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arxiv: 2605.27781 · v1 · pith:O2MUMMR7new · submitted 2026-05-27 · 📊 stat.AP · cs.SY· eess.SY

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

Keyi Wang , Jiaxiang Ji , Mahan Mansouri , Ahmed Aziz Ezzat This is my paper

Pith reviewed 2026-06-29 09:55 UTC · model grok-4.3

classification 📊 stat.AP cs.SYeess.SY
keywords electricity price forecastinggroup lassoday-ahead forecastingmultivariate forecastingCAISOtemporal group effectsprobabilistic forecastingstatistical forecasting
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The pith

A multivariate Group Lasso method improves day-ahead electricity price forecasts by capturing persistent temporal group effects in explanatory variables.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a Group Lasso-based multivariate model to forecast vectors of day-ahead electricity prices. It identifies that influences from explanatory variables on prices persist across consecutive time blocks due to economic and operational drivers in real CAISO data. The approach is shown to deliver better point and probabilistic forecasts than a range of statistical and deep learning baselines on two years of CAISO data, and it placed second in a recent international forecasting challenge while using less information than competitors. The method is also validated against two operational CAISO systems and maintains interpretability with low computational cost.

Core claim

Electricity price signals exhibit complex temporal group effects where the influence of explanatory variables persists across consecutive blocks of time; a multivariate Group Lasso formulation that explicitly leverages these multi-feature temporal group effects produces improved day-ahead forecasts for the full price vector.

What carries the argument

Multivariate Group Lasso formulation that groups regression coefficients across time blocks to enforce shared sparsity patterns reflecting persistent temporal effects.

If this is right

  • The method yields measurable gains in both point forecast accuracy and probabilistic calibration on two full years of CAISO prices.
  • It achieves second place in an international electricity price forecasting challenge while using significantly less input information than top entries.
  • It matches or exceeds the performance of two existing operational forecasting systems deployed in CAISO.
  • The formulation preserves interpretability through sparse coefficient groups and runs with low computational complexity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same grouped temporal structure could be tested in other energy time series such as load or renewable generation forecasts.
  • If the group effects are market-specific, the penalty structure would need re-tuning when moving to different regions or price regimes.
  • The approach may serve as a lightweight benchmark for more complex neural models that also aim to capture multi-scale temporal dependence.

Load-bearing premise

The complex temporal group effects observed in CAISO pricing signals persist in a way that can be captured and exploited by a Group Lasso penalty for better out-of-sample forecasts.

What would settle it

On held-out CAISO data or new market data, the Group Lasso method fails to improve point or probabilistic metrics relative to the strongest non-grouped lasso or deep learning baselines.

Figures

Figures reproduced from arXiv: 2605.27781 by Ahmed Aziz Ezzat, Jiaxiang Ji, Keyi Wang, Mahan Mansouri.

Figure 1
Figure 1. Figure 1: Pearson correlation heatmaps between LMPs and forecasts of regional load (a), solar generation (b), and natural gas generation (c), respectively, during 2025 in CAISO. The plots reveal strong cross-hour (non-local) temporal dependencies between key system variables and LMPs, wherein each column shows the dependence between a single-hour variable (e.g., regional load at hour 8) and the correspondent intra-d… view at source ↗
Figure 2
Figure 2. 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 … view at source ↗
Figure 3
Figure 3. Figure 3: Conceptual difference between the regularization structure in LEAR (left) versus its proposed multivariate extension, CING-LEAR (right). where 𝜺𝑑 ∈ ℝ24 collects the hourly errors. Stacking all days, we collect the pricing vectors and error terms in the matrices 𝐏 and 𝐄, respectively, defined as: 𝐏 = ⎡ ⎢ ⎢ ⎣ 𝐩 ⊤ 1 ⋮ 𝐩 ⊤ 𝑁 ⎤ ⎥ ⎥ ⎦ ∈ ℝ 𝑁×24 , 𝐄 = ⎡ ⎢ ⎢ ⎣ 𝜺 ⊤ 1 ⋮ 𝜺 ⊤ 𝑁 ⎤ ⎥ ⎥ ⎦ ∈ ℝ 𝑁×24 . Then, the formulation … view at source ↗
Figure 4
Figure 4. 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). The red shaded region indicates the 90% prediction interval produced by CING-LEAR, showing faithful probabil… view at source ↗
Figure 5
Figure 5. Figure 5: The left set of panels (A1-A4) display the estimated coefficients of each feature across the 24 hours, averaged over the entire test period, where black indicates zero coefficients and yellow colors correspond to absolute coefficient magnitudes. The right set of panel (B1-B4) show the correlation matrices of the coefficients across the 24 hourly, where red and blue denote positive and negative correlations… view at source ↗
Figure 6
Figure 6. Figure 6: Estimated sample complexity parameter 𝜃̂ with respect to the support size 𝑠 for LEAR and CING-LEAR. sample complexity parameter: 𝜃(𝑁,𝑀,𝐁) = 𝑁 2 𝜓(𝐁) log(𝑀 − 𝑠) , (16) where 𝑠 denotes the number of support features (non-zero). The term 𝜓(𝐁), referred to as the sparsity overlap function, depends on both the structure of 𝐁 and the covariance structure, and is defined as: 𝜓(𝐁) = ‖ ‖ ‖ 𝐙 ⊤ 𝑆 𝚺 −1 𝑆𝑆𝐙𝑆 ‖ ‖ ‖2 , … view at source ↗
read the original abstract

Electricity price signals in modern power systems exhibit complex dependence structures that render forecasting inherently challenging. Our analysis of real-world pricing signals from the California Independent System Operator (CAISO) reveals complex temporal group effects, whereby the influence of explanatory variables on electricity prices persists across consecutive blocks of time due to underlying economic and operational drivers. In response, we propose a multivariate statistical method based on a Group Lasso formulation to forecast the vector of day-ahead electricity prices, by leveraging multi-feature temporal group effects. Our approach is evaluated on two full years of electricity prices from CAISO, demonstrating considerable improvements in point and probabilistic forecast metrics compared to a wide array of statistical and deep learning methods. Theoretical and 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a multivariate Group Lasso method for day-ahead electricity price forecasting that exploits identified temporal group effects in CAISO data. It claims considerable improvements in both point and probabilistic forecast metrics over a range of statistical and deep learning baselines on two full years of CAISO data, a second-place ranking in a recent international electricity price forecasting challenge (despite using less information than competitors), competitive performance against two operational CAISO systems, and supporting theoretical and empirical analyses confirming the method's ability to model realistic group effects while preserving interpretability and low computational cost.

Significance. If the reported empirical gains hold under rigorous verification, the work provides a statistically grounded, interpretable alternative to black-box models for electricity price forecasting. The use of held-out CAISO data, an external challenge benchmark, and operational validation, together with the emphasis on group-structured temporal dependence, represents a practical contribution to the field. The low computational complexity and interpretability are additional strengths that could facilitate adoption in real-time market operations.

major comments (2)
  1. §4 (Results on CAISO data): The central claim of 'considerable improvements' in point and probabilistic metrics is load-bearing for the paper's contribution, yet the provided abstract supplies no numerical values, confidence intervals, or statistical significance tests; the full results section must include these (e.g., specific MAE, RMSE, CRPS deltas versus each baseline) to allow assessment of effect size and robustness.
  2. §5 (Challenge evaluation): The second-place ranking claim is central to the practical relevance argument, but requires explicit documentation of the exact test period, the precise information set available to competing entries, the evaluation metric, and the ranking methodology to substantiate that the method achieved this with 'significantly less information'.
minor comments (2)
  1. Abstract: Consider adding one or two concrete quantitative highlights (e.g., 'X% reduction in MAE') to make the performance claims immediately verifiable without requiring the reader to reach the results tables.
  2. Notation: Ensure consistent use of boldface or other conventions for vectors (e.g., the day-ahead price vector) throughout the method and results sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation of minor revision. The points raised help clarify the presentation of our empirical results. We address each major comment below.

read point-by-point responses

  1. Referee: §4 (Results on CAISO data): The central claim of 'considerable improvements' in point and probabilistic metrics is load-bearing for the paper's contribution, yet the provided abstract supplies no numerical values, confidence intervals, or statistical significance tests; the full results section must include these (e.g., specific MAE, RMSE, CRPS deltas versus each baseline) to allow assessment of effect size and robustness.

    Authors: We agree that explicit numerical deltas, confidence intervals, and significance tests improve assessment of the results. While §4 already reports MAE, RMSE, and CRPS values for the proposed method against all baselines on the full two-year CAISO dataset, we will revise the section to add: (i) explicit performance deltas relative to each baseline, (ii) 95% bootstrap confidence intervals around the metrics, and (iii) paired statistical tests (e.g., Diebold-Mariano) for significance. These additions will be included in the revised manuscript. revision: yes

  2. Referee: §5 (Challenge evaluation): The second-place ranking claim is central to the practical relevance argument, but requires explicit documentation of the exact test period, the precise information set available to competing entries, the evaluation metric, and the ranking methodology to substantiate that the method achieved this with 'significantly less information'.

    Authors: We agree that greater explicitness strengthens the claim. Section §5 currently summarizes the retrospective evaluation and notes the limited information set, but we will expand it with a dedicated paragraph or table that states: the precise test period dates, the exact inputs used by our method versus those available to competitors, the evaluation metric, and the ranking procedure. This will directly substantiate the 'significantly less information' statement. The revision will be made. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is an empirical result: a multivariate Group Lasso method, motivated by observed temporal group effects in CAISO electricity price data, is evaluated on two full years of held-out CAISO data plus an external international forecasting challenge, where it achieves measurable improvements in point/probabilistic metrics and a second-place ranking. No equations, derivations, or self-citations are presented that reduce the reported performance gains to quantities defined by construction from the fitted parameters or inputs of the same dataset. The method is presented as a standard penalized regression approach whose effectiveness is confirmed by out-of-sample testing, rendering the derivation chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that temporal group effects exist in electricity price data and can be captured by Group Lasso penalties; no free parameters, invented entities, or additional axioms are stated in the abstract.

axioms (1)
  • domain assumption Complex temporal group effects persist across consecutive blocks of time in electricity pricing signals due to economic and operational drivers.
    Invoked in the opening analysis of CAISO data as the motivation for the Group Lasso formulation.

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discussion (0)

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