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Medium-Term Multi-Resolution Electric Load Forecasting using Economic Data and Foundation Model

Lindas Eloi, Goude Yannig, Ciais Philippe

arXiv:2609.31806v1cs.LG

TL;DR

Medium-term load forecasting needs both trend extrapolation and variability modeling, but the value of socioeconomic predictors across forecast horizons and resolutions is uncertain. The paper tests a feature-selection ensemble with a tabular Foundation Model on French daily and monthly load forecasts. Selected economic predictors improve performance by around 20% across lead times, while their feature importance grows with forecast horizon.

  • Problem

    For medium-term load forecasting, it remains unclear whether socioeconomic predictors improve accuracy and which factors matter at different lead times and resolutions.

    Source: §1 · p. 2, §4 · pp. 9–10

  • Method

    The study uses a feature-selection pipeline that ensembles models with diverse covariate subsets, then evaluates forecasts with a rolling procedure across lead times.

    Source: §5 · p. 17

  • Results

    Around 20% improvement over the model without economic predictors was reported across all lead times for TabICL with economic indicators.

    Source: §5 · p. 17

  • Takeaways & Limitations

    Economic predictors' feature importance increases with forecast horizon, supporting their utility for longer-term predictions.

    Source: §5 · p. 17

    The study uses observed weather and socioeconomic inputs in a hindcast setting and focuses on point forecasts rather than probabilistic predictions.

    Source: §3.1 · p. 7, §4 · p. 12

Abstract

from arXiv · show

Accurate medium-term, from a few months to a few years, electricity load forecasts are crucial for informed decision-making in power plant maintenance scheduling, load dispatch and price settlement. Being comprised between Long-Term Load Forecasting (LTLF) which uses mostly economic projections and appliances development scenarios, and Short-Term Load Forecasting (STLF) driven by weather, calendar and autoregressive patterns, Medium-Term Load Forecasting (MTLF) requires both extrapolation capabilities and variability modeling. Yet, it remains unclear if MTLF can benefit from economic indicators, and especially at which forecast horizon and resolution. To address these challenges we investigated the impact of socioeconomic data on predictions issued 1 month and up to 48 months in advance for France at monthly and daily resolution using a tabular Foundation Model (FM). A dataset covering 20 years of observations of electricity load, weather variables and economic features such as consumer price and production indices, electric vehicle counts or employment is created for the study. To avoid noisy data, we used a new feature selection pipeline, creating ensemble of expert models with diverse feature subsets, to demonstrate that selected economic covariates improve forecast skill by 20% over 2015-2025. This enhancement is steady across lead times and resolutions limiting the Mean Absolute Percentage Error to 4% for monthly granularity and 5% for daily granularity. Explainability of the models is investigated through feature and context importance. Results showed that the FM is limited in the context it leverages pointing towards potential computational savings with a reduced context, while feature importance of economic predictors grows with the forecast horizon. This suggests that including economic data in MTLF could bridge the gap with LTLF leading to seamless forecasts.

1 Introduction

Medium-term load forecasting (MTLF) must extrapolate global time-series characteristics while retaining variability, but it remains unclear whether socioeconomic data improve predictions and which predictors matter at different horizons and resolutions. The paper investigates these questions using a tabular Foundation Model and compares it with linear and gradient-boosting models.

1 Introduction

  • Load forecasts support grid balancing and avoiding demand shortages, as well as maintenance scheduling, infrastructure planning, and price settlement.These varied uses make accurate forecasts valuable for informed decisions.Source: §1 · p. 1
  • MTLF is understudied relative to short- and long-term forecasting, whose influential drivers are better established.Short-term studies emphasize weather and calendar patterns, while long-term forecasts use socioeconomic factors such as economic growth, housing, policies, and appliance deployment.Source: §1 · p. 2
  • MTLF combines extrapolation of global time-series characteristics with retention of variability, yet the most helpful predictors and the benefit of socioeconomic data remain unclear.The paper asks whether predictor usefulness changes with forecast lead time or temporal resolution.Source: §1 · p. 2
  • Foundation Models use pretraining on real and synthetic datasets to enable inference on new data without task-specific parameter tuning, a setup called zero-shot prediction.They can also be fine-tuned by updating model parameters on task data.Source: §1 · p. 2
  • Time-series Foundation Models can lack covariate inputs and control over look-back context, motivating the paper's use of tabular models adapted with time-dependent features.The paper describes tabular Foundation Models as offering feature-importance capabilities.Source: §1 · p. 3
  • The paper evaluates socioeconomic covariates in forecasts issued 1–48 months ahead at daily and monthly resolutions, comparing a tabular Foundation Model with linear and gradient-boosting models.It also examines model interpretability to inform which factors practitioners should include.Source: §1 · p. 3

2 Data

The study assembles French load, weather, calendar, and socioeconomic data, then aligns their temporal coverage and spatial scale for daily and monthly forecasting. The resulting dataset spans March 2005 to December 2025 and is divided between covariate selection and rolling evaluation.

2.1 Electricity Demand Data

  • France's electricity-load record extends back to 1995; daily demand is resampled from hourly data, yielding a 25-year dataset.The authors note that older data lack the TSO's quality guarantees available for more recent real-time data.Source: §2.1 · p. 4

2.2 Socio-Economic Data

  • The socioeconomic collection includes about 40 variables spanning production, inflation, growth, population, tourism, heat pumps, and transport.The selected long-history indicators exclude housing characteristics because their definitions or measurement methods did not provide a coherent history longer than ten years.Source: §2.2 · p. 4

2.3 Weather Data

  • Weather inputs include ERA5 temperature and other apparent-temperature factors; regional heating and cooling thresholds are estimated from population-weighted temperatures and regional load.The resulting dataset contains nine weather predictors, including three derived from temperature to represent nonlinear load–temperature relationships.Source: §2.3 · pp. 4–5

2.4 Calendar Data

  • Calendar predictors encode periodic features with sine and cosine, while weekend, public-holiday, and school-vacation features represent recurring load drops.At monthly resolution, weekend and holiday features count days within each month.Source: §2.4 · pp. 5–6

2.5 Preprocessing

  • Registered electric and hybrid vehicle counts are yearly predictors available only since 2011, so earlier city-level values are linearly approximated and clipped at zero.The authors assume the pre-2011 vehicle share is too small to affect national electricity consumption.Source: §2.5 · p. 6
  • The final dataset covers March 2005–December 2025, with March 2005–December 2015 used for covariate selection and January 2016–December 2025 for rolling evaluation.Service Production Index availability before March 2005 limits the shared history; spatially resolved data are aggregated nationally, and differing raw feature frequencies are duplicated to match the target resolution.Source: §2.5 · p. 6

3 Methods

The study compares daily and monthly load forecasts from one month to four years ahead, using a feature-selection and modeling framework evaluated with rolling forecasts. It also examines feature and context importance to characterize model behavior.

3.1 Horizon & Resolution

  • Forecasts span one month to four years at daily and monthly resolution, without autoregressive effects, to assess whether socioeconomic predictors’ utility changes with horizon.The study uses observational weather and socioeconomic data in a hindcast setting, without addressing forecast availability or accuracy for those covariates.Source: §3.1 · pp. 6–7

3.2 Feature Selection

  • Forward selection adds predictors iteratively to a useful calendar-and-weather baseline, stopping when further additions no longer improve held-out scores.The study begins with 63 covariates and ranks subsets using RMSE.Source: §3.2 · pp. 7–8
  • Selection proceeds in three rounds by covariate frequency, allowing coarser economic features to be considered after higher-frequency predictors while reducing search cost.This is intended to reduce the risk that economic data are overlooked because of their lower frequency.Source: §3.2 · p. 7
  • Aggregated hold-out selection with rolling-window cross-validation yields a different selected feature subset for each of 10 folds, producing an ensemble of models.Each fold shifts by one month and has a four-year test period.Source: §3.2 · pp. 7–8

3.3 Models

  • TabICL is the primary tabular Foundation Model; XGBoost and a linear model provide comparisons, and the study focuses on point forecasts.The authors omit XGBoost hyperparameter tuning and use default values.Source: §3.3 · p. 8

3.4 Evaluation & Interpretability

  • The final prediction averages 10 models with different covariate subsets, and performance is evaluated through rolling forecasts from 2016 to 2025.The ensemble is described as experts making predictions, not as a probabilistic ensemble.Source: §3.4 · p. 8
  • Feature selection frequency and Shapley values are used to examine which covariates contribute to predictions across experts and forecast windows.Shapley values are computed for each model before averaging contributions for the final prediction.Source: §3.4 · p. 9
  • Context importance compares scores with all training context against scores after removing one-year blocks, with 16 blocks assessed per forecast horizon.The score is RMSE; positive context importance indicates that removing a block worsened the score, while negative values indicate it improved the score.Source: §3.4 · p. 9

4 Results & Discussions

The section evaluates socioeconomic predictors across models, forecast horizons, and daily and monthly resolutions. Their benefit varies by model and resolution, while feature-importance patterns indicate greater economic-predictor importance at longer horizons.

Economic predictors and forecast performance

  • 20%: Socioeconomic predictors improve TabICL’s daily forecasts across the studied horizons, while the monthly-resolution gain approaches 0% at 48 months.The reported economic-data gain is around 20% across horizons for TabICL; the monthly and daily panels show RMSE evolution by model and horizon.Source: §4 · pp. 9–10, Figure 2 · p. 10

Model comparison

  • TabICL outperforms the other models across resolutions with and without economic covariates, except for a small linear-model advantage at monthly resolution over horizons of 1–2 years with them.The linear model’s error rises sharply beyond two years; at daily resolution it does not compete, while XGBoost narrows its gap to TabICL when more samples are available.Source: §4 · p. 10

Forecast accuracy

  • Below 1,000 MW (2% MAPE): monthly Foundation Model errors stay under 2,000 MW (4%) beyond one year; daily TabICL and XGBoost errors stay below 3,000 MW (5%) at 48 months.The daily forecasts for horizons between one and three years have errors ranging from 2,000 MW (2.5%) to 2,800 MW (4%).Source: §4 · pp. 10–11

Crisis-period performance

  • Economic inputs help models predict recession-related load changes during the COVID and post-Ukraine-war periods, when calendar-and-weather-only models plateau.The analysis evaluates the crisis periods using realized socioeconomic data; the authors note that operational input forecasts would increase the error margin.Source: §4 · pp. 11–12

Scope

  • The study focuses on point forecasts; the authors note that it could be replicated probabilistically using probabilistic predictions or quantile loss.Source: §4 · p. 12

Vehicle and heat-pump ablation

  • Removing electric-vehicle and heat-pump predictors avoids the 36-month error overshoot in linear models, which the authors attribute to post-2020 predictor growth breaking learned linearity.Adding these predictors does not improve XGBoost or TabICL; the difference is small monthly and larger at daily resolution.Source: Figure 3 · p. 11, §4 · p. 12

Feature selection

  • Economic-feature selection lacks consensus: most such predictors appear in fewer than 30% of TabICL and XGBoost subsets, while expert diversity is associated with overall performance gains.At monthly resolution, TabICL selects the transport-and-storage production index and electric public transport in at least half of subsets; at daily resolution, it selects the electricity, gas, and steam index and hybrid public transport at that rate.Source: Figure 4 · p. 12, §4 · p. 13

Feature importance

  • Economic-feature importance generally rises with forecast horizon, although weather and calendar predictors remain more important overall; second-order Shapley analysis yields no valuable insights.The increasing trend appears for TabICL, XGBoost, and the linear model, and is most pronounced for the linear model.Source: §4 · p. 13

S_CVS-CJO

One listed covariate is electric_heavy_utilitary_vehicle.

S_CVS-CJO

M_CVS-CJO

The section examines how feature importance and the usefulness of historical context vary across models and forecast horizons.

M_CVS-CJO

  • Figure 5 plots Shapley-based feature contributions for selected covariates by model, with shaded 95% bootstrapped confidence intervals.Source: Figure 5 · p. 15
  • TabICL’s context importance is dominated by recent blocks even at longer leads, consistent with an attention-range bottleneck limiting use of long history.Source: M_CVS-CJO · p. 15
  • Figure 6 places models in columns and six-month-spaced forecast leads in rows; higher-numbered context blocks represent more recent data.Source: Figure 6 · p. 16
  • XGBoost draws on the full history, while the linear model shifts from recent blocks at shorter leads to a more even distribution above 24 months.Source: M_CVS-CJO · p. 16
  • Low-importance context blocks may contain little useful or redundant information; removing negative-importance blocks could reduce training or Foundation Model inference time.Source: M_CVS-CJO · p. 17

5 Conclusion

This section summarizes the forecasting setup and supporting analyses, including covariates, regional parameters, evaluation metrics, and comparisons of forecast skill and feature choices across horizons. It highlights evidence that selected socioeconomic predictors improve medium-term load forecasts, with economic-feature importance increasing at longer horizons.

5 Conclusion

  • A roughly 20-year dataset and an ensemble feature-selection pipeline supported rolling forecasts from 1 to 48 months, showing economic covariates improved accuracy across lead times and resolutions.The pipeline combined expert models with different covariate subsets, averaged their predictions, and evaluated them using a rolling forecast approach.Source: §5 · p. 17
  • Around 20% improvement over the model without economic predictors across lead times; TabICL’s MAPE stayed at or below 4% monthly and 5% daily.With economic indicators, TabICL’s RMSE did not exceed 2,000 MW monthly and 3,000 MW daily; the models were also better suited to forecasting the COVID and Ukraine-war sobriety periods.Source: §5 · p. 17
  • Economic predictors’ feature importance increased with forecast horizon, while the ensemble’s gains were attributed to diverse feature subsets rather than a consensus set of covariates.Long training histories were useful when they covered events representative of the forecast period, but Foundation Models’ attention bottleneck limited the value of older data.Source: §5 · p. 17
  • Socioeconomic inputs could help bridge medium- and long-term load forecasting and, with climate projections and Shared Socioeconomic Pathways, enable unified demand projections up to 2100.Source: §5 · p. 17

B Appendix B : Description of covariates considered

C Appendix C : Degree Days Regional Model Parameters

D Appendix D : Metric Definition

  • The metric appendix defines evaluation notation using sample count N, true values y, predictions ŷ, and an MSE decomposition that includes irreducible residual error.It models the regression problem as y = f(x) + ε.Source: D Appendix D : Metric Definition · p. 27

E Appendix E: Performance evolution with forecast horizon for other metrics

  • MAPE, bias, and variance are plotted across 1–48-month horizons for monthly and daily resolutions, with 95% bootstrapped confidence intervals.The MAPE figure’s y-axis is clipped for linear models for visibility.Source: Figure 9 · p. 28, Figure 10 · p. 29, Figure 11 · p. 30

F Appendix F: Skill Scores evolution with forecast horizon

  • The skill-score appendix compares forecasts with and without socioeconomic predictors as the reference, with positive scores indicating improvement and negative scores degradation.For RMSE and MAPE, a perfect forecast has zero error.Source: F Appendix F: Skill Scores evolution… · p. 31
  • Appendix F plots RMSESS and MAPESS skill-score trajectories over 1–48-month horizons at monthly and daily resolutions.Source: Figure 12 · p. 31, Figure 13 · p. 32

G Appendix G: Inter Model Performance Comparison

H Appendix H: Performance evolution with forecast horizon during economic crisis

I Appendix I: Selected Features for the Daily Model

  • Appendix I reports daily feature-selection ratios and notes that monthly selection began from a reduced subset of weather, calendar, and holiday covariates.Source: Figure 18 · p. 37

J Appendix J: Feature Selection Utility

  • Daily economic-covariate forecasts improved with feature selection: TabICL RMSE was 1.800–3.000 MW versus 1.900–5.000 MW without selection, while XGBoost error rose 800 MW without it.For weather-and-calendar-only inputs, selection offered no advantage at daily resolution and little to none monthly; monthly gains with economic data were less clear.Source: J Appendix J: Feature Selection Utility · p. 38

K Appendix K: Context Ablation

The appendices test whether TabICL’s context can be shortened and estimate complexity savings from reducing context and features. Context trimming is not uniformly harmful, while combined reductions produce substantial estimated savings.

K Appendix K: Context Ablation

  • 70% context yields lower RMSE than the full context from horizon 22 months, while 80% context does so from horizon 32 months.For 70–90% context, error increases by about 10%; retaining only 50% increases it by about 15%.Source: K Appendix K: Context Ablation · p. 39, Figure 20 · p. 39

L Appendix L: TabICL Complexity

  • The complexity analysis varies feature count and retained context across the row counts encountered in rolling evaluation, for monthly and daily data.The initial dataset has 55 features, reduced to 9–16 per expert through feature selection.Source: L Appendix L: TabICL Complexity · p. 40, Figure 21 · p. 40
  • 55–85% complexity savings from feature reduction at monthly resolution fall to 20–35% daily; combined reductions reach 50–60% daily and 65–90% monthly.The complexity curves are normalized against the model with 55 features and full context.Source: L Appendix L: TabICL Complexity · p. 40, Figure 21 · p. 40
  • The complexity comparisons focus on computation cost and do not account for predictive performance; actual compute time also depends on hardware and software.The analysis is presented as a theoretical illustration.Source: L Appendix L: TabICL Complexity · pp. 40–41

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