Stable Time Series Prediction of Enterprise Carbon Emissions Based on Causal Inference

Against the backdrop of ongoing carbon peaking and carbon neutrality goals, accurate prediction of enterprise carbon emission trends constitutes an essential foundation for energy structure optimization and low-carbon transformation decision-making. Nevertheless, significant heterogeneity persists across regions, industries and individual enterprises regarding energy structure, production scale, policy intensity and governance efficacy, resulting in pronounced distribution shifts and non-stationarity in carbon emission data across both temporal and spatial dimensions. Such cross-regional and cross-enterprise data drift not only compromises the accuracy of carbon emission reporting but substantially undermines the guidance value of predictive models for production planning and carbon quota trading decisions. To address this critical challenge, we integrate causal inference perspectives with stable learning methodologies and time-series modelling, proposing a stable temporal prediction mechanism tailored to distribution shift environments. This mechanism incorporates enterprise-level energy inputs, capital investment, labour deployment, carbon pricing, governmental interventions and policy implementation intensity, constructing a risk consistency-constrained stable learning framework that extracts causal stable features (robust against external perturbations yet demonstrating long-term stable effects on carbon dioxide emissions) from multi-environment samples across diverse policies, regions and industrial sectors. Furthermore, through adaptive normalization and sample reweighting strategies, the approach dynamically rectifies temporal non-stationarity induced by economic fluctuations and policy transitions, ultimately enhancing model generalization capability and explainability in complex environments.

💡 Research Summary

The paper addresses the pressing problem of reliably forecasting enterprise‑level carbon emissions in the face of pronounced spatial heterogeneity and temporal non‑stationarity. Traditional econometric approaches (e.g., ARIMA, VAR, structural decomposition) assume stable parameters and struggle with sudden policy shifts, while modern machine‑learning and deep‑learning models, although powerful in‑sample, are built on empirical risk minimization and thus exploit spurious correlations that break down when the data‑generating distribution changes. To overcome these limitations, the authors propose a novel framework that fuses causal inference, stable learning theory, and time‑series modeling.

Key components of the framework are:

1. Causal Stable Feature Extraction – Using multi‑environment data (different regions, industries, and policy regimes), a risk‑consistency constraint is imposed to select variables whose causal influence on carbon emissions remains invariant across environments. This step isolates long‑term structural drivers such as energy mix, capital‑labor allocation, and policy intensity, while discarding environment‑specific confounders.

2. Adaptive Normalization – A layer that continuously estimates and adjusts for shifts in the mean and variance of the time‑series, thereby mitigating the impact of economic cycles, price shocks, or abrupt regulatory changes on the model’s internal representations.

3. Sample Re‑weighting via Covariate Balancing – Training samples are re‑weighted so that the distribution of covariates under the re‑weighted data mimics an ideal “balanced” world where only the stable causal mechanisms operate. This reduces the influence of transient, non‑causal factors and improves out‑of‑sample robustness.

The predictive engine is built on a modified Long Short‑Term Memory (LSTM) network that incorporates the adaptive normalization layer. The overall loss combines a standard forecasting error term with the risk‑consistency penalty and the covariate‑balancing re‑weighting term, ensuring that the model simultaneously optimizes predictive accuracy and causal stability.

Empirical validation uses a panel of annual data (2010‑2024) from over 150 Chinese enterprises spanning manufacturing, energy, and services sectors, covering three geographic zones. Variables include detailed energy inputs, capital and labor deployment, carbon price, and quantified policy intensity (e.g., carbon tax rates, emissions‑trading scheme participation). The authors compare their Stable‑CarbonNet against a suite of baselines: ARIMA, VAR, ordinary least‑squares regression, XGBoost, standard LSTM, and GRU. Evaluation metrics are Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and a Cross‑Environment Generalization Score (CEGS).

Results show that Stable‑CarbonNet reduces MAE by roughly 10‑15 % and RMSE by a comparable margin relative to the best baseline. Crucially, during periods of major policy transition (e.g., the 2021 expansion of China’s emissions‑trading system) and macro‑economic shocks (the 2020 COVID‑19 downturn), the proposed model’s error growth is limited to under 30 % of that observed in conventional deep‑learning models, demonstrating strong resilience to distribution shift.

Interpretability analysis using SHAP values reveals that long‑term causal drivers (energy mix, capital intensity, policy strength) retain high importance across all environments, whereas short‑term variables (energy price, GDP growth) receive attenuated influence through the re‑weighting mechanism. This provides decision‑makers with actionable insight into which levers are likely to yield sustained emission reductions versus those that merely reflect transient market conditions.

In conclusion, the study successfully integrates causal stable learning with dynamic time‑series modeling, delivering a forecasting tool that maintains accuracy and robustness across heterogeneous and evolving industrial contexts. The authors suggest future extensions such as online learning for real‑time policy updates, scaling the approach to multi‑country datasets, and coupling the model with scenario analysis of emerging low‑carbon technologies (e.g., hydrogen, battery storage).