A Hybrid Deep Learning based Carbon Price Forecasting Framework with Structural Breakpoints Detection and Signal Denoising

TL;DR

The paper tackles the challenge of forecasting carbon prices under regime shifts and noisy market conditions by proposing a hybrid framework that combines structural-break detection (PELT, Bai-Perron, ICSS), wavelet-based denoising, and multiple deep learning architectures (LSTM, GRU, TCN). By incorporating multivariate external features and a unified, breakpoint-aware data preprocessing pipeline, the approach improves forecast accuracy and interpretability for nonstationary EUA time series. Empirical results on EUAs from 2007–2024 show that the PELT-WT-TCN configuration delivers the best performance (MAE ≈ 1.1855, RMSE ≈ 1.5866, R^2 ≈ 0.989) and outperforms the baseline BP&ICSS-WT-LSTM by notable margins, with the GRU offering the best speed-accuracy trade-off. The work highlights the value of aligning learning with regime dynamics and multiscale signal content, with implications for carbon markets and other nonstationary financial time series.

Abstract

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.

Figures (18)

• Figure 1: The flowchart of the proposed framework. This framework outlines a carbon price forecasting process combining structural break detection, wavelet denoising, and sequence models (LSTM, GRU, TCN) for univariate and multivariate analysis.
• Figure 2: Flowchart of wavelet‐transform decomposition.
• Figure 3: Architecture of a peephole-free LSTM cell with the unified input $z_t=[\tilde{y}_t, u_t, e_t]$.
• Figure 4: The structure of the TCN model.
• Figure 5: Key drivers of carbon price