## 3 Results
### Forecasts  
While the _Annual Energy Outlook_ from the Energy Information Administration provides forecasts for gasoline and electrical consumption, the data are provided annually for dollars per one million British Thermal Units ($/MBtu) through 2050, which ignores the seasonality and is less useful for consumers [31]. Figure 4 is a graph for 2018-2026 from the _Annual Energy Outlook_.  
Figure 4: Energy price forecasts from the U.S. Energy Information Administration in $/MMBtu.  
Figure 3: The additive decomposition of cents/kWh illustrates the significant trend and seasonal components of the time series.  
To facilitate decision-making over the life-span of a vehicle, an 8-year horizon for gasoline and kWh costs was estimated using error/trend seasonality (ETS) and auto-regressive integrated moving average (ARIMA) models. The best performing models for both kWh and gasoline prices based on the mean absolute scaled error (MASE, a ratio of the model's mean absolute error divide by the mean absolute error of a seasonal naive model) were used for forecasting. The MASE provides a comparative metric of forecasting performance by leveraging a model's performance versus a seasonal naive model. Values of MASE less than 1 indicate model performance better than the seasonal naive [32].  
The \"ets\" and \"auto.arima\" functions [32] in [33] were used on both the price per kWh and the price per gallon of gas. For both variables, ETS models proved to have the best accuracy based on MASE scores when predicting a 20% validation set. When using the entirety of the data, the model selected for price per kWh was a Holt-Winter's ETS (smoothed error, trend, and seasonality components) with multiplicative error, additive trend, and additive seasonality components. The resulting MASE was 0.36, indicating a far superior performance to the seasonal naive model. The model selected for the price per gallon of gasoline was another Holt-Winter's ETS with multiplicative error, additive trend, and multiplicative error. The MASE was 0.23, far superior to a seasonal naive model. Table 3 depicts the metrics for both variables and the optimized ETS and ARIMA models.  
Forecasts using these models were generated for eight-years, which is quite a long forecast generating large error bands. Figure 5 illustrates both forecasts. Each of the 8 year \(\times\) 12 month = 96 forecasts for each variable are used to feed the simulation model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **ME** & **RMSE** & **MAE** & **MPE** & **MAPE** & **MASE** \\ \hline ETS Gasoline & 0.450 & 13.096 & 8.538 & 0.082 & 3.835 & 0.235 \\ ARIMA Gasoline & 0.666 & 12.689 & 8.802 & 0.220 & 3.881 & 0.242 \\ ETS kWh & 0.004 & 0.133 & 0.102 & 0.043 & 0.990 & 0.355 \\ ARIMA kWH & 0.003 & 0.134 & 0.103 & 0.043 & 0.995 & 0.358 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The accuracy metrics for the forecast models are shown below. ME is the mean error (a measure of bias), RMSE is the root mean squared error (a measure of variability), MAE is the mean absolute error (a measure of variability), MPE is the mean percent error (a measure of bias), MAPE is the mean absolute percent error (a measure of variability), and MASE is the mean absolute scaled error (a comparative measure of performance versus the seasonal naive with lower values meaning better performance.  
Figure 5: Forecasts for cents/kWh and cents/gallon of gasoline for the best error/trend seasonality (ETS) models are shown. The large forecast period results in error bands being wide.