1. Team Project:
Total Gasoline Consumption in the United States forecast for the
years 2015 - 2017
Team Alpha:
Patrick Carter
Wendel Friedl
Robert Niess
Brent Welcher
This forecast culminates the effort of Team Alpha, specifically Patrick Carter, Wendel Friedl,
Robert Niess, and Brent Welcher, to project gasoline through 2017. This written report follows
up the Oral presentation of Monday, June 22nd
by the same aforementioned group members.
1. Introduction
To forecast the total U.S. consumption of gasoline, measured in thousands of barrels (42 gallons
per barrel), for the years 2015 through 2017, our team completed four separate projections each
using a different forecasting technique. The resulting forecast for each technique, as well as the
structure, details, and analysis of individual results, are detailed in the following sections of this
paper. This paper concludes with a summary of overall results. All supplementary tables and
graphs are attached in an appendix. An initial literature review was conducted to generate a list
of possible variables and model specifications. Details as to the specific academic papers
reviewed as well as website addresses for all data sources are listed in SITREP 3.
2. Causal Time-Series Analysis
The pool of independent variables considered for this section included: Population (measured by
civilian non-institutional or Total U.S population including armed forces overseas) from FRED,
Disposable Real Income per capita (in 2009 dollars) from the BEA, Miles Driven (Total miles
and miles per capita were both separately considered) from the DOT, Real price per gallon of
Gasoline (in 2009 dollars) from the BLS, Unemployment Rate (FRED), Employment to
Population Ratio (FRED), and the 1-year Treasury Bill Yield (FRED).
2. Preliminary regressions using yearly data from 1945 – 2014 exhibited severe positive
autocorrelation (Durbin-Watson statistics in the range of .10 to .27) and multicollinearity (VIF
scores in the high teens to high twenties) with all combinations of independent variables tested.
Adopting a double-log model specification as well as the use of the 1st
differences of all yearly
data were both attempted to reduce autocorrelation and multicollinearity, with very limited
success. While positive autocorrelation and multicollinearity were both reduced, they largely
remained well within the “severe” range and the regression yielded an extremely low R2
.
A second round of regressions using monthly data from January 1976- March 2015 largely
eliminated the problems of autocorrelation and multicollinearity, as evidenced by the Durbin-
Watson and VIF statistics, after dropping several of the above-mentioned independent variables.
The two most consistently statistically significant independent variables were disposable real
income and gasoline price. Attempting to add either measure of population considered (total or
non-institutional) as a third independent variable to a regression with income and price caused
multicollinearity between population and price (figure 2-A), verified with a correlation matrix
(figure 2-B). Unlike the yearly data regressions, a linear model specification produced slightly
better overall results in terms of adjusted R2
when using monthly data. Residual plots showed no
likely heteroscedasticity for either independent variable.
After comparing regression results, of the seven independent variables originally considered only
income and price were included in the final model. Some measure of market size (population,
number of drivers, miles driven, etc.) seems to be most important element left out of this model,
and I believe that finding an appropriate, non-multicollinear market measure would improve the
accuracy of the model. The final model used for forecasts in this section was:
Predicted Consumption = 118,894.17 – Gas Price*3,147.09 + Disposable Income*4.54
To test the accuracy of the forecast model, a 13-month holdout period “backcast” regression was
conducted (figure 2-C). Results showed that for the 13-month period examined, this model
overestimated gasoline consumption by an average of 9.04%.
The Holt-Winters Exponential Smoothing Model was used to forecast 33 months of future values
for gasoline prices and 32 months of future values for real disposable income per capita. Future
values (or actual values for 2015, where available) were plugged into the model equation to
3. arrive at the forecasted consumption of gasoline for each year from 2015 through 2017. The
monthly results are shown in figure 2-D, and the abbreviated and rounded yearly consumption
projections were 3.51 billion barrels in 2015, 3.64 billion barrels in 2016, and 3.67 billion barrels
in 2017. Adjusting these figures based upon the 9% average projection over-estimation found
when performing the 13-month “backcast,” the yearly figures are 3.2 billion barrels in 2015,
3.31 billion barrels in 2016, and 3.34 billion barrels in 2017 (error adjustments non-
compounded).
3. Trend Time-Series Analysis
The dependent variable used for the trend time-series analysis was annual U.S. product supplied
of finished motor gasoline (in thousands of barrels) from 1945-2014 (EIA). Time and one
dummy variable to account for the consumption shift, caused presumably by implementation of
CAFÉ legislation, serve as the independent variables.
A line graph of gasoline consumption from 1945-2014 shows a nearly linear upward trend, with
a significant economic shock around the year of 1984. Without the use of a dummy variable, the
regression analysis rendered a .95 adjusted R2
with a highly significant t-statistic of 37.8. Adding
a dummy variable to account for the year that it looked like the intercept changed showed that
the dummy variable was statistically significant. For the year of 1982, a dummy variable was
created that gave a slightly better R2
than did the regression run without a dummy variable.
Continuing to change the dummy variable for different years to see if the adjusted R2
would
improve showed slight improvement until the year of 1985, which gave an adjusted R2
of 0.96, f-
statistic of 903.98, and t-statistic of -4.34. Using the dummy variable for this year helped us
realize that the sweet spot was back in 1984 with an adjusted R2
of 0.96, f-statistic of 906.48, and
t-statistic of -4.36 (figure 3-A). The correlation matrix shows a slightly stronger correlation
between the time and dummy independent variables than between the dummy and the dependent
variable, indicating that multicollinearity may be an issue with the model (figure 3-B). Fixing
possible multicollinearity within the trend time-series model is, however, beyond the scope of
this paper.
The final model used to generate forecasts in this section was:
4. Predicted Consumption = -88,539,501 + (45,951*Date) - (337,542*Dummy)
Using this model, projected consumption for 2015 was 3.72 billion, 3.76 billion barrels for 2016,
and 3.81 billion barrels for 2017. The trend time-series regression model forecasts the U.S.
product supplied of finished motor gasoline (in thousands of barrels) to continue to follow an
upward linear trend.
4. Traditional Stochastic Time-Series Analysis
For the traditional stochastic time-series forecast, several models were tested looking for the
model that would best fit the data while keeping to the lowest MAPE. The time-series models
tested were the Simple Moving Average (SMA) model, the Simple Exponential Smoothing
(SES) model, the Holt’s (double) Exponential Smoothing (HES) model, and the (Holt) Winter’s
Exponential Smoothing (WES) model. All models in this section used monthly U.S. product
supplied of finished motor gasoline (in thousands of barrels) from 1945-2015 (EIA) to forecast
33 months of future consumption (through December 2017).
The SMA forecast yielded a MAPE of 5.57%. The SMA model was deemed inappropriate for
this project, as it is best suited for very short-term projections while we were forecasting 33
periods of data. The SES produced a forecast with a MAPE of 5.33%. This model fit the data
better than did the SMA model but, as SES is unsuitable for projecting data with a trend,
additional models were tested. The HES model produced a MAPE of 5.31%. The WES model
produced by far the lowest MAPE of the four models considered, at 2.06%. However, since the
WES model is an extended test of the HES model that accounts for seasonality, the added
mathematical complexity was judged unnecessary given the similarity in the monthly forecast
numbers between the WES and HES models. Holt’s model was used to generate consumption
forecasts in this section (figure 4-A).
The HES model bore projections of 3.25 billion barrels of gasoline for 2015, 3.29 billion barrels
for 2016, and 3.33 billion barrels for 2017.
5. 5. Multivariate Cross-Sectional Analysis
Independent variables considered for this section were: Motor gasoline price in dollars per
million BTU by state for 2013 (EIA), disposable real income per capita by state for 2013 (BEA),
total population by state for 2013 (Census), unemployment rate by state for 2013 (BLS), and
Average miles driven per capita by state for 2013 (DOT).
An initial regression using all listed independent variables produced an R2
of 97%, indicating
severe multicollinearity was a possibility. The VIF for the initial regression was a huge 74.56,
providing further evidence of multicollinearity. A correlation matrix showed possible
multicollinearity between the total population per state and average miles driven, so those two
independent variables were dropped from subsequent regressions. After dropping the
multicollinear variables, a regression produced an R2
of only 20%. Looking to increase the R2
,
the double-log model specification was adopted. The double-log specification made the model
much stronger, with a 33% R2
. The VIF for this model fell to 1.5, indicating that
multicollinearity was no longer a problem. A correlation matrix confirmed that multicollinearity
among these variables was unlikely (figure 5-A). Residual plots for variables showed no distinct
patterns, so heteroscedasticity did not appear to be an issue. As this section uses a cross
sectional model, the unlikelihood of autocorrelation made generating a Durbin-Watson statistic
unnecessary.
The final model used for forecasts in this section was:
ln Predicted Consumption = 31.8 + (-7.7 * ln Gas Price) + (-.33 * ln Disposable Income) +
(1.4 * ln Unemployment rate)
The Holt Exponential Smoothing Model was used to forecast 3 years of future annual values for
gasoline prices, real disposable income per capita, and unemployment. Plugging these projected
figures into the model equation resulted in forecasts of 3.49 billion barrels of gasoline
consumption in 2015, 3.56 billion barrels in 2016, and 3.6 billion barrels in 2017.
6. 6. Summary
Yearly gasoline consumption totals were relatively consistent among the four models (figure 6-A
and 6-B).The Trend Time-Series model consistently produced the highest forecast figures, while
the Traditional Time-Series using Holt’s model consistently produced the lowest. The overall
spread of the projections for each year was 467 million barrels in 2015 (14.4%), 474 million
barrels in 2016 (14.42%), and 479 million barrels in 2017 (14.39%).
