresiddji(t)

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

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

Correlation DJIAutocorrelation shows signs of evolutionary data

ADF Test (DJI)T-statistic: 0.571% Level:-3.435% Level:-2.8710% Level:-2.5Shows signs that there exists a unit root

First Difference DDJITo remove the evolutionary aspects of DJI we take the first difference

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

ADF Test (DDJI)T-statistic -10.421% Level-3.445% Level-2.8710% Level -2.57Reject unit root

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

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

ADF Test (W)T-statistic:-10.021% Level-3.445% Level-2.8710% Level -2.57

Part E : Fitting a distributed lag model

Part E : fitting a distributed lag modelDOILP CAUSES DDJI

Part E : fitting a distributed lag modelLags 3,11, 13, 29 are significant

Part E : fitting a distributed lag model

Part E : fitting a distributed lag model

Part E : fitting a distributed lag model

Part E : fitting a distributed lag model

Normality

Part E : fitting a distributed lag model

Heteroskedasticity

Part F: ForecastingForecasting: 2011m05 2011m06

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)