# Temporal Convolutional Network for Carbon Tax Projection: A Data-Driven Approach
## 3 Data and Methodology  
### Data  
We utilized the World Carbon Pricing Database [19], which offers comprehensive information on global carbon pricing initiatives. This dataset encompasses historical carbon prices, emissions data, and relevant economic indicators for various countries and regions. Our analysis focused on a subset of 30 countries with established carbon tax systems, covering the period from 2000 to 2022.  
The dataset includes the following key features: (1) carbon tax prices (in USD per tCO\({}_{2}\)e); (2) CO\({}_{2}\) emissions (in million metric tons); (3) GDP (in billion USD); (4) energy consumption (in quadrillion BTU); and (5) renewable energy share (as a percentage of total energy consumption).  
The World Carbon Pricing Database is a valuable resource for researchers and policymakers, providing a standardized and comprehensive collection of carbon pricing data across different jurisdictions. It includes information on both carbon taxes and emissions trading systems, allowing for comparative analyses of different carbon pricing approaches. The database is regularly updated to reflect the latest policy changes and price adjustments, ensuring the relevance and accuracy of the data.  
We preprocessed the data by normalizing all features to a common scale and handling missing values through interpolation. The time series data were then structured into input-output pairs, where each input consisted of a 5-year historical window, and the output was the carbon tax price for the subsequent year. This sliding window approach allowed the model to capture both short-term fluctuations and longer-term trends in carbon pricing dynamics.  
It is important to acknowledge the limitations and challenges associated with our dataset. Carbon pricing varies widely between countries, and the availability and quality of data can differ significantly. To address these issues, we employed the following strategies: (1) Missing data handling: Where short gaps in time series data were present, we used linear interpolation to estimate missing values. For longer periods of missing data, we applied multiple imputation techniques, specifically using the multivariate imputation by chained equations (MICE) algorithm. This approach allowed us to maintain the temporal structure of the data, while minimizing bias. (2) Data quality assessment: We conducted thorough quality checks on the data, identifying and investigating outliers using the interquartile range (IQR) method. Outliers were either removed if deemed erroneous or retained if they represented genuine extreme events, with appropriate documentation. (3) Cross-country comparability: To ensure comparability across different countries, we normalized all monetary values to USD using historical exchange rates. Additionally, we applied purchasing power parity (PPP) adjustments to account for differences in the cost of living and inflation rates across countries. (4) Potential biases: We acknowledge that our dataset may be subject to reporting biases, particularly in countries with less developed carbon pricing systems. To mitigate this, we focused our analysis on countries with established carbon tax systems and reliable reporting mechanisms. However, this may limit the generalizability of our findings to countries with nascent carbon pricing policies. (5) Temporal coverage: The dataset covers the period from 2000 to 2022, which may not capture very recent policy changes or long-term historical trends. We addressed this limitation by focusing our analysis on medium-term projections and explicitly noting when recent policy shifts may have impacted our model's performance. By implementing these strategies, we aimed to minimize the impact of data limitations and potential biases on our analysis. However, we acknowledge that these challenges are inherent to cross-country studies of carbon pricing, and our results should be interpreted with these limitations in mind.