II. Data Description
The data collected was the spot prices of crude oil measured in dollars per barrel. Data from May 20, 1987 was used because that was the first date the prices were available for both the locations; Cushing, Oklahoma and Europe. The data ends at March 9, 2004 because that was the last date available. The frequency of the data is five day weeks (no weekends) beginning with Wednesday May 20th. The data was obtained from the government agency the Energy Information Administration, which reports to the U.S. Department of Energy, and the website is http//www.eia.doe.gov/oil_gas/petroleum/info_glance/prices.html.
At first glance, the data seemed extremely thorough, but a closer inspection revealed missing data points. December 25th and January 1st were never included most likely due to these being holidays every year and government officials not working on those days to collect the data. Still, Thanksgiving was always included as were other popular holidays, so it still remains unclear why Christmas and New Years were left out. Also, two other data points from each year were continually left out, but these two days were random. They almost always occurred in either April or May. Again, the reason these days were not included or not recorded is uncertain. To model the data in eviews, the full range of data points is needed. Therefore, the two days surrounding each missing data point were averaged and then substituted to give a full range of data. This was done for about 60 data points out of over 4000; as a result, it is assumed that these averaged data points did not have an effect on the modeling of the data.
Empirical work on the data began by reviewing these graphs:
An interesting observation on the government came from an attempt to acquire more information about the data. The excel spreadsheet of the data came with a phone number and email address of the government official who serves as the data administrator. The phone number was out of service and the person never responded to emails. This sounds like a typical government official. In addition, the data has not been updated since March 10th. Again, it seems the data administrator does not have the time to keep up with these records. One would believe the crude oil prices to be an important statistic for many companies making important decisions and also for government representatives trying to make policies. If this data is not updated regularly, then these companies and government officials are making judgments with out of date data and therefore, these decisions are not as precise as they could be.
III. Empirical Methods
The graphs of crude oil prices for Cushing, OK and Europe looked like they had a positive quadratic trend. The variables trend =@trend(5/19/1986) and trend2 = trend*trend were created to capture this movement in the data. First a linear trend was tested just to be sure the hypothesis was correct. Running the regressions: Cushing = c + b1*trend and Europe = c + b1*trend proved that the linear trend helped describe the data but did not describe it very well. The trend variable was significant for both locations. The t-statistic for trend in the Cushing regression was 38.93 while in the Europe regression it was 35.34 higher than the critical value of about 1.6 at the 5% significance level. The adjusted R-squared of the Cushing regression with a linear trend was .2568 while the Europe’s regression was only .222. The information criteria were about the same for each location: 5.9 for both the Akaike and Schwarz. Since nothing else (seasonality, cycles) had been accounted for this information alone could not tell us what kind of trend the data has.
Comparing this data with the quadratic trend regressions: Cushing = c + b1*trend + b2*trend2 and Europe = c + b1*trend + b2*trend2 however, proved that a quadratic trend explained the data better than a linear trend. The trend2 variables were significant too with t-statistics of 31.83 and 30.61 for the Cushing and Europe regressions respectively. Both the quadratic trend regressions were better than those with a linear trend. The adjusted R-squares were higher- the Cushing regression’s rose to .396 and the Europe regression’s rose to .358. Both the Akaike and Schwarz information criterion fell to about 5.7 for both locations.
The regression for Cushing after modeling trend was
And the trend regression for Europe was:
The graphs of the residuals for a quadratic trend for both locations confirm that this is the correct trend as well. The residuals follow the quadratic trend line fairly well. However, there is definitely still serial correlation among the residuals because the cycles have not been accounted for in the model.
Before capturing the cycles the model was checked to see if there was a seasonal effect that needed to be accounted for. Five dummy variables D1, D2, D3, D4, and D5 were created for the five days of the week. Since the data starts on a Wednesday, the dummy variable D1 = 1000010000100001…. represents Wednesday, the dummy variable D2 = 01000010000100001….. represents Thursday, and so on. The models Cushing = c + b1*trend + b2*trend2 + b3*D2 + b4*D3 + b5*D4 + b6*D5 and Europe = c + b1*trend + b2*trend2 + b3*D2 + b4*D3 + b5*D4 + b6*D5 were tested with D1 left out so all results would be with respect to Wednesday. None of the seasonal dummy variables for either regression were significant- the t statistics were all about .1. Removing the dummy variables one by one did not give significance to any of them. Neither did running the regression with a different dummy D2, D3, etc left out. Since none of the seasonal dummies had significance, they were left out of the best fit model.
Next, we tested for a broken trend. By observing the graph of the data, it looked like there could be a broken trend around 1987. Up until this point, the data seems to have a similar slope, but then it dips and has a positive slope afterward. Therefore, the following test was run to see if there was a broken trend at the point October 1st, 1999.
At first glance, the broken trend variable, SER01, is significant, but when a lag was added, SER01 became very insignificant. The AR(1) term explains so much of the data that the broken trend does influence the model anymore. In conclusion, there is not a broken trend in the data and the same conclusions were drawn for the Europe data.
Up until now, very little of the data was getting explained. By adding a lag, the model became significantly better. The following is the correlogram of the Cushing data:
Cushing correlogram (just Cushing and c in model)
Here is the correlogram for the Europe data:
After studying these correlograms, using MA was unreasonable due the number of terms required. Many more than the first 8 terms were outside the confidence interval for autocorrelation. Since only the first term for partial correlation was outside the confidence interval, an AR(1) lag was added to each model. Here are the resulting eviews outputs, with seasonality included just to make sure it was still insignificant with the lag.
Cushing
Europe
Finally, the overall best model for the data was determined. After carefully studying whether the variable trend made the model better, it was decided the model did a better job without this variable. The adjusted R-squared was very similar with or without the trend variable included, but the information criteria went down slightly and the F-statistic increased a significant amount when trend was left out.
Cushing best model
Best model for Europe
As one can see, the final correlograms are random.
Cushing
Europe
Cushing Forecast Graph
Europe Forecast Graph
V. Conclusion
Crude oil spot prices have been very volatile over the last 20 years. After modeling our data, and finding it to have a quadratic fit for both markets, we tested for seasonality, to see what makes oil prices rise and fall so much. We were unable to find that any day of the week was more or less significant than any other. We tested for a broken trend, with negative results as well. We could not find an explanatory variable of the correct data type and frequency. The volatility can only be explained by a series of price shocks caused by many factors including OPEC production changes and wars and unrest in the Middle East..
The first noticeable trend is that Oil prices are higher in times of economic growth and lower during a recession. Our data begins during a time of recession, and thus prices are falling. The steady drop in prices from 1996 to 1999 can be tied to the economic crisis in Asia, as well as Iraq resuming its production, which increased supply. Oil prices fell sharply after the terrorist attacks on September 11th, 2001. This is due to worldwide fears the there is going to be an economic downturn.
Another trend we noticed is wars and turmoil in the Middle East generally drives the price of oil up. Warring countries cannot produce as much oil and may have even had their wells destroyed. The first big price shock we see occurs in both markets in 1990. Prices soar because of problems in the Middle East. In 1990, Iraq invaded Kuwait and the US sent troops, starting the Gulf War. Prices remain high until the end of the war in early 1991 when they drop back to average levels. Since 2002, oil prices have been on the rise again with the military presence in the Middle East as well as the strike in Venezuela. The huge spike in 1999 and 2000 is due to multiple factors including an unusually strong demand coupled with OPEC production cuts and huge economic boom the United States.
Since the two markets are in competition with one another, any change in one market will be reflected in the other. This can be seen in simply observing the two graphs, which appear to follow one another. Our forecast calls for prices to continue rising gradually, and continuing to be volatile since we cannot predict the factors which effect oil price.
References
Data Obtained from:
United States Department of Energy. “U.S. Petroleum Prices”.
.
Works Cited:
American Petroleum Institute. "Oil and Natural Gas: We Keep America Going Strong"
<http://api-ec.api.org/filelibrary/2004%20Cand%20Indust%20Rep.pdf >2004.
Leiby, Paul N. "Economics of Energy Security Policy: Oil Shocks and Strategic Oil Shocks." USAEE
Policy Symposium. Cambridge, MA.
12/2003.
Williams, James L. "Energy Economics Newsletter." WTRG Economics.
<http://www.wtrg.com/prices.htm> 2003.