# Temporal Convolutional Network for Carbon Tax Projection: A Data-Driven Approach
## 4 Results and Discussion
### Performance across Different Time Horizons  
To assess the model's performance over different time horizons, we calculated the MAE for 1-year, 3-year, and 5-year projections. The results are presented in Table 3.  
The results in Table 3 demonstrate that while all the advanced models showed improved performance over ARIMA across the different time horizons, the TCN model consistently outperformed both the LSTM and ARIMA-LSTM models. This suggests that a TCN's ability to capture both short-term fluctuations and long-term trends is superior to that of other advanced machine learning approaches. Several observations can be made from these results: (1) Short-term accuracy: All models performed best in short-term (1-year) projections, with the TCN model showing the lowest MAE. Compared to ARIMA, the TCN model achieved a 30.0% lower MAE, while it outperformed LSTM by 14.5% and ARIMA-LSTM by 5.6% for 1-year projections. This indicates that the TCN model is particularly effective at capturing recent trends and short-term fluctuations in carbon tax prices, even compared to other advanced machine learning approaches. (2) Consistent outperformance: The TCN model maintained its superiority over all other models across all time horizons. The performance gap between the TCN and other models tended to widen for longer-term projections, especially compared \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Average MAE (USD/tCO2e)** & **Average RMSE (USD/tCO2e)** & **MAPE(\%)** \\ \hline ARIMA & 3.54 (\(\pm\)0.41) & 4.92 (\(\pm\)0.57) & 12.8 (\(\pm\)1.5) \\ LSTM & 2.87 (\(\pm\)0.35) & 3.95 (\(\pm\)0.46) & 10.4 (\(\pm\)1.2) \\ ARIMA-LSTM & 2.61 (\(\pm\)0.31) & 3.58 (\(\pm\)0.42) & 9.5 (\(\pm\)1.1) \\ TCN & 2.43 (\(\pm\)0.29) & 3.31 (\(\pm\)0.38) & 8.8 (\(\pm\)1.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average performance comparison across all countries (standard deviation in parentheses). \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **1-Year MAE** & **3-Year MAE** & **5-Year MAE** \\ \hline ARIMA & 2.87 (\(\pm\)0.35) & 3.98 (\(\pm\)0.49) & 5.21 (\(\pm\)0.68) \\ LSTM & 2.35 (\(\pm\)0.29) & 3.24 (\(\pm\)0.40) & 4.26 (\(\pm\)0.55) \\ ARIMA-LSTM & 2.13 (\(\pm\)0.26) & 2.95 (\(\pm\)0.36) & 3.87 (\(\pm\)0.50) \\ TCN & 2.01 (\(\pm\)0.26) & 2.89 (\(\pm\)0.37) & 3.95 (\(\pm\)0.51) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model performance across different time horizons (MAE in USD/tCO2e, standard deviation in parentheses). to ARIMA and LSTM. This suggests that the TCN model is better able to capture the underlying long-term dynamics of carbon tax prices, leveraging its ability to model complex temporal dependencies. (3) Graceful degradation: While all models showed increasing error for longer time horizons, the TCN model exhibited the most gradual increase in MAE. From 1-year to 5-year projections, the TCN's MAE increased by 96.5%, compared to 81.5% for ARIMA, 81.3% for LSTM, and 81.7% for ARIMA-LSTM. This indicates that the TCN model was more robust against the inherent uncertainty in long-term forecasts, maintaining its predictive power more effectively than other approaches as the forecast horizon was extended. (4) Hybrid model performance: The ARIMA-LSTM hybrid model showed improved performance over both ARIMA and LSTM individually, indicating the benefits of combining traditional statistical methods with deep learning approaches. However, the TCN model still outperformed this hybrid approach, suggesting that its architectural advantages provide superior modeling capabilities for this task. (5) Practical implications: The TCN model's superior performance across different time horizons, even when compared to other advanced machine learning models, makes it a particularly versatile and powerful tool for policymakers and stakeholders. It can provide the most reliable short-term projections for immediate decision-making, while also offering the most valuable insights for long-term policy planning and strategy development.