Day-Ahead Electricity Price Forecasting Using a Multivariate Group Lasso Method

The gist: The proposed CING-LEAR model is a multivariate statistical method that accounts for cross-hour feature group effects in electricity pricing signals by leveraging a Group Lasso formulation to forecast day-ahead electricity prices, demonstrating considerable improvements in point and probabilistic forecast metrics compared to other methods.

Motivation

Electricity price signals exhibit complex dependence structures that render forecasting inherently challenging, with the analysis of real-world pricing signals from the California Independent System Operator (CAISO) revealing complex temporal group effects where the influence of explanatory variables on electricity prices persists across consecutive blocks of time due to underlying economic and operational drivers. This observation is supported by Pearson correlation heatmaps showing clear vertical band structures, suggesting that a given hourly feature is strongly correlated with LMPs across several consecutive hourly blocks rather than being localized to the corresponding hourly LMP. The paper proposes a multivariate statistical model called the “Cross-INfluence-Group-Lasso-Estimated Auto-Regressive” model, or CING-LEAR, to model these cross-hour group effects by generalizing the LEAR model to a multivariate setting through a group regularization.

Model Formulation (CING-LEAR)

The CING-LEAR model generalizes the LEAR model to a multi-output setting and is formulated with a Group Lasso regularizer, enabling the joint selection of covariate effects across the full forecast horizon. The conceptual difference between LEAR and CING-LEAR lies in how coefficients are organized: LEAR estimates 24 hour-specific coefficient vectors and applies an l1 penalty to each independently, whereas CING-LEAR organizes the coefficients so that each predictor forms a single group across the 24 hourly outputs. This design directly mirrors the vertical-band structure shown in Figure 1, where if a covariate tends to consistently influence electricity prices across hourly blocks, it is natural to treat its day-ahead hourly coefficients as one structured object and then regularize it jointly.

The multivariate linear regression model adopted in CING-LEAR is expressed as pd = B⊤xd + epsilond, where the input features include historical day-ahead prices of the previous three and seven days, day-ahead forecasts of the K exogenous variables for days d, d − 1 and d − 7, a vector of dummy variables denoting the day-of-week variation, and stacking all features available on day d − 1 into a single vector xd. To enforce joint feature selection across hours, a group Lasso penalty is applied to the rows of B, defined as Ω(B) = ∑Mphi=1‖bphi,⋅‖2, which encourages entire rows of B to shrink to zero. This encourages feature selection by exploiting the cross-hour group structure in electricity pricing signals.

Training and Evaluation

The model is trained using a sliding window approach, combining forecasts generated by the same model trained over multiple calibration windows, rather than selecting a single window length. The set of calibration windows considered includes four short-term windows: 28, 56, 84, and 112 days (corresponding to 4, 8, 12, and 16 weeks), as well as three long-term windows of one, two, and three years. The resulting base forecasts are then combined adaptively through a weighted ensemble where weights are determined based on each model’s most recent predictive performance.

Evaluation metrics used include Mean absolute error (MAE), Root mean squared error (RMSE), and Continuous ranked probability score (CRPS). The results show that CING-LEAR consistently outperforms LEAR and DNN, with the exception of RMSE and CRPS in 2024, where DNN is leading. When compared against the top three ranked teams from the 2024 PG&E Energy Analytics Challenge, CING-LEAR achieved second place among all participants without relying on additional features. Furthermore, CING-LEAR demonstrates consistently competitive performance when benchmarked against two models currently deployed by a major U.S. utility.

Key Findings and Insights

The forecasts produced by CING-LEAR exhibit smoother temporal profiles due to the inclusion of group effects in the feature selection, which enables CING-LEAR to be more consistent with actual LMP patterns, leading to improved accuracy. The analysis of estimated coefficients shows that CING-LEAR selects a broader set of features by capturing temporal group effects, and it reinforces certain informative features already identified by LEAR. Theoretical analysis using the sample complexity parameter θ(N,M,B) suggests that for the same support size, CING-LEAR appears to maintain stronger feature recoverability than LEAR. The comparison between CING-LEAR and Chronos-2 shows that while Chronos-2 benefits from large-scale pretraining, CING-LEAR achieves better performance than the zero-shot TSFM and remains within a narrow margin of the fine-tuned version. The ensemble constructed as the mean of predictions from CING-LEAR and Chronos-2 (fine-tuned) achieves a significantly better performance over its member constituents, suggesting that “the whole may be greater than the sum of its parts”.

Future Directions

Future research directions include proposing more advanced ensemble strategies that exploit when and under which conditions these models perform better, for example based on performance, volatility, or regime indicators. Additionally, the proposed multivariate framework can be extended to jointly model electricity prices across multiple locations, enabling the explicit incorporation of spatial dependencies that are native to electricity pricing signals. The paper concludes that the future of electricity price forecasting may lie not in replacing domain-tailored forecasting methods with TSFMs, but potentially in combining their complementary strengths for improved forecast accuracy.

Acknowledgment

This research is supported in part by the U.S. National Science Foundation, ECCS 2114422. The references listed are [1] through [36].

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Day-Ahead Electricity Price Forecasting

Figure 2: Time series illustration of LMPs and exogenous variables over a three-day horizon. The vertical dashed line in panel (a) denotes the day-ahead market closure time (10:00am), at which the LMP for day d + 1 is forecasted. Across all panels, solid lines indicate information that are available before the market closure time, while dashed lines represent information that are not available and therefore must be forecasted.

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Day-Ahead Electricity Price Forecasting

Figure 2: Time series illustration of LMPs and exogenous variables over a three-day horizon. The vertical dashed line in panel (a) denotes the day-ahead market closure time (10:00am), at which the LMP for day d + 1 is forecasted.

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Day-Ahead Electricity Price Forecasting

Figure 3: Conceptual difference between the regularization structure in LEAR (left) versus its proposed multivariate extension, CING-LEAR (right).

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Day-Ahead Electricity Price Forecasting

Figure 3: Conceptual difference between the regularization structure in LEAR (left) versus its proposed multivariate extension, CING-LEAR (right).

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Day-Ahead Electricity Price Forecasting

Figure 4: Comparison of actual LMPs and correspondent day-ahead forecasts over a representative period of one week in April 2025. The dashed line denotes the actual LMPs, while solid lines represent the forecasts produced by the different models (Red = CING-LEAR, Blue = LEAR, Green = DNN, Purple = Chronos-2)

1. Implementation of CING-LEAR for Cross-Hour Group Effects: The improved system can forecast day-ahead electricity prices by leveraging a multivariate statistical model that accounts for cross-hour feature group effects that are prevalent in electricity pricing signals. This allows the model to capture the vertical-band structure shown in Figure 1 by enforcing joint selection of covariate effects across the full forecast horizon.

2. Enhanced Feature Selection via Group Lasso Regularization: The system will utilize a Group Lasso penalty on the rows of B, which encourages entire rows of the coefficient matrix to shrink to zero, resulting in a mechanism where feature j is either selected for all hours or removed simultaneously from the model. This enforces consistent feature selection across hours rather than independent hourly estimation.

3. Improved Probabilistic Forecasting with Cross-Hour Error Modeling: The system can generate more robust uncertainty outputs by imposing a distributional assumption on the error vector, allowing it to express the conditional distribution of prices as p d x d F(B̂⊤x d, Σ), where Σ is a symmetric positive definite matrix capturing the dependence structure of forecast errors across different hours.

4. Adaptive Ensemble Forecasting Strategy: The improved system will employ an adaptive ensemble where weights are determined by the model's recent performance, specifically using the formula w l,c = ε l−1,c − 1/∑C j=1 ε l−1,j − 1, ensuring that the ensemble achieves a significantly better performance over its member constituents.

5. Intrinsically Interpretable Forecast Signatures: Unlike black-box models like TSFMs, the system provides explainability because "CING-LEAR is intrinsically interpretable, allowing forecast users to directly examine the contributions of exogenous variables, diagnose abnormal predictions, and probe the market and system conditions driving forecast behavior."

Electricity price signals in modern power systems exhibit complex dependence structures that render forecasting inherently challenging. Our analysis of real-world electricity pricing signals reveals complex temporal group effects, whereby the influence of explanatory variables on electricity prices persists across consecutive blocks of time due to underlying economic, system, and operational drivers. In response, we propose a multivariate statistical method based on a Group Lasso formulation to jointly forecast the vector of day-ahead electricity prices (h = 1,..., 24), by leveraging multi-feature temporal group effects. Our approach is evaluated on two full years of electricity prices from the California Independent System Operator (CAISO), demonstrating considerable improvements in point and probabilistic forecast metrics compared to a wide array of statistical and deep learning methods. Empirical analyses confirm the effectiveness of the proposed approach in modeling realistic group effects, maintaining both interpretability and low computational complexity. When retrospectively evaluated on test data from a recent international electricity price forecasting challenge, the proposed method ranked in second place, despite having access to significantly less information than competing approaches. Finally, the proposed method is independently validated against two operational electricity price forecasting systems in CAISO, demonstrating competitive predictive performance and practical relevance.