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A causal graph-informed temporal convolution architecture for interpretable retail electricity price forecasting

Yufan Ji, Abdollah Shafieezadeh, Noah Dormady

arXiv:2608.26234v1stat.APcs.LG

TL;DR

Existing electricity-price forecasting models offer limited insight into driving mechanisms, while much of the literature remains correlation-based. The paper proposes a causal-graph-informed temporal convolutional approach and reports superior forecasting accuracy alongside causal insight into long- and short-horizon price dynamics.

  • Problem

    Existing forecasting models remain largely black-box, and much of the literature is correlation-based rather than focused on identifying true causes.

  • Method

    The paper proposes a Causal-Graph-informed Temporal Convolutional Network using causal multi-scale time-series decomposition.

  • Results

    The proposed CG-TCN achieves superior forecasting accuracy relative to benchmark models and indicates that wholesale forward prices primarily shape long-horizon trend components.

  • Takeaways & Limitations

    Integrating causal information into deep-learning forecasting can improve predictive performance and provide more interpretable insight into retail electricity price dynamics.

  • Takeaways & Limitations

    The study emphasizes methodological depth over breadth by focusing on a single utility territory.

Abstract

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Retail electricity markets in deregulated systems face significant price volatility and complex interactions with forward and futures products, posing challenges for effective operational decision-making. This study introduces a Causal Graph-Informed Temporal Convolutional Network (CG-TCN), a forecasting architecture that integrates a learned causal graph into a temporal convolutional network via a graph-neural embedding to enhance both forecasting accuracy and interpretability of retail electricity price dynamics. It first applies a multi-resolution decomposition to isolate semiannual, quarterly, and monthly trends from high-frequency fluctuations. A causal graph is then discovered over these components and key covariates, including wholesale forward prices and retail contract attributes such as early termination fees, with domain constraints that preserve causal directionality and exogeneity. The learned causal structure is encoded as an adjacency embedding that conditions the TCN's convolutions and attention, aligning representation learning with causal pathways. Using ten years of daily 12-month fixed-price residential contracts from Ohio's deregulated market, we find that wholesale forward prices primarily determine long-term retail price trends, whereas contract attributes influence short-term fluctuations. CG-TCN consistently outperforms benchmark models, achieving mean absolute percentage errors of 3.08%, 3.82%, and 5.43% for one-, ten-, and fifteen-step-ahead forecasts of daily retail electricity median prices, respectively. By combining predictive performance with interpretability, CG-TCN provides transparent, policy-relevant insight to support market analytics, consumer protection, regulatory oversight, risk assessment and procurement planning in competitive electricity markets.

1. Introduction

Retail electricity prices reflect both wholesale market conditions and contract-level features, but prior research largely examined these drivers separately. CG-TCN addresses this gap by combining multi-scale decomposition, causal discovery, and neural forecasting to produce accurate, interpretable predictions.

  • Motivation: Retail electricity prices affect consumer expenditures, supplier and policymaker decisions, procurement, risk management, and efficiency adoption.
  • Price formation: Wholesale costs, retail market design, contract attributes, futures-related fundamentals, regulatory interventions, and evolving contracts jointly shape retail price volatility.
  • Research gap: Existing studies largely examine wholesale and retail drivers in isolation, leaving limited evidence on their combined influence on retail price formation.
  • Research gap: Many forecasting models remain black boxes or correlation-based, providing limited mechanism insight and weak directional, invariant relationships for regime shifts and policy shocks.
  • Proposed approach: CG-TCN learns a directed causal graph and injects it into a temporal convolutional network through a graph-neural embedding aligned with causal pathways.
  • Proposed approach: The framework combines one-sided multi-resolution decomposition, constrained causal discovery, graph-informed forecasting, and spike-aware modeling for accurate, interpretable price predictions.

2. The proposed CG-TCN forecasting framework

CG-TCN jointly models structural causality across variables and temporal causality across lags through a DAG-conditioned temporal forecaster. Its causal graph, multiscale decomposition, graph-neural conditioning, and interpretability outputs support transparent retail price forecasting.

  • Framework motivation: CG-TCN explicitly encodes structural causality across variables and temporal causality along the timeline in one forecasting framework.The framework targets both cross-variable causal influences and past-to-future effects at multiple lags.
  • Causal graph discovery: The model estimates a sparse directed causal graph over decomposed price components and covariates using differentiable acyclicity and domain constraints.The constraints preserve economically admissible directions, prevent targets from acting as parents, and maintain exogeneity of exogenous inputs.
  • Graph-temporal fusion: A graph-neural embedding aggregates information along parent links and conditions temporal convolutions through feature fusion and channel-wise gating.This couples graph structure with dilated causal convolutions that capture long- and short-range lagged dependencies while preserving chronological order.
  • Multiscale decomposition: Retail prices are decomposed into semiannual, quarterly, monthly, and high-frequency components that enter both causal discovery and forecasting.The decomposition uses causal, one-sided information available up to time t and supports alternative STL- and Butterworth-based procedures.
  • Interpretability and evaluation: The framework produces causal graphs, effective forecaster adjacencies, and temporal saliency maps that attribute long-horizon versus short-term price influences.These outputs support procurement timing, hedging design, and policy evaluation; ablations report improved accuracy and stability over purely temporal baselines.

3. Data

The study constructs daily median and minimum price series from Ohio residential electricity contracts, combining contract-level attributes with wholesale and calendar covariates. The data cover 12-month fixed-price offers from 2014–2023, with temporally ordered training, validation, and testing procedures.

  • Data source and scope: The database contains residential retail electricity offers filed with PUCO between January 2014 and December 2023.Unlike aggregated utility or EIA summaries, the data capture consumer-facing prices and contractual terms.
  • Study setting: The analysis focuses on Duke Energy Ohio, a policy-relevant territory with pronounced pricing heterogeneity and strategic supplier behavior.The territory represents the greater Cincinnati metropolitan area and surrounding regions.
  • Price measures: Two daily series summarize 12-month fixed residential contracts: median price represents typical offers, while minimum price captures the lowest available contract.The minimum series provides a robustness test under more volatile and extreme pricing conditions.
  • Evaluation design: Each price series is split independently into 85% training and 15% testing data, with time-series cross-validation used for model selection.Final performance is evaluated on the held-out test set while preserving temporal ordering.
  • Covariates: Covariates combine contract attributes, wholesale forward prices aligned to each contract’s 12-month delivery horizon, and calendar indicators.Contract attributes include fixed monthly and early termination fees; calendar features capture weekday, monthly seasonality, and federal-holiday effects.

4. Results and Discussions

The results show that causal multi-scale decomposition separates retail-price behavior by horizon, while CG-TCN delivers strong and stable forecasts across horizons and price definitions. Constrained causal graphs also produce sparser, more economically interpretable dependencies than unconstrained discovery.

  • 4.2. Time series decomposition results: Semiannual, quarterly, monthly, and fluctuation components represent long-run trends, intermediate cycles, seasonal deviations, and short-lived shocks.The components contribute additively to observed prices, supporting horizon-specific forecasting and causal analysis.
  • 4.2. Time series decomposition results: Minimum prices exhibit sharper cyclical movements and more pronounced short-lived drops and spikes than median prices.The decomposition attributes these extremes to competitive pricing behavior and promotional offers.
  • 4.3. Forecast accuracy and stability: CG-TCN achieves the best median-price performance, including MAE 0.2772, MSE 0.1534, RMSE 0.3917, NRMSE 4.04%, and R2 0.9693.The reported scale-dependent metrics are lower for errors and higher for explained variance than competing models.
  • 4.3. Forecast accuracy and stability: CG-TCN reproduces aggregate and decomposed price dynamics across horizons, although extreme high-frequency spikes are slightly attenuated.Its predictions track long-run declines, medium-term adjustments, short-horizon oscillations, and high-frequency variability.
  • 4.3. Forecast accuracy and stability: At H = 10, CG-TCN records RMSE 0.499 and R2 = 0.934, while at the 15-day horizon it retains the lowest MAE and RMSE and highest R2.The authors report greater robustness to error accumulation as the multi-step horizon increases.
  • 4.5.1. Causal DAG: Constrained causal graphs align directions with theoretical expectations, whereas unconstrained discovery produces dense, feedback-like structures that complicate interpretation.The constrained DAG operationalizes explainability by incorporating institutional and theoretical expectations into graph learning.
  • 4.5.1. Causal DAG: Nonlinear NOTEARS identifies fewer strong links involving wholesale forward prices, contract fees, and price-trend components.The authors report similar predictive accuracy between linear and nonlinear variants, with marginal nonlinear improvements but greater linear stability under the current data regime.

5. Discussion

The discussion reports that integrating causal graphs with temporal convolution improves predictive performance and interpretability, while decomposition isolates heterogeneous temporal dynamics. It also identifies distinct roles for wholesale forward prices and contract attributes in shaping retail price movements, with implications for policy and market applications.

  • Causal graph integration with temporal convolution substantially improves predictive performance and interpretability in retail electricity forecasting.
  • Decomposition isolates heterogeneous temporal dynamics, with longer windows and deeper representations capturing slower trends and spike-aware mechanisms responding to rare fluctuations.The design aligns model architecture with the multi-scale nature of retail electricity price formation.
  • The learned causal graphs provide interpretable insights into retail price formation mechanisms that standard black-box models make difficult to obtain.
  • Wholesale forward prices primarily shape long-horizon trends, whereas monthly fees and early termination fees more strongly influence short-term fluctuations and discrete price adjustments.The fee effects are discussed as flexible instruments for responding to market conditions and managing risk exposure without uniformly raising headline energy prices.
  • The framework can support anticipating elevated price risk and assessing how default service rates or contract fee structures may influence retail price magnitudes or volatility.The stated applications include consumer protection, market monitoring, competition enforcement, welfare analysis, affordability assessment, procurement, and private-sector market use.
  • The empirical analysis focuses on a single utility territory, although the authors describe the methodology as generalizable to other deregulated markets.The study also emphasizes richer behavioral detail and product heterogeneity in retail offer data compared with wholesale market data.

6. Conclusion

The paper presents CG-TCN as a causal-forecasting framework for retail electricity prices, combining multi-resolution decomposition, causal graph discovery, and temporal deep learning. It reports improved forecasting accuracy and interpretability, with insights into wholesale-market and retail-contract effects.

  • CG-TCN combines multi-resolution signal decomposition, causal graph discovery, and hybrid temporal deep learning for retail electricity price prediction.
  • The framework separates semiannual, quarterly, monthly, and high-frequency dynamics while modeling causal links with wholesale forward prices, contract attributes, and calendar effects.
  • CG-TCN achieves superior forecasting accuracy relative to transformer-based and statistical benchmarks.
  • The model improves interpretability by revealing how different market drivers propagate through distinct temporal layers of retail prices.
  • Learned causal structures provide economically meaningful insights into interactions between wholesale markets and retail contract design.
  • The resulting models bridge predictive accuracy and interpretability, producing transparent and policy-relevant outputs for retail electricity markets.

Appendix A. The Potential Factors

Appendix A identifies potential factors in three groups: retail electricity contract variables, energy-market variables, and time features. It also specifies selected calendar indicators for contract publication dates.

  • Potential factors are organized into retail electricity contract, energy market, and time feature groups.
  • The time features include contract publication day, publication month, and whether the publication date is a US holiday.

Appendix A.1. Construction of Forward Wholesale Electricity Prices

The study constructs a forward-looking wholesale electricity price for each retail contract by averaging monthly forward prices across its full delivery horizon. This aligns wholesale hedging costs with the retail offer’s duration.

  • The constructed wholesale measure approximates the expected procurement cost for a supplier hedging the contract at origination.
  • For each contract, the measure averages monthly wholesale forward prices over the contract’s full delivery period.
  • Modulo and floor operations ensure correct calendar-month cycling and delivery-year adjustment across multi-year contract horizons.
  • Wholesale forward prices come from PJM’s West Hub, the most liquid trading hub and proximate wholesale market for Duke Energy Ohio’s service territory.

Appendix B. Time-Series Cross-Validation Strategy

The study uses time-series cross-validation to preserve chronological order and prevent future information from influencing training. Sequential rolling or expanding windows provide a more realistic evaluation under changing market conditions.

  • Traditional random k-fold splits can leak future information into training and violate time-series causality.
  • All experiments use time-series cross-validation, training on observations through t_i and validating on the subsequent interval (t_i, t_i+1].
  • The training window rolls or expands forward through time, ensuring forecasts use historical data to predict unseen future values.
  • TSCV preserves causality by enforcing strict temporal order and preventing implicit access to future information.
  • Testing across multiple historical windows assesses generalization under changing market regimes and volatility conditions.
  • Overall, TSCV provides a more realistic and causally consistent evaluation than traditional random-split cross-validation.

Appendix C. Spike-Aware Algorithm

The spike-aware algorithm identifies economically significant deviations from a smoothed price baseline and gives these rare events greater influence during training. It balances attention to extreme volatility with preservation of the underlying data distribution.

  • Spikes are defined as large positive or negative deviations from a smoothed baseline exceeding a specified z-score threshold.These windows capture short-lived episodes of market stress and heightened volatility.
  • Spike windows guide both sampling and the loss function during model training.Oversampling targets a fixed expected batch proportion, while higher loss weights amplify errors within spike windows.
  • The mechanism improves responsiveness to abrupt price surges without artificially altering the underlying data distribution.The diagnostic checks that spike detection is neither overly aggressive nor overly conservative.
  • 667 of 3,583 windows, or 18.62%, are identified as spike windows in the final price series.The algorithm is applied to the reconstructed retail price series, treating extreme movements at the consumer-facing price level.

Appendix D. Sensitivity of One-Sided Decomposition to Window Lengths

The appendix evaluates how one-sided STL and TSN decomposition window lengths affect one-step-ahead forecasting of daily median and minimum retail prices. Moderate medium-horizon smoothing with short short-horizon components generally balances stability and responsiveness, although optimal settings vary by price statistic.

  • Interpretation: Window selection controls component smoothness, phase lag, and responsiveness, balancing noise reduction against preservation of predictive information.The best-performing settings are adopted in subsequent forecasting experiments.
  • Median prices: STL with windows (180, 60, 20) achieves the best median-price accuracy, with MAE 0.2685, RMSE 0.3609, and R2 0.9648.The comparison uses identical model architectures and training procedures across configurations.
  • Median prices: TSN with windows (180, 60, 10) provides the strongest overall median-price performance, achieving R2 = 0.9290.Shorter short-horizon windows are more effective for this decomposition.
  • Minimum prices: Minimum-price decomposition requires different STL smoothing: (180, 90, 15) performs best because a longer medium-term horizon stabilizes extreme lower-bound movements.Minimum prices are described as more volatile and spike-prone than median prices.
  • Minimum prices: TSN with windows (180, 60, 10) again delivers the strongest minimum-price performance, with MAE 0.2772 and R2 0.9693.The results reinforce the value of short short-horizon windows for abrupt price movements.

Appendix E. Hyperparameter Optimization

The hyperparameter optimization procedure is designed to make comparisons among CG-TCN, MTGNN, and Autoformer systematic and fair. Each model is tuned within its standard architectural design rather than through ad hoc manual calibration.

  • Optuna is used to tune CG-TCN, MTGNN, and Autoformer within their standard architectural designs.The stated goal is a fair and systematic comparison without ad hoc manual calibration.

Appendix E.1. Optuna-based optimization framework

The Optuna-based framework searches model-specific architectural and training spaces using validation loss with time-series cross-validation. It retrains each selected configuration on the full training set before test evaluation, while pruning reduces the cost of unsuccessful trials.

  • Optimization framework: Optuna uses a define-by-run search space and the Tree-structured Parzen Estimator to balance exploration and exploitation.Searches include model-specific architectural and training-related hyperparameters.
  • Optimization framework: Pruning terminates unpromising trials early based on intermediate validation performance, substantially reducing training cost.The procedure is also intended to mitigate overfitting to specific hyperparameter choices.
  • Evaluation procedure: The objective minimizes validation loss on a held-out training subset evaluated with time-series cross-validation.The best configuration is then retrained on the full training set and evaluated on the test set.
  • CG-TCN search: CG-TCN optimization jointly includes learning, architecture, dropout, graph, and spike-aware parameters.The search covers spike detection threshold, spike loss weight, and spike-window sampling probability alongside TCN and GNN settings.
  • Baseline searches: MTGNN and Autoformer use model-specific searches covering temporal, graph, transformer, decomposition, and standard training parameters.Their selected configurations are reported separately from CG-TCN's.

Appendix F. Comparison with the Causality from CTCN Model

The appendix contrasts baseline CTCN saliency and attribution with CG–TCN’s explicit hierarchical causal representation. CTCN emphasizes long-term trends, while CG–TCN routes exogenous effects through interpretable causal pathways rather than treating all inputs as direct predictors.

  • Baseline CTCN attribution: CTCN saliency concentrates predictive influence on the long-horizon Trend 180 component, especially at distant historical lags.The heatmap reports relative feature importance across historical lags, and shorter-horizon components receive less emphasis.
  • Baseline CTCN attribution: Trend 60, Trend 20, IMF sum, MonthlyFee, and EarlyTerminationFee receive emphasis, whereas calendar indicators receive comparatively little weight.The appendix describes the baseline as emphasizing long-term trend components while underutilizing exogenous or calendar-based features.
  • Baseline CTCN limitations: CTCN’s saliency patterns capture temporal persistence but cannot distinguish true causal drivers from merely correlated features.Its flat attribution structure treats covariates as direct contributors and can conflate correlation with causation when inputs share temporal structure.
  • CG–TCN causal representation: CG–TCN embeds an explicit causal graph that hierarchically organizes dependencies and channels exogenous effects through decomposed price trends.In the schematic representation, exogenous features influence intermediate price trends through learned causal links before those trends jointly determine retail price.
  • CG–TCN causal representation: CG–TCN redistributes attribution across interpretable causal pathways, grounding retail-price prediction in structured causal reasoning rather than purely empirical correlations.This layered formulation is presented as a more faithful and interpretable representation of retail electricity price dynamics.
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