Total Vehicle Sales Forecast
Economic Forecasting 309-01W
For this project I created a twelve month forecast for Total Vehicle Sales in the United States using four different methods. These four techniques are called exponential smoothing, decomposition, ARIMA, and multiple regression. To do so I picked one dependent (Y) variable along with two independent (X) variables and collected 80 monthly observations for each variable. This historical data allowed me to create four different forecasting models which predict future Vehicle Sales with low risk of error. The best model according to the lowest error measures was winter’s exponential smoothing method because it had the lowest MAPE along with the lowest RMSE for the fit period as well as the forecast period.
I chose the Y variable to be Total Vehicle Sales in the United States because I have a strong interest in the auto industry and would like to work for a German car maker in the future. The auto industry is very vulnerable to the state of the economy because people tend to postpone high-item purchases like a car when times are tough. Therefore, the variables that cause a change in vehicle sales numbers must be indicators of economic performance. In order to forecast the dependent variable Y (Total Vehicle Sales), I chose two independent variables, X1 and X2 that are closely related to Y. These are going to be Employment non-farm and the Personal Saving Rate. The hypothesis I make for the first X variable is that employment numbers are logically related to vehicle sales because the more people are in the workforce, the more people earn an income which is necessary to make high-item purchases like a personal car. The hypothesis for the second X variable is that the personal saving rate has an inverse linear relationship to vehicle sales because the more people hold on to their disposable income, the less spending occurs which hurts vehicle sales numbers.
Since I am using three completely different variables in my forecast, the means, ranges, and standard deviations for each variable are going to differ from each other. In order to avoid forecasting difficulty, it is important to look at the variations about the mean value for each variable. The Y variable Total Vehicle Sales has a mean value of 1130.5, a range of 919.9, and a standard deviation of 243.0. Since it is important that the standard deviation is less than 50% of the mean value to avoid forecasting difficulty, these numbers indicate that I should be able to get a pretty accurate forecast. The X variable Employees non-farm shows a mean value of 133,784 with a standard deviation of 3,463 and a low range of 11,769 which are great numbers for an independent variable. The X variable Personal Saving Rate with a mean value of 4.157 and a standard deviation of 1.389 also indicate that I should not run into difficulties producing a forecast. Below are descriptive statistics for all the variables used:
Descriptive Statistics: Total Vehicle Sales, Employees non farm, Saving Rate
Variable N N* Mean SE Mean StDev Minimum Q1 Median Total Vehicle Sales 68 0 1130.5 29.5 243.0 670.3 967.4 1090.3 Employees non farm 68 0 133784 420 3463 127374 130916 133209 Saving Rate 68 0 4.157 0.168 1.389 2.000 2.800 4.350
Variable Q3 Maximum
Total Vehicle Sales 1282.5 1590.2
Employees non farm 137029 139143
Saving Rate 5.200 8.300
Looking at the time series plot for the Y variable Total Vehicle Sales, one can notice a slight negative trend over the 68 observations studied. This characteristic is proven by the autocorrelation function which shows that the autocorrelation coefficients remain fairly large for several time periods before slowly declining. Furthermore, there could be a...
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