## 4 Analyzing Historical Data and Future Forecast
### Scenario Forecasts  
As the last part in this research, the scenario forecasts for 2025-2035 are investigated (see Figure 14 ) using both Prophet and SARIMAX, under two assumptions:  
* Optimistic: Battery prices drop 10% faster than baseline.  
\begin{table}
\begin{tabular}{c c} \hline
**Feature Pair** & **Key Insight** \\ \hline \multirow{2}{*}{Charger\_Density\_Index \(\times\) Battery\_Price\_USD\_kWh} & Mild synergy—Higher sales occur when infrastructure expands and battery prices fall, though charger density is the stronger driver. \\ \hline \end{tabular}
\end{table}
Table 6: _Cont._  
Figure 13: UK EV sales forecast (2026–2035) using the Prophet and SARIMAX models.  
The Scenario Forecast Insights table (Table 8) provides a structured comparison of projected EV sales under optimistic and pessimistic assumptions across both Prophet and SARIMAX models. By explicitly modeling uncertainty--such as faster battery cost declines or delayed policy implementation--this table highlights the sensitivity of future market trajectories to key external drivers. It enables policymakers and analysts to assess potential risk bands, understand divergence between models, and evaluate how different assumptions could materially impact EV adoption through 2035.  
The distinct modeling philosophies behind XGBoost, Prophet, and SARIMAX complement each other and provide a rich framework for both retrospective and prospective analysis. Prophet and SARIMAX exhibit broadly similar forecasting behavior but serve different roles in modeling electric vehicle (EV) sales. Prophet is particularly well-suited for long-term projections, as it captures nonlinear growth trends, seasonal effects, and policy impacts in an interpretable framework. However, it may over-project future outcomes if key external drivers evolve in ways not reflected in historical data. SARIMAX, by contrast, is more conservative in its predictions, leveraging autoregressive structures and short-term dependencies to provide stable, trend-following forecasts. Its responsiveness to sudden policy shifts or infrastructure changes is limited unless those effects are strongly encoded through exogenous variables. XGBoost, while not used for forecasting due to its lack of time-awareness, plays an important diagnostic role in this study. Applied to historical data from 2015 to 2024, XGBoost effectively uncovers the most influential drivers of EV sales--highlighting year-over-year growth trends, charger density, battery prices, and GDP growth as key contributors. Together, these three models offer a comprehensive  
Figure 14: Forecasted Annual EV Sales in the UK: Baseline vs. Optimistic vs. Pessimistic Scenarios.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Aspect** & **Prophet** & **SARIMAX** \\ \hline Optimistic Scenario & Growth is fast and smooth; it reaches 3.1 million by 2035. Driven by cheaper batteries. & Reaches \(\sim\)3.2 million by 2035. Slightly steeper acceleration post-2029. \\ \hline Pessimistic Scenario & Growth is moderated, ending at \(\sim\)2.5 million. Delayed policy and infrastructure have a visible drag. & Reaches \(\sim\)2.7 million, but maintains steadier growth compared to Prophet. \\ \hline Model Comparison & Prophet is more sensitive to input changes (especially in the early years). & SARIMAX is more inertial, but overtakes Prophet by 2035 in both scenarios. \\ \hline Difference by 2035 & Prophet optimistic vs. pessimistic: \(\sim\)444 k units gap & SARIMAX optimistic vs. pessimistic: \(\sim\)501 k units gap \\ \hline \hline \end{tabular}
\end{table}
Table 8: Scenario Forecast Insights (2025–2035).  
toolkit: XGBoost explains the past, while Prophet and SARIMAX explore the future under various scenarios.