Carbon Price Forecasting with Structural Breaks: A Comparative Study of Deep Learning Models

Accurately forecasting carbon prices is essential for informed energy market decision-making, guiding sustainable energy planning, and supporting effective decarbonization strategies. However, it remains challenging due to structural breaks and high-frequency noise caused by frequent policy interventions and market shocks. Existing studies, including the most recent baseline approaches, have attempted to incorporate breakpoints but often treat denoising and modeling as separate processes and lack systematic evaluation across advanced deep learning architectures, limiting the robustness and the generalization capability. To address these gaps, this paper proposes a comprehensive hybrid framework that integrates structural break detection (Bai-Perron, ICSS, and PELT algorithms), wavelet signal denoising, and three state-of-the-art deep learning models (LSTM, GRU, and TCN). Using European Union Allowance (EUA) spot prices from 2007 to 2024 and exogenous features such as energy prices and policy indicators, the framework constructs univariate and multivariate datasets for comparative evaluation. Experimental results demonstrate that our proposed PELT-WT-TCN achieves the highest prediction accuracy, reducing forecasting errors by 22.35% in RMSE and 18.63% in MAE compared to the state-of-the-art baseline model (Breakpoints with Wavelet and LSTM), and by 70.55% in RMSE and 74.42% in MAE compared to the original LSTM without decomposition from the same baseline study. These findings underscore the value of integrating structural awareness and multiscale decomposition into deep learning architectures to enhance accuracy and interpretability in carbon price forecasting and other nonstationary financial time series.

Temporal Network Representation Learning via Historical Neighborhoods Aggregation

Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant progress has been made on this problem in recent years, several important challenges remain, such as how to properly capture temporal information in evolving networks. In practice, most networks are continually evolving. Some networks only add new edges or nodes such as authorship networks, while others support removal of nodes or edges such as internet data routing. If patterns exist in the changes of the network structure, we can better understand the relationships between nodes and the evolution of the network, which can be further leveraged to learn node representations with more meaningful information. In this paper, we propose the Embedding via Historical Neighborhoods Aggregation (EHNA) algorithm. More specifically, we first propose a temporal random walk that can identify relevant nodes in historical neighborhoods which have impact on edge formations. Then we apply a deep learning model which uses a custom attention mechanism to induce node embeddings that directly capture temporal information in the underlying feature representation. We perform extensive experiments on a range of real-world datasets, and the results demonstrate the effectiveness of our new approach in the network reconstruction task and the link prediction task.