Statistically Validated Multi-Horizon Electricity Load Forecasting with Weather-Augmented Machine Learning under Walk-Forward Evaluation

Statistically Validated Multi-Horizon Electricity Load Forecasting with Weather-Augmented Machine Learning under Walk-Forward Evaluation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Statistically Validated Multi-Horizon Electricity Load Forecasting with Weather-Augmented Machine Learning under Walk-Forward Evaluation Meherab Hossain Shafin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9285801/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Short-term electricity load forecasting is essential for maintaining grid reliability, supporting generation scheduling, and enabling efficient operation of modern energy systems. This study develops a weather-augmented multi-horizon forecasting framework for electricity demand prediction using hourly load observations from the ENTSO-E Transparency Platform combined with meteorological data obtained from the NASA POWER dataset. Four forecasting approaches are evaluated within a unified benchmarking framework: Seasonal Naïve persistence, SARIMAX, Gradient Boosting Regression (GBR), and a weather-augmented GBR variant incorporating exogenous meteorological covariates. In addition, the probabilistic DeepAR neural forecasting model implemented using GluonTS is included as a distributional reference model for uncertainty-aware comparison. Forecast performance is assessed across three operationally relevant prediction horizons (t + 1, t + 24, and t + 168) using an expanding-window rolling-origin walk-forward validation strategy. The feature set includes calendar encodings, autoregressive lag features, rolling demand statistics, and wind-related meteorological indicators. Results demonstrate that Gradient Boosting models consistently outperform statistical and persistence baselines across all forecasting horizons. Horizon-specific Diebold–Mariano tests further indicate that weather augmentation provides statistically significant improvements primarily at longer prediction intervals. Across 17 walk-forward evaluation folds, the best-performing configuration achieved a mean RMSE of 88.44 MW (± 29.62) and a mean MAE of 66.69 MW. Probabilistic evaluation produced empirical 80% prediction interval coverage of 0.759, indicating moderate under-calibration relative to nominal uncertainty levels. These findings highlight the effectiveness of feature-driven ensemble methods for structured electricity demand forecasting and demonstrate the value of statistically validated multi-horizon benchmarking frameworks for operational load prediction under limited-data conditions. Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Electricity demand forecasting is a fundamental component of modern power-system operation, supporting generation scheduling, reserve allocation, transmission planning, and energy market participation. Accurate short-term forecasts enable transmission system operators to maintain grid reliability while minimizing operational costs under dynamically evolving consumption patterns. Because electricity demand varies across multiple temporal scales, forecasting models must provide reliable predictions over short-term, day-ahead, and week-ahead horizons to support both operational and strategic decision-making. Electricity consumption exhibits strong periodic structure driven by human activity cycles and environmental conditions. Daily demand patterns reflect residential usage behavior and industrial operating schedules, while weekly and seasonal variations correspond to broader economic activity and climatic influences. In addition to these temporal effects, meteorological variables such as temperature, wind conditions, and solar radiation contribute substantially to demand variability, particularly at longer forecasting horizons where the predictive value of recent observations decreases. Traditional short-term load forecasting methods have relied primarily on statistical time-series models such as autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA), which effectively capture linear temporal dependencies and recurring seasonal patterns in electricity demand data. However, these approaches are often limited in their ability to represent nonlinear relationships between demand and exogenous predictors. To address this limitation, machine learning models—particularly tree-based ensemble methods—have increasingly been applied to electricity demand prediction tasks, demonstrating strong performance when combined with engineered lag features and calendar encodings. More recently, deep learning architectures have enabled probabilistic forecasting of electricity demand by modeling sequential dependencies directly from historical observations and producing predictive uncertainty estimates. Despite these methodological advances, systematic comparison across statistical, machine learning, and probabilistic deep learning approaches remains limited for weather-augmented multi-horizon electricity demand forecasting under realistic operational evaluation settings. Many existing studies evaluate individual model families using fixed train–test splits or single-horizon prediction tasks, which restricts interpretability of comparative performance across forecasting paradigms. In particular, the contribution of meteorological covariates across multiple prediction horizons has not been extensively examined within a unified expanding-window walk-forward validation framework supported by formal statistical significance testing. This study addresses that gap by developing a reproducible multi-horizon benchmarking framework for electricity demand forecasting that enables statistically grounded comparison of forecasting paradigms under realistic deployment conditions. Accurate multi-horizon electricity demand forecasting supports renewable integration planning, reserve allocation strategies, and short-term grid balancing in systems with increasing variability from weather-dependent generation sources. The proposed benchmarking framework therefore contributes to operational decision-support tools required for reliable low-carbon energy system management. . Research Gap Although electricity load forecasting has been extensively studied using statistical, machine learning, and deep learning approaches, existing research remains fragmented across forecasting paradigms and evaluation strategies. Many prior studies evaluate models within a single methodological family, which limits interpretability of comparative performance across alternative forecasting frameworks under consistent experimental conditions [ 41 , 42 ]. In addition, a substantial portion of the literature relies on fixed train–test splits or single-horizon prediction tasks that do not accurately represent operational forecasting environments where models must generate rolling predictions across multiple temporal horizons [ 43 ]. Recent advances in probabilistic forecasting have improved uncertainty representation in electricity demand prediction; however, comparative evaluation between deterministic statistical models, feature-driven ensemble learners, and probabilistic neural forecasting architectures remains limited within unified benchmarking pipelines that incorporate expanding-window walk-forward validation [ 44 ]. As a result, the relative strengths of these model classes across short-, day-ahead-, and week-ahead forecasting horizons remain insufficiently characterized in realistic deployment scenarios. Furthermore, while meteorological variables are widely recognized as important predictors of electricity demand variability, their horizon-specific contribution to forecasting accuracy has not been systematically quantified using formal statistical hypothesis testing across multiple forecasting paradigms [ 45 ]. Existing weather-augmented forecasting studies frequently evaluate temperature-driven demand effects but provide limited evidence regarding the comparative impact of alternative environmental predictors under constrained regional datasets and engineered feature representations [ 46 ]. Another limitation in current literature concerns the evaluation of forecasting models under limited-data operational settings. Many deep learning forecasting frameworks demonstrate strong performance when trained on large collections of related time series; however, their effectiveness relative to tree-based ensemble methods and classical statistical models remains insufficiently examined for single-region electricity demand datasets with restricted temporal coverage [ 47 ]. To address these limitations, this study develops a reproducible multi-horizon benchmarking framework that integrates expanding-window walk-forward validation with horizon-specific Diebold–Mariano statistical testing to support rigorous comparison between statistical, machine learning, and probabilistic neural forecasting approaches. The proposed framework further quantifies the contribution of meteorological covariates across prediction horizons, providing operational insight into model selection for electricity demand forecasting under limited-data deployment conditions. Research Objectives This study addresses the following research questions: How does forecasting performance vary across statistical, machine learning, and probabilistic neural forecasting models under an expanding-window walk-forward evaluation framework? How does the contribution of meteorological covariates change across short-term (t + 1), day-ahead (t + 24), and week-ahead (t + 168) prediction horizons? To what extent do Gradient Boosting ensemble models improve forecasting accuracy relative to classical SARIMAX and persistence baselines under limited-data operational conditions? How well do probabilistic forecasting methods capture predictive uncertainty in multi-horizon electricity demand prediction? Contributions of This Study The main contributions of this study are summarized as follows: • Development of a reproducible multi-horizon benchmarking framework for short-term electricity load forecasting • Integration of expanding-window walk-forward validation for realistic operational evaluation • Horizon-wise statistical comparison of forecasting models using Diebold–Mariano hypothesis testing • Comparative assessment across statistical, machine learning, and probabilistic neural forecasting paradigms under a unified experimental setup • Empirical analysis of meteorological covariate effects across short-, day-ahead-, and week-ahead prediction horizons • Practical guidance for selecting forecasting models under limited-data operational environments 2. Literature Review Short-term electricity load forecasting plays a central role in modern power-system operation by supporting generation scheduling, reserve allocation, transmission planning, and market participation. Because electricity demand exhibits strong temporal structure driven by behavioral cycles and environmental conditions, forecasting methods must capture both periodic patterns and nonlinear interactions between demand and external predictors. Early forecasting studies relied primarily on autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models, which remain widely used due to their interpretability and ability to represent structured seasonal dynamics in electricity demand series [ 4 , 5 ]. Extensions incorporating exogenous predictors (SARIMAX) further improved performance by integrating weather variables into linear time-series formulations [ 14 ]. Despite their effectiveness under stable seasonal conditions, classical statistical models often struggle to capture nonlinear dependencies between electricity demand and meteorological or calendar features. To address these limitations, machine learning approaches have increasingly been adopted for short-term load forecasting. Ensemble learning algorithms such as gradient boosting and random forests have demonstrated strong predictive accuracy for structured electricity demand datasets because they model nonlinear feature interactions without requiring strict parametric assumptions [ 1 , 6 , 7 , 15 ]. Comparative benchmarking studies consistently show that tree-based ensemble methods outperform traditional statistical models when extensive lag features and calendar encodings are available [ 16 , 17 ]. In parallel with ensemble learning approaches, deep learning architectures have gained increasing attention for electricity demand prediction tasks. Recurrent neural networks and long short-term memory (LSTM) models are particularly effective for capturing sequential temporal dependencies in high-frequency demand data [ 8 , 18 ]. More recently, probabilistic neural forecasting frameworks such as DeepAR have enabled distributional prediction of future electricity demand by learning autoregressive representations of temporal structure while simultaneously estimating predictive uncertainty [ 3 , 19 ]. Transformer-based forecasting architectures have also been introduced to address limitations of recurrent models in long-horizon sequence modelling, demonstrating promising performance in multi-step forecasting scenarios [ 20 , 21 ]. However, deep neural forecasting approaches typically require large training datasets and careful hyperparameter tuning, which may limit their effectiveness in operational environments with limited historical observations [ 22 ]. Another important direction in electricity load forecasting research involves incorporating meteorological information into forecasting pipelines. Environmental variables such as temperature, humidity, solar radiation, and wind speed strongly influence electricity demand patterns, particularly in regions with climate-dependent heating and cooling loads [ 9 , 23 ]. Weather-augmented forecasting frameworks have therefore become standard components of modern load prediction systems. Several studies have shown that temperature-driven demand variability can significantly affect forecast accuracy, especially for day-ahead and week-ahead prediction horizons where autoregressive information becomes less informative [ 10 , 24 ]. Recent research further demonstrates that combining meteorological variables with engineered temporal features improves forecasting robustness across seasonal demand regimes [ 25 , 26 ]. Recent methodological advances in forecasting research have also emphasized the importance of evaluation protocol selection when comparing predictive models. Traditional fixed train–test splits frequently produce optimistic performance estimates that do not reflect real-world forecasting deployment scenarios. Rolling-origin walk-forward validation has therefore emerged as a preferred evaluation strategy for time-series forecasting because it preserves temporal ordering and prevents information leakage between training and evaluation datasets [ 11 , 12 , 27 ]. Expanding-window validation schemes further enable realistic simulation of operational forecasting pipelines in which models are updated as new observations become available [ 28 ]. Multi-horizon forecasting introduces additional methodological challenges because predictive performance may vary substantially across prediction intervals depending on the relative importance of autoregressive structure and exogenous predictors. Recursive, direct, and hybrid multi-step forecasting strategies have been proposed to address these challenges, each offering different trade-offs between bias and variance in long-horizon prediction tasks [ 13 , 29 ]. Horizon-specific evaluation has therefore become increasingly important for identifying model suitability across operational forecasting time scales [ 30 ]. In addition to point-forecast accuracy, probabilistic forecasting has emerged as an essential component of modern electricity demand prediction systems. Distributional forecasting methods enable explicit representation of uncertainty, which supports risk-aware decision-making in energy markets and system operation [ 31 ]. Quantile regression, Bayesian forecasting methods, and neural probabilistic models such as DeepAR have been widely applied to generate prediction intervals for electricity demand forecasting tasks [ 3 , 32 ]. However, several studies report systematic under-coverage in probabilistic prediction intervals when uncertainty calibration is not explicitly addressed, highlighting the importance of evaluation metrics such as pinball loss and empirical coverage reliability [ 33 ]. Benchmarking studies comparing statistical, machine learning, and deep learning forecasting approaches increasingly emphasize the importance of reproducible evaluation frameworks and standardized datasets for fair model comparison [ 34 , 35 ]. Nevertheless, relatively few investigations perform statistically validated multi-horizon comparisons within a unified expanding-window walk-forward evaluation framework using identical feature representations and datasets. In particular, the integration of horizon-specific Diebold–Mariano hypothesis testing with rolling-origin validation remains limited in electricity demand forecasting literature. This study addresses that methodological gap by providing statistically grounded comparison of forecasting paradigms across operational prediction horizons within a reproducible benchmarking framework. . 3. Data Sources Electricity Demand Data Electricity demand data were obtained from the ENTSO-E Transparency Platform. The dataset contains hourly electricity load measurements for Ireland covering the full year of 2024. Total observations: 8784 hourly records Reason for Selecting ENTSO-E Earlier attempts to use alternative electricity data APIs resulted in inconsistent or incomplete datasets. The ENTSO-E platform was selected because it provides standardized, publicly accessible electricity demand data with reliable timestamp indexing and consistent coverage. Weather Data Meteorological data were obtained from the NASA POWER Project dataset. The dataset provides global weather observations suitable for renewable energy and electricity demand modeling. Weather data were aligned with electricity demand data using hourly timestamps to ensure temporal consistency. 3.1 Weather Variable Specification Weather variables used in this study include: • Wind onshore generation (proxy for wind conditions) • Wind missingness indicator Temperature and solar radiation are widely recognized as dominant exogenous predictors in short-term electricity demand forecasting. However, consistent hourly temperature observations aligned with the ENTSO-E dataset were not available for the selected study period. As a result, wind-related variables were used as proxy meteorological indicators. The absence of temperature covariates represents an important limitation that may reduce explanatory power at shorter forecasting horizons and should be addressed in future extensions of the proposed framework. 4. Data Preprocessing Several preprocessing steps were applied before model training. Timestamp Alignment Electricity demand and weather datasets were synchronized using hourly timestamps to ensure that both datasets shared identical temporal indices. Missing Value Handling Missing weather observations were handled using median imputation derived from the training dataset. Missing target values created by horizon shifting were removed to prevent information leakage. Feature Scaling Tree-based models such as gradient boosting do not require feature normalization. However, numerical features used in neural network models were scaled to ensure stable training. Weather Feature Aggregation Weather data were extracted from the nearest geographic coordinate representing Ireland's grid region. Hourly meteorological variables were aligned with electricity demand timestamps. 5. Feature Engineering The forecasting dataset includes several feature groups. Calendar Features Calendar features capture periodic demand patterns. Examples include: hour of day day of week month day of year Cyclical Encoding Periodic features were transformed using sine and cosine encoding. Examples: sin(hour) cos(hour) This transformation preserves the cyclical nature of time variables. Lag Features Historical demand values were included as predictive variables. Examples: load_lag_1 load_lag_24 load_lag_48 load_lag_168 Rolling Statistics Rolling statistics capture recent demand trends. Examples: rolling_mean_24 rolling_std_24 Weather Features Weather variables incorporated into the forecasting dataset include wind generation indicators and weather availability flags. 6. Forecasting Models Five forecasting models were evaluated. Seasonal Naïve Predicts future demand using previously observed values from the same seasonal position. SARIMAX A seasonal autoregressive integrated moving average model with exogenous variables. Used as the primary statistical baseline. Gradient Boosting Regressor Tree-based ensemble model trained using quantile regression to produce probabilistic forecasts. Weather-Augmented GBR Extended gradient boosting model incorporating weather covariates. DeepAR Probabilistic neural forecasting model implemented using GluonTS. Expanded Methodology Interpretation Why Gradient Boosting Performs Well Gradient Boosting models perform particularly well for structured tabular forecasting problems because they can capture nonlinear relationships between engineered features and target variables. Unlike linear statistical models, tree-based ensembles can model interactions between lag features, calendar variables, and weather signals. This flexibility allows the model to capture complex patterns in electricity demand. Why DeepAR Performs Poorly Deep neural forecasting models such as DeepAR typically require large datasets to fully exploit their sequence modeling capabilities. In this study, the dataset consists of approximately one year of hourly observations. This dataset size is relatively small for deep learning models, which may lead to underfitting or unstable training behavior. Additionally, DeepAR primarily learns temporal patterns from sequential data rather than engineered tabular features. Because the forecasting dataset includes extensive feature engineering, tree-based models are better suited to exploit the available structured information. Why Weather Improves Longer Horizon Forecasts Weather variables become more important as the prediction horizon increases. Short-term forecasts rely heavily on recent demand observations captured through lag features. However, as the forecasting horizon extends, the predictive value of recent demand decreases. Environmental conditions provide additional information about future electricity demand patterns. For example, temperature and solar radiation are known to influence heating and cooling demand, but were not included in the final modeling pipeline due to availability constraints, while wind conditions affect renewable generation dynamics. Consequently, incorporating weather variables improves forecasting accuracy, particularly for day-ahead and week-ahead predictions. Model Configuration Table This table addresses the concern regarding insufficient methodological specification . Table 1 Model Configuration and Training Settings Model Key Parameters Training Configuration Seasonal Naïve Seasonal lag = 24 hours Deterministic baseline SARIMAX (p,d,q) = (2,1,2), (P,D,Q,s) = (1,1,1,24) Maximum likelihood estimation using training dataset Gradient Boosting Regressor n_estimators = 300, learning_rate = 0.03, max_depth = 4, min_samples_leaf = 10, subsample = 1.0 Quantile regression for probabilistic forecasts Weather-Augmented GBR Same as GBR + weather covariates Trained on augmented feature space DeepAR context_length = 168, prediction_length = horizon dependent epochs = 50, batch_size = 32, learning_rate = 1e-3 Interpretation The SARIMAX configuration was selected after evaluating several parameter combinations based on Akaike Information Criterion (AIC). The Gradient Boosting hyperparameters were selected through validation experiments balancing model complexity and generalization performance. DeepAR training parameters were selected according to recommended configurations from the GluonTS implementation. 7. Experimental Design To ensure robust and realistic model evaluation, an expanding-window walk-forward validation strategy was employed. The dataset was partitioned into sequential folds, where each fold simulates a real-world forecasting scenario: • The model is trained on historical data up to time t • Forecasts are generated for the subsequent fixed horizon window • The training window expands forward for the next fold A total of 17 walk-forward folds were constructed using a step size of 168 hours (one week). This approach ensures that all evaluations are performed on strictly future data, eliminating data leakage and providing a realistic assessment of model performance over time. Forecast accuracy was evaluated separately for each prediction horizon (t + 1, t + 24, and t + 168) within the walk-forward validation framework. Performance metrics were aggregated across folds for each horizon independently, enabling statistically robust comparison of forecasting accuracy across short-, day-ahead-, and week-ahead prediction intervals. This approach prioritizes realistic evaluation of model performance under evolving demand conditions. Within each fold: • Model selection was performed using an internal validation split derived from the training window • Final evaluation was conducted on the fold-specific test window Performance metrics were aggregated across folds using: • Mean performance (expected accuracy) • Standard deviation (performance variability) This evaluation framework provides a statistically robust comparison of forecasting models. 7.1 Implementation Environment All experiments were conducted using Python 3.10 . Statistical time-series models were implemented using the statsmodels library. Machine learning models were implemented using scikit-learn , while the probabilistic DeepAR model was implemented using the GluonTS forecasting framework. Data processing and feature engineering were performed using pandas and NumPy , while visualization was conducted using matplotlib . 7.2 Evaluation Metrics Forecast performance was evaluated using both point and probabilistic metrics. Point Forecast Metrics: • Root Mean Squared Error (RMSE) • Mean Absolute Error (MAE) Probabilistic Metrics: • Pinball loss (quantile loss) • Empirical coverage of 80% prediction intervals Metrics were computed for each walk-forward fold and aggregated using mean and standard deviation to capture both accuracy and variability. 8. Results Interpretation Forecast accuracy declines as prediction horizons increase. The weather-augmented Gradient Boosting model consistently achieves the lowest error across all horizons, demonstrating that environmental signals significantly enhance predictive accuracy. Model Performance Table Table 2 Walk-Forward Model Performance Summary Model Strategy RMSE (Mean ± Std) MAE (Mean ± Std) Seasonal Naïve 316.51 ± — 236.90 ± — SARIMAX 315.89 ± 130.10 259.71 ± 130.10 Gradient Boosting (GBR) 88.44 ± 29.62 66.69 ± 19.85 Interpretation The walk-forward evaluation reveals a substantial performance gap between the Gradient Boosting model and baseline approaches. The GBR model achieves a mean RMSE of 88.44 MW, significantly outperforming both SARIMAX (315.89 MW) and the Seasonal Naïve benchmark (316.51 MW). This represents an improvement of approximately 72% in forecasting error relative to classical baselines. Additionally, SARIMAX exhibits high variability across folds (standard deviation of 130.10 MW), indicating unstable performance under changing temporal conditions. In contrast, the GBR model demonstrates more consistent behavior, with lower variance across evaluation windows. These results highlight the limitations of linear statistical models for structured electricity demand forecasting tasks and confirm the effectiveness of feature-driven ensemble learning approaches in capturing nonlinear demand patterns. Model Performance Analysis The results demonstrate that weather-augmented Gradient Boosting models outperform both classical statistical approaches and deep neural forecasting models. This outcome can be attributed to the structured nature of the forecasting dataset. Electricity demand forecasting in this study relies heavily on engineered tabular features such as lagged demand values, rolling statistics, and calendar variables. Tree-based ensemble models are particularly well suited to this type of feature representation because they can capture nonlinear interactions among predictors. Deep neural architectures such as DeepAR are optimized for learning temporal dependencies directly from sequential data. However, when extensive feature engineering is already performed, tree-based models often outperform neural networks, particularly when the dataset size is limited. Furthermore, the results show that weather variables provide increasing predictive value as the forecasting horizon expands. Environmental conditions influence electricity demand patterns in ways that cannot be fully captured through historical demand alone. Incorporating weather variables therefore improves model performance, particularly for longer forecast horizons such as t + 24 and t + 168. Table 3 Statistical Distribution of Model Error (Walk-Forward Folds) Evaluation Aspect Value (MW) Performance Significance Mean RMSE 88.44 Baseline expected error across the dataset. RMSE Standard Deviation 29.62 Measure of model stability across time windows. Minimum Fold RMSE 56.34 Peak performance (Best Case Scenario). Maximum Fold RMSE 162.08 Maximum observed volatility (Worst Case Scenario). Forecast performance varies substantially across walk-forward folds, with RMSE ranging from 56.34 MW to 162.08 MW. This variability reflects changing demand dynamics across different temporal segments of the dataset, including periods of stable demand and periods of high volatility. While the average performance remains strong, the observed variation highlights that forecasting accuracy is context-dependent and influenced by underlying demand patterns. This reinforces the importance of walk-forward evaluation, as single-split evaluation would fail to capture this temporal variability. Table 4 Forecast performance across horizons Horizon Model RMSE MAE t + 1 GBR 91.26 64.91 t + 1 Weather-GBR 91.38 65.94 t + 1 SARIMAX 282.77 218.18 t + 1 Seasonal Naïve 236.62 165.63 t + 24 GBR 85.11 61.34 t + 24 Weather-GBR 84.98 61.27 t + 24 SARIMAX 281.38 215.15 t + 24 Seasonal Naïve 284.21 t + 168 GBR 84.90 62.39 t + 168 Weather-GBR 85.32 62.11 t + 168 SARIMAX 255.70 196.88 t + 168 Seasonal Naïve 211.53 148.97 Horizon-wise evaluation shows that gradient boosting models substantially outperform statistical and persistence baselines across all forecasting horizons. At the ultra-short horizon (t + 1), plain GBR achieved the lowest RMSE (91.26 MW), while weather-augmented GBR showed comparable performance (91.38 MW). At the day-ahead horizon (t + 24), the weather-augmented model produced the best performance (RMSE 84.98 MW). At the week-ahead horizon (t + 168), both models remained competitive, with only marginal differences between variants. In contrast, SARIMAX and seasonal naïve baselines exhibited substantially higher forecast errors across all horizons. Key findings:- Table 5 Diebold–Mariano statistical comparison of forecast errors across horizons Comparison Result Weather-GBR vs GBR significant only at t + 168 GBR vs SARIMAX significant at all horizons GBR vs Seasonal Naïve significant at all horizons SARIMAX vs Seasonal Naïve weak difference at long horizon Statistical significance was evaluated at the 5% level using two-sided Diebold–Mariano tests under squared-error loss, with fold-level forecast errors treated as independent evaluation samples. Diebold–Mariano testing confirms that Gradient Boosting models significantly outperform SARIMAX and seasonal naïve baselines across all horizons (p < 0.001). Differences between weather-augmented and non-augmented Gradient Boosting models are statistically insignificant at short and day-ahead horizons but become significant at the week-ahead horizon, indicating increasing importance of meteorological information for longer-range prediction. 9. Feature Importance Analysis Because the weather-augmented Gradient Boosting model achieved the best forecasting performance, feature importance analysis was conducted to understand the variables most responsible for predictive accuracy. Tree-based ensemble models provide natural measures of feature importance based on the contribution of each predictor to reducing prediction error during model training. Feature importance analysis indicates that the most influential predictors include: load_lag_24 (previous day demand) load_lag_168 (previous week demand) hour_of_day wind generation proxy variable Lagged demand variables dominate short-term forecasts, reflecting strong temporal autocorrelation in electricity consumption patterns. However, weather variables contribute more significantly to longer-horizon forecasts, particularly for the t + 24 and t + 168 horizons where historical demand alone becomes less informative. This analysis confirms that both temporal features and environmental signals play important roles in electricity demand forecasting. 10. Discussion The experimental results demonstrate that feature-driven Gradient Boosting models consistently outperform classical statistical baselines and probabilistic neural forecasting architectures across all evaluated prediction horizons. This performance advantage can be attributed primarily to the structured nature of the forecasting dataset, which combines lagged demand variables, rolling statistics, calendar encodings, and proxy meteorological indicators within a tabular feature representation. Tree-based ensemble models are well suited to exploiting nonlinear interactions among such predictors without requiring strong parametric assumptions regarding temporal structure. In contrast, SARIMAX models rely on linear dependence structures and therefore exhibit reduced flexibility when modeling nonlinear demand dynamics influenced by calendar effects and environmental variability. The observed instability of SARIMAX across walk-forward folds, reflected by high error variance, indicates limited robustness under evolving temporal demand regimes. These findings are consistent with prior benchmarking studies reporting that ensemble learning approaches outperform classical time-series models when extensive engineered features are available for electricity demand prediction tasks. The probabilistic DeepAR model did not achieve performance comparable to Gradient Boosting variants in this study. Deep neural forecasting architectures typically require larger training corpora to learn stable sequential representations of temporal structure. Because the dataset used in this work consists of approximately one year of hourly observations from a single regional demand series, the available training data are insufficient for fully exploiting the representational capacity of recurrent probabilistic neural networks. Under limited-data conditions, feature-driven ensemble models therefore provide a more efficient forecasting solution. Horizon-specific evaluation further reveals that meteorological variables contribute increasing predictive value as the forecasting horizon extends. At ultra-short prediction intervals, demand persistence captured through autoregressive lag features dominates predictive performance. However, as the forecasting horizon increases to day-ahead and week-ahead intervals, the predictive influence of recent observations weakens and exogenous environmental signals become more informative. The Diebold–Mariano statistical comparison confirms that weather augmentation produces significant improvements primarily at the week-ahead horizon, supporting the interpretation that environmental covariates provide complementary predictive structure beyond autoregressive information at longer forecast intervals. Prediction interval evaluation indicates moderate under-calibration relative to the nominal 80% coverage level, with empirical coverage of 0.759. This result suggests that the probabilistic forecasting framework underestimates uncertainty in periods of elevated demand variability. Such behavior is commonly observed in quantile-based forecasting models when conditional variance structure is not fully captured by available predictors. Although the generated prediction intervals successfully track general demand variability during stable periods, improved calibration techniques such as conformal prediction or post-hoc interval adjustment may further enhance probabilistic reliability in operational deployment settings. Walk-forward evaluation additionally highlights that forecasting accuracy varies across temporal segments of the dataset. Higher prediction errors occur during periods characterized by rapid demand transitions and peak consumption intervals, where lag-based predictors provide weaker guidance for future demand trajectories. Nevertheless, Gradient Boosting variants maintain stable performance rankings across folds and prediction horizons, indicating robustness to non-stationary consumption behavior commonly observed in real-world electricity demand series. This stability supports the suitability of ensemble learning approaches for operational forecasting environments requiring consistent predictive performance under evolving demand conditions. Overall, the results demonstrate that model–data alignment plays a critical role in electricity demand forecasting performance. When forecasting pipelines incorporate structured temporal features and operate under limited-data conditions, ensemble learning approaches provide a practical and computationally efficient alternative to deep probabilistic forecasting architectures while maintaining strong predictive accuracy across multiple operational horizons. 11. Forecast Uncertainty Analysis Interpretation Prediction intervals generated by the probabilistic models exhibit under-coverage relative to the nominal 80% confidence level. This indicates that the predictive uncertainty intervals are narrower than required for well-calibrated probabilistic forecasts. 12. Forecast Visualization Interpretation The median forecast tracks the general demand pattern closely and successfully captures daily demand cycles. Forecast uncertainty increases during peak demand periods, reflected by wider prediction intervals. 13. Forecasting Pipeline Architecture Explanation : The forecasting system combines multiple datasets, transforms them into structured features, and evaluates multiple forecasting models within a reproducible machine learning workflow. 14. Study Limitations Despite the promising results, several limitations should be acknowledged. First, the dataset used in this study covers only a single year of hourly observations. A longer historical dataset would likely improve model training, particularly for deep learning models such as DeepAR that require large volumes of sequential data. Second, the set of meteorological variables included in the forecasting pipeline is limited. Additional weather features such as humidity, precipitation, and atmospheric pressure may provide further predictive information. Future work will incorporate multi-year datasets to validate temporal generalization of the proposed framework Third, the forecasting experiments focus on a single geographic region (Ireland). Electricity demand patterns vary across different climates and grid systems, so further research is needed to evaluate whether the findings generalize to other regions. Finally, probabilistic forecast calibration remains an open challenge. Although prediction intervals were generated using quantile regression and probabilistic modeling, empirical coverage remained below the desired level. Future research should explore calibration techniques to improve uncertainty estimation. Future work will evaluate multi-year datasets to assess temporal transferability across seasonal demand regimes. 15. Key Challenges Several challenges were encountered during development: aligning multiple datasets with different temporal resolutions handling missing weather observations achieving reliable probabilistic forecast calibration configuring deep learning models for limited dataset sizes 16. Future Work Future research may explore: transformer-based forecasting models improved probabilistic calibration techniques larger historical datasets multi-region electricity forecasting Future work may also evaluate horizon-specific model calibration using conformal prediction methods. 17. Conclusion This study developed a weather-augmented electricity demand forecasting framework capable of predicting load across multiple horizons. Experimental results demonstrate that gradient boosting models achieve the highest predictive accuracy among the evaluated methods, while weather augmentation provides statistically significant improvements at longer prediction horizons. The findings emphasize the importance of environmental variables in electricity demand forecasting and highlight the effectiveness of ensemble machine learning methods for structured tabular time-series forecasting problems. The results suggest that feature-driven ensemble models can outperform both classical statistical methods and deep probabilistic models under limited data regimes, highlighting the importance of model–data alignment in time-series forecasting tasks.The study contributes a statistically validated evaluation framework for multi-horizon electricity load forecasting that enables consistent comparison between statistical, machine learning, and probabilistic forecasting paradigms under realistic operational conditions. Declarations Funding This research received no external funding. Author Contributions MHS conceived the study, designed the methodology, implemented the forecasting models, conducted the experiments, analyzed the results, and prepared the manuscript. Competing Interests MHS declares no competing interests. Data Availability The datasets used in this study are publicly available from the ENTSO-E Transparency Platform and NASA POWER. The code and processed data supporting this study are available at: https://github.com/MeherabHS/Statistically-Validated-Multi-Horizon-Electricity-Load-Forecasting-with-Weather-Augmented-ML Code Availability The forecasting pipeline, preprocessing scripts, and evaluation framework developed for this study are publicly available in the GitHub repository listed above. Ethics Approval This study does not involve human participants or animals and therefore does not require ethical approval. Consent to Participate Not applicable. 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Kong W, Dong ZY, Jia Y, Hill DJ, Xu Y, Zhang Y. Short-term residential load forecasting using LSTM. IEEE Trans Smart Grid. 2017;10(1):841–51. Lim B, Arık SÖ, Loeff N, Pfister T. Temporal fusion transformers for multi-horizon forecasting. Int J Forecast. 2021;37(4):1748–64. Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H. Informer: Transformer for long sequence forecasting. AAAI. 2021;35(12):11106–15. Benth FE, Šaltytė-Benth J. The effect of temperature on electricity demand. Energy Econ. 2013;37:1–9. Chen H, Canizares CA, Singh A. ANN-based short-term load forecasting. IEEE Trans Smart Grid. 2017;8(1):130–40. Dordonnat V, Koopman SJ, Ooms M, Dessertaine A, Collet J. Electricity load forecasting with weather integration. Int J Forecast. 2016;32(2):532–46. Tashman LJ. Out-of-sample tests of forecasting accuracy. Int J Forecast. 2000;16(4):437–50. Bergmeir C, Benítez JM. Cross-validation for time series evaluation. Inf Sci. 2012;191:192–213. Hyndman RJ. Rolling forecasts framework. Monash University; 2014. Hewamalage H, Bergmeir C, Bandara K. Forecast evaluation for data scientists: Common pitfalls and best practices. Data Min Knowl Discov. 2023;37:788–832. Ben Taieb S, Atiya AF. Bias–variance for multi-step forecasting. IEEE Trans Neural Netw Learn Syst. 2016;27(1):62–76. Chevillon G. Direct multi-step forecasting. J Econ Surv. 2007;21(4):746–85. Taieb SB, Bontempi G. Recursive vs direct forecasting. Pattern Recognit Lett. 2012;33(10):1367–77. Gneiting T, Katzfuss M. Probabilistic forecasting. Annu Rev Stat Appl. 2014;1:125–51. Koenker R, Bassett G. Regression quantiles. Econometrica. 1978;46(1):33–50. Taylor JW. Density forecasting for electricity demand. Int J Forecast. 2015;31(3):806–17. Makridakis S, Spiliotis E, Assimakopoulos V. M4 competition results. Int J Forecast. 2020;36(1):54–74. Makridakis S, Spiliotis E, Assimakopoulos V. M5 competition results. Int J Forecast. 2022;38(4):1346–64. Weron R. Electricity price forecasting: A review. Int J Forecast. 2014;30(4):1030–81. Nowotarski J, Weron R. Recent advances in electricity price forecasting. Int J Forecast. 2018;34(4):637–59. Lago J, De Ridder F, De Schutter B. Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark. Appl Energy. 2021;293:116983. Cerqueira V, Torgo L, Mozetič I. Evaluating time series forecasting models: An empirical study. Mach Learn. 2020;109:1997–2028. Hyndman RJ, Koehler AB. Measures of forecast accuracy. Int J Forecast. 2006;22(4):679–88. Ziel F. Forecasting electricity spot prices using LASSO regression. Energy Econ. 2017;65:428–34. Angelopoulos AN, Bates S. Conformal prediction review. Found Trends Mach Learn. 2023;16(4):494–591. Lago J, Marcjasz G, De Schutter B, Weron R. Forecasting electricity demand: From classical methods to modern machine learning. (Use as contextual citation if needed in discussion sections). Ziel F, Weron R. Forecasting electricity prices using machine learning: Evidence from high-dimensional structures. Energy Econ. 2018;70:396–420. Nowotarski J, Weron R. Recent advances in electricity price forecasting: A review. Int J Forecast. 2018;34(4):637–59. Tashman LJ. Out-of-sample tests of forecasting accuracy: An analysis and review. Int J Forecast. 2000;16(4):437–50. Salinas D, Flunkert V, Gasthaus J, Januschowski T. DeepAR: Probabilistic forecasting with autoregressive recurrent networks. Int J Forecast. 2020;36(3):1181–91. Fan S, Hyndman RJ. Short-term load forecasting based on a semi-parametric additive model. IEEE Trans Power Syst. 2012;27(1):134–41. Dordonnat V, Koopman SJ, Ooms M, Dessertaine A, Collet J. An hourly periodic state space model for electricity load forecasting. Int J Forecast. 2016;32(2):532–46. Hewamalage H, Bergmeir C, Bandara K. Forecast evaluation for data scientists: Common pitfalls and best practices. Data Min Knowl Discov. 2023;37:788–832. 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Introduction","content":"\u003cp\u003eElectricity demand forecasting is a fundamental component of modern power-system operation, supporting generation scheduling, reserve allocation, transmission planning, and energy market participation. Accurate short-term forecasts enable transmission system operators to maintain grid reliability while minimizing operational costs under dynamically evolving consumption patterns. Because electricity demand varies across multiple temporal scales, forecasting models must provide reliable predictions over short-term, day-ahead, and week-ahead horizons to support both operational and strategic decision-making.\u003c/p\u003e \u003cp\u003eElectricity consumption exhibits strong periodic structure driven by human activity cycles and environmental conditions. Daily demand patterns reflect residential usage behavior and industrial operating schedules, while weekly and seasonal variations correspond to broader economic activity and climatic influences. In addition to these temporal effects, meteorological variables such as temperature, wind conditions, and solar radiation contribute substantially to demand variability, particularly at longer forecasting horizons where the predictive value of recent observations decreases.\u003c/p\u003e \u003cp\u003eTraditional short-term load forecasting methods have relied primarily on statistical time-series models such as autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA), which effectively capture linear temporal dependencies and recurring seasonal patterns in electricity demand data. However, these approaches are often limited in their ability to represent nonlinear relationships between demand and exogenous predictors. To address this limitation, machine learning models\u0026mdash;particularly tree-based ensemble methods\u0026mdash;have increasingly been applied to electricity demand prediction tasks, demonstrating strong performance when combined with engineered lag features and calendar encodings. More recently, deep learning architectures have enabled probabilistic forecasting of electricity demand by modeling sequential dependencies directly from historical observations and producing predictive uncertainty estimates.\u003c/p\u003e \u003cp\u003eDespite these methodological advances, systematic comparison across statistical, machine learning, and probabilistic deep learning approaches remains limited for weather-augmented multi-horizon electricity demand forecasting under realistic operational evaluation settings. Many existing studies evaluate individual model families using fixed train\u0026ndash;test splits or single-horizon prediction tasks, which restricts interpretability of comparative performance across forecasting paradigms. In particular, the contribution of meteorological covariates across multiple prediction horizons has not been extensively examined within a unified expanding-window walk-forward validation framework supported by formal statistical significance testing. This study addresses that gap by developing a reproducible multi-horizon benchmarking framework for electricity demand forecasting that enables statistically grounded comparison of forecasting paradigms under realistic deployment conditions. Accurate multi-horizon electricity demand forecasting supports renewable integration planning, reserve allocation strategies, and short-term grid balancing in systems with increasing variability from weather-dependent generation sources. The proposed benchmarking framework therefore contributes to operational decision-support tools required for reliable low-carbon energy system management.\u003c/p\u003e \u003cp\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eResearch Gap\u003c/b\u003e \u003c/p\u003e \u003cp\u003eAlthough electricity load forecasting has been extensively studied using statistical, machine learning, and deep learning approaches, existing research remains fragmented across forecasting paradigms and evaluation strategies. Many prior studies evaluate models within a single methodological family, which limits interpretability of comparative performance across alternative forecasting frameworks under consistent experimental conditions [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. In addition, a substantial portion of the literature relies on fixed train\u0026ndash;test splits or single-horizon prediction tasks that do not accurately represent operational forecasting environments where models must generate rolling predictions across multiple temporal horizons [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRecent advances in probabilistic forecasting have improved uncertainty representation in electricity demand prediction; however, comparative evaluation between deterministic statistical models, feature-driven ensemble learners, and probabilistic neural forecasting architectures remains limited within unified benchmarking pipelines that incorporate expanding-window walk-forward validation [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. As a result, the relative strengths of these model classes across short-, day-ahead-, and week-ahead forecasting horizons remain insufficiently characterized in realistic deployment scenarios.\u003c/p\u003e \u003cp\u003eFurthermore, while meteorological variables are widely recognized as important predictors of electricity demand variability, their horizon-specific contribution to forecasting accuracy has not been systematically quantified using formal statistical hypothesis testing across multiple forecasting paradigms [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Existing weather-augmented forecasting studies frequently evaluate temperature-driven demand effects but provide limited evidence regarding the comparative impact of alternative environmental predictors under constrained regional datasets and engineered feature representations [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAnother limitation in current literature concerns the evaluation of forecasting models under limited-data operational settings. Many deep learning forecasting frameworks demonstrate strong performance when trained on large collections of related time series; however, their effectiveness relative to tree-based ensemble methods and classical statistical models remains insufficiently examined for single-region electricity demand datasets with restricted temporal coverage [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo address these limitations, this study develops a reproducible multi-horizon benchmarking framework that integrates expanding-window walk-forward validation with horizon-specific Diebold\u0026ndash;Mariano statistical testing to support rigorous comparison between statistical, machine learning, and probabilistic neural forecasting approaches. The proposed framework further quantifies the contribution of meteorological covariates across prediction horizons, providing operational insight into model selection for electricity demand forecasting under limited-data deployment conditions.\u003c/p\u003e \u003cp\u003e \u003cb\u003eResearch Objectives\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThis study addresses the following research questions:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eHow does forecasting performance vary across statistical, machine learning, and probabilistic neural forecasting models under an expanding-window walk-forward evaluation framework?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eHow does the contribution of meteorological covariates change across short-term (t\u0026thinsp;+\u0026thinsp;1), day-ahead (t\u0026thinsp;+\u0026thinsp;24), and week-ahead (t\u0026thinsp;+\u0026thinsp;168) prediction horizons?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo what extent do Gradient Boosting ensemble models improve forecasting accuracy relative to classical SARIMAX and persistence baselines under limited-data operational conditions?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eHow well do probabilistic forecasting methods capture predictive uncertainty in multi-horizon electricity demand prediction?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eContributions of This Study\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe main contributions of this study are summarized as follows:\u003c/p\u003e \u003cp\u003e\u0026bull; Development of a reproducible multi-horizon benchmarking framework for short-term electricity load forecasting\u003c/p\u003e\n\u003cp\u003e\u0026bull; Integration of expanding-window walk-forward validation for realistic operational evaluation\u003c/p\u003e\n\u003cp\u003e\u0026bull; Horizon-wise statistical comparison of forecasting models using Diebold\u0026ndash;Mariano hypothesis testing\u003c/p\u003e\n\u003cp\u003e\u0026bull; Comparative assessment across statistical, machine learning, and probabilistic neural forecasting paradigms under a unified experimental setup\u003c/p\u003e\n\u003cp\u003e\u0026bull; Empirical analysis of meteorological covariate effects across short-, day-ahead-, and week-ahead prediction horizons\u003c/p\u003e\n\u003cp\u003e\u0026bull; Practical guidance for selecting forecasting models under limited-data operational environments\u003c/p\u003e\n"},{"header":"2. Literature Review","content":"\u003cp\u003eShort-term electricity load forecasting plays a central role in modern power-system operation by supporting generation scheduling, reserve allocation, transmission planning, and market participation. Because electricity demand exhibits strong temporal structure driven by behavioral cycles and environmental conditions, forecasting methods must capture both periodic patterns and nonlinear interactions between demand and external predictors. Early forecasting studies relied primarily on autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models, which remain widely used due to their interpretability and ability to represent structured seasonal dynamics in electricity demand series [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Extensions incorporating exogenous predictors (SARIMAX) further improved performance by integrating weather variables into linear time-series formulations [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite their effectiveness under stable seasonal conditions, classical statistical models often struggle to capture nonlinear dependencies between electricity demand and meteorological or calendar features. To address these limitations, machine learning approaches have increasingly been adopted for short-term load forecasting. Ensemble learning algorithms such as gradient boosting and random forests have demonstrated strong predictive accuracy for structured electricity demand datasets because they model nonlinear feature interactions without requiring strict parametric assumptions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Comparative benchmarking studies consistently show that tree-based ensemble methods outperform traditional statistical models when extensive lag features and calendar encodings are available [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn parallel with ensemble learning approaches, deep learning architectures have gained increasing attention for electricity demand prediction tasks. Recurrent neural networks and long short-term memory (LSTM) models are particularly effective for capturing sequential temporal dependencies in high-frequency demand data [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. More recently, probabilistic neural forecasting frameworks such as DeepAR have enabled distributional prediction of future electricity demand by learning autoregressive representations of temporal structure while simultaneously estimating predictive uncertainty [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Transformer-based forecasting architectures have also been introduced to address limitations of recurrent models in long-horizon sequence modelling, demonstrating promising performance in multi-step forecasting scenarios [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. However, deep neural forecasting approaches typically require large training datasets and careful hyperparameter tuning, which may limit their effectiveness in operational environments with limited historical observations [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAnother important direction in electricity load forecasting research involves incorporating meteorological information into forecasting pipelines. Environmental variables such as temperature, humidity, solar radiation, and wind speed strongly influence electricity demand patterns, particularly in regions with climate-dependent heating and cooling loads [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Weather-augmented forecasting frameworks have therefore become standard components of modern load prediction systems. Several studies have shown that temperature-driven demand variability can significantly affect forecast accuracy, especially for day-ahead and week-ahead prediction horizons where autoregressive information becomes less informative [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Recent research further demonstrates that combining meteorological variables with engineered temporal features improves forecasting robustness across seasonal demand regimes [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRecent methodological advances in forecasting research have also emphasized the importance of evaluation protocol selection when comparing predictive models. Traditional fixed train\u0026ndash;test splits frequently produce optimistic performance estimates that do not reflect real-world forecasting deployment scenarios. Rolling-origin walk-forward validation has therefore emerged as a preferred evaluation strategy for time-series forecasting because it preserves temporal ordering and prevents information leakage between training and evaluation datasets [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Expanding-window validation schemes further enable realistic simulation of operational forecasting pipelines in which models are updated as new observations become available [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMulti-horizon forecasting introduces additional methodological challenges because predictive performance may vary substantially across prediction intervals depending on the relative importance of autoregressive structure and exogenous predictors. Recursive, direct, and hybrid multi-step forecasting strategies have been proposed to address these challenges, each offering different trade-offs between bias and variance in long-horizon prediction tasks [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Horizon-specific evaluation has therefore become increasingly important for identifying model suitability across operational forecasting time scales [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn addition to point-forecast accuracy, probabilistic forecasting has emerged as an essential component of modern electricity demand prediction systems. Distributional forecasting methods enable explicit representation of uncertainty, which supports risk-aware decision-making in energy markets and system operation [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Quantile regression, Bayesian forecasting methods, and neural probabilistic models such as DeepAR have been widely applied to generate prediction intervals for electricity demand forecasting tasks [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. However, several studies report systematic under-coverage in probabilistic prediction intervals when uncertainty calibration is not explicitly addressed, highlighting the importance of evaluation metrics such as pinball loss and empirical coverage reliability [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBenchmarking studies comparing statistical, machine learning, and deep learning forecasting approaches increasingly emphasize the importance of reproducible evaluation frameworks and standardized datasets for fair model comparison [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Nevertheless, relatively few investigations perform statistically validated multi-horizon comparisons within a unified expanding-window walk-forward evaluation framework using identical feature representations and datasets. In particular, the integration of horizon-specific Diebold\u0026ndash;Mariano hypothesis testing with rolling-origin validation remains limited in electricity demand forecasting literature. This study addresses that methodological gap by providing statistically grounded comparison of forecasting paradigms across operational prediction horizons within a reproducible benchmarking framework.\u003c/p\u003e \u003cp\u003e.\u003c/p\u003e"},{"header":"3. Data Sources","content":"\u003cp\u003e\u003cstrong\u003eElectricity Demand Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eElectricity demand data were obtained from the ENTSO-E Transparency Platform. The dataset contains hourly electricity load measurements for Ireland covering the full year of 2024.\u003c/p\u003e\n\u003cp\u003eTotal observations: \u003cstrong\u003e8784 hourly records\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eReason for Selecting ENTSO-E\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEarlier attempts to use alternative electricity data APIs resulted in inconsistent or incomplete datasets. The \u003cstrong\u003eENTSO-E platform\u003c/strong\u003e was selected because it provides standardized, publicly accessible electricity demand data with reliable timestamp indexing and consistent coverage.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWeather Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMeteorological data were obtained from the \u003cstrong\u003eNASA POWER Project\u003c/strong\u003e dataset. The dataset provides global weather observations suitable for renewable energy and electricity demand modeling.\u003c/p\u003e\n\u003cp\u003eWeather data were aligned with electricity demand data using hourly timestamps to ensure temporal consistency.\u003c/p\u003e\n\u003cdiv id=\"Sec4\"\u003e\n \u003ch2\u003e3.1 Weather Variable Specification\u003c/h2\u003e\n \u003cp\u003eWeather variables used in this study include:\u003c/p\u003e\n \u003cp\u003e• Wind onshore generation (proxy for wind conditions)\u003c/p\u003e\n \u003cp\u003e• Wind missingness indicator\u003c/p\u003e\n \u003cp\u003eTemperature and solar radiation are widely recognized as dominant exogenous predictors in short-term electricity demand forecasting. However, consistent hourly temperature observations aligned with the ENTSO-E dataset were not available for the selected study period. As a result, wind-related variables were used as proxy meteorological indicators. The absence of temperature covariates represents an important limitation that may reduce explanatory power at shorter forecasting horizons and should be addressed in future extensions of the proposed framework.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Data Preprocessing","content":"\u003cp\u003eSeveral preprocessing steps were applied before model training.\u003c/p\u003e \u003cp\u003e \u003cb\u003eTimestamp Alignment\u003c/b\u003e \u003c/p\u003e \u003cp\u003eElectricity demand and weather datasets were synchronized using hourly timestamps to ensure that both datasets shared identical temporal indices.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMissing Value Handling\u003c/b\u003e \u003c/p\u003e \u003cp\u003eMissing weather observations were handled using median imputation derived from the training dataset. Missing target values created by horizon shifting were removed to prevent information leakage.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFeature Scaling\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTree-based models such as gradient boosting do not require feature normalization. However, numerical features used in neural network models were scaled to ensure stable training.\u003c/p\u003e \u003cp\u003e \u003cb\u003eWeather Feature Aggregation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eWeather data were extracted from the nearest geographic coordinate representing Ireland's grid region. Hourly meteorological variables were aligned with electricity demand timestamps.\u003c/p\u003e"},{"header":"5. Feature Engineering","content":"\u003cp\u003eThe forecasting dataset includes several feature groups.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCalendar Features\u003c/b\u003e \u003c/p\u003e \u003cp\u003eCalendar features capture periodic demand patterns.\u003c/p\u003e \u003cp\u003eExamples include:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ehour of day\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eday of week\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003emonth\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eday of year\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eCyclical Encoding\u003c/b\u003e \u003c/p\u003e \u003cp\u003ePeriodic features were transformed using sine and cosine encoding.\u003c/p\u003e \u003cp\u003eExamples:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003esin(hour)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ecos(hour)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis transformation preserves the cyclical nature of time variables.\u003c/p\u003e \u003cp\u003e \u003cb\u003eLag Features\u003c/b\u003e \u003c/p\u003e \u003cp\u003eHistorical demand values were included as predictive variables.\u003c/p\u003e \u003cp\u003eExamples:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eload_lag_1\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eload_lag_24\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eload_lag_48\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eload_lag_168\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eRolling Statistics\u003c/b\u003e \u003c/p\u003e \u003cp\u003eRolling statistics capture recent demand trends.\u003c/p\u003e \u003cp\u003eExamples:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003erolling_mean_24\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003erolling_std_24\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eWeather Features\u003c/b\u003e \u003c/p\u003e \u003cp\u003eWeather variables incorporated into the forecasting dataset include wind generation indicators and weather availability flags.\u003c/p\u003e"},{"header":"6. Forecasting Models","content":"\u003cp\u003eFive forecasting models were evaluated.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSeasonal Na\u0026iuml;ve\u003c/b\u003e \u003c/p\u003e \u003cp\u003ePredicts future demand using previously observed values from the same seasonal position.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSARIMAX\u003c/b\u003e \u003c/p\u003e \u003cp\u003eA seasonal autoregressive integrated moving average model with exogenous variables.\u003c/p\u003e \u003cp\u003eUsed as the primary statistical baseline.\u003c/p\u003e \u003cp\u003e \u003cb\u003eGradient Boosting Regressor\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTree-based ensemble model trained using quantile regression to produce probabilistic forecasts.\u003c/p\u003e \u003cp\u003e \u003cb\u003eWeather-Augmented GBR\u003c/b\u003e \u003c/p\u003e \u003cp\u003eExtended gradient boosting model incorporating weather covariates.\u003c/p\u003e \u003cp\u003e \u003cb\u003eDeepAR\u003c/b\u003e \u003c/p\u003e \u003cp\u003eProbabilistic neural forecasting model implemented using GluonTS.\u003c/p\u003e \u003cp\u003e \u003cb\u003eExpanded Methodology Interpretation\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eWhy Gradient Boosting Performs Well\u003c/b\u003e \u003c/p\u003e \u003cp\u003eGradient Boosting models perform particularly well for structured tabular forecasting problems because they can capture nonlinear relationships between engineered features and target variables. Unlike linear statistical models, tree-based ensembles can model interactions between lag features, calendar variables, and weather signals. This flexibility allows the model to capture complex patterns in electricity demand.\u003c/p\u003e \u003cp\u003e \u003cb\u003eWhy DeepAR Performs Poorly\u003c/b\u003e \u003c/p\u003e \u003cp\u003eDeep neural forecasting models such as DeepAR typically require large datasets to fully exploit their sequence modeling capabilities. In this study, the dataset consists of approximately one year of hourly observations. This dataset size is relatively small for deep learning models, which may lead to underfitting or unstable training behavior.\u003c/p\u003e \u003cp\u003eAdditionally, DeepAR primarily learns temporal patterns from sequential data rather than engineered tabular features. Because the forecasting dataset includes extensive feature engineering, tree-based models are better suited to exploit the available structured information.\u003c/p\u003e \u003cp\u003e \u003cb\u003eWhy Weather Improves Longer Horizon Forecasts\u003c/b\u003e \u003c/p\u003e \u003cp\u003eWeather variables become more important as the prediction horizon increases. Short-term forecasts rely heavily on recent demand observations captured through lag features. However, as the forecasting horizon extends, the predictive value of recent demand decreases.\u003c/p\u003e \u003cp\u003eEnvironmental conditions provide additional information about future electricity demand patterns. For example, temperature and solar radiation are known to influence heating and cooling demand, but were not included in the final modeling pipeline due to availability constraints, while wind conditions affect renewable generation dynamics. Consequently, incorporating weather variables improves forecasting accuracy, particularly for day-ahead and week-ahead predictions.\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel Configuration Table\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThis table addresses the concern regarding \u003cb\u003einsufficient methodological specification\u003c/b\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel Configuration and Training Settings\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKey Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTraining Configuration\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSeasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeasonal lag\u0026thinsp;=\u0026thinsp;24 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDeterministic baseline\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSARIMAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(p,d,q) = (2,1,2), (P,D,Q,s) = (1,1,1,24)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaximum likelihood estimation using training dataset\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGradient Boosting Regressor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003en_estimators\u0026thinsp;=\u0026thinsp;300, learning_rate\u0026thinsp;=\u0026thinsp;0.03, max_depth\u0026thinsp;=\u0026thinsp;4, min_samples_leaf\u0026thinsp;=\u0026thinsp;10, subsample\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eQuantile regression for probabilistic forecasts\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeather-Augmented GBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSame as GBR\u0026thinsp;+\u0026thinsp;weather covariates\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTrained on augmented feature space\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDeepAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtext_length\u0026thinsp;=\u0026thinsp;168, prediction_length\u0026thinsp;=\u0026thinsp;horizon dependent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eepochs\u0026thinsp;=\u0026thinsp;50, batch_size\u0026thinsp;=\u0026thinsp;32, learning_rate\u0026thinsp;=\u0026thinsp;1e-3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003cb\u003eInterpretation\u003c/b\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe SARIMAX configuration was selected after evaluating several parameter combinations based on Akaike Information Criterion (AIC). The Gradient Boosting hyperparameters were selected through validation experiments balancing model complexity and generalization performance. DeepAR training parameters were selected according to recommended configurations from the GluonTS implementation.\u003c/p\u003e"},{"header":"7. Experimental Design","content":"\u003cp\u003eTo ensure robust and realistic model evaluation, an expanding-window walk-forward validation strategy was employed.\u003c/p\u003e\n\u003cp\u003eThe dataset was partitioned into sequential folds, where each fold simulates a real-world forecasting scenario:\u003c/p\u003e\n\u003cp\u003e\u0026bull; The model is trained on historical data up to time t\u003c/p\u003e\n\u003cp\u003e\u0026bull; Forecasts are generated for the subsequent fixed horizon window\u003c/p\u003e\n\u003cp\u003e\u0026bull; The training window expands forward for the next fold\u003c/p\u003e\n\u003cp\u003eA total of 17 walk-forward folds were constructed using a step size of 168 hours (one week).\u003c/p\u003e\n\u003cp\u003eThis approach ensures that all evaluations are performed on strictly future data, eliminating data leakage and providing a realistic assessment of model performance over time.\u003c/p\u003e\n\u003cp\u003eForecast accuracy was evaluated separately for each prediction horizon (t\u0026thinsp;+\u0026thinsp;1, t\u0026thinsp;+\u0026thinsp;24, and t\u0026thinsp;+\u0026thinsp;168) within the walk-forward validation framework. Performance metrics were aggregated across folds for each horizon independently, enabling statistically robust comparison of forecasting accuracy across short-, day-ahead-, and week-ahead prediction intervals.\u003c/p\u003e\n\u003cp\u003eThis approach prioritizes realistic evaluation of model performance under evolving demand conditions.\u003c/p\u003e\n\u003cp\u003eWithin each fold:\u003c/p\u003e\n\u003cp\u003e\u0026bull; Model selection was performed using an internal validation split derived from the training window\u003c/p\u003e\n\u003cp\u003e\u0026bull; Final evaluation was conducted on the fold-specific test window\u003c/p\u003e\n\u003cp\u003ePerformance metrics were aggregated across folds using:\u003c/p\u003e\n\u003cp\u003e\u0026bull; Mean performance (expected accuracy)\u003c/p\u003e\n\u003cp\u003e\u0026bull; Standard deviation (performance variability)\u003c/p\u003e\n\u003cp\u003eThis evaluation framework provides a statistically robust comparison of forecasting models.\u003c/p\u003e\n\u003cdiv id=\"Sec9\"\u003e\n \u003ch2\u003e7.1 Implementation Environment\u003c/h2\u003e\n \u003cp\u003eAll experiments were conducted using \u003cstrong\u003ePython 3.10\u003c/strong\u003e. Statistical time-series models were implemented using the \u003cstrong\u003estatsmodels\u003c/strong\u003e library. Machine learning models were implemented using \u003cstrong\u003escikit-learn\u003c/strong\u003e, while the probabilistic \u003cstrong\u003eDeepAR\u003c/strong\u003e model was implemented using the \u003cstrong\u003eGluonTS\u003c/strong\u003e forecasting framework.\u003c/p\u003e\n \u003cp\u003eData processing and feature engineering were performed using \u003cstrong\u003epandas\u003c/strong\u003e and \u003cstrong\u003eNumPy\u003c/strong\u003e, while visualization was conducted using \u003cstrong\u003ematplotlib\u003c/strong\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003e7.2 Evaluation Metrics\u003c/h2\u003e\n \u003cp\u003eForecast performance was evaluated using both point and probabilistic metrics.\u003c/p\u003e\n \u003cp\u003ePoint Forecast Metrics:\u003c/p\u003e\u0026bull; Root Mean Squared Error (RMSE)\u003cp\u003e\u0026bull; Mean Absolute Error (MAE)\u003c/p\u003eProbabilistic Metrics:\u003cbr\u003e\n \u003cp\u003e\u0026bull; Pinball loss (quantile loss)\u003c/p\u003e\n \u003cp\u003e\u0026bull; Empirical coverage of 80% prediction intervals\u003c/p\u003eMetrics were computed for each walk-forward fold and aggregated using mean and standard deviation to capture both accuracy and variability.\n\u003c/div\u003e"},{"header":"8. Results","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eInterpretation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eForecast accuracy declines as prediction horizons increase. The weather-augmented Gradient Boosting model consistently achieves the lowest error across all horizons, demonstrating that environmental signals significantly enhance predictive accuracy.\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel Performance Table\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWalk-Forward Model Performance Summary\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel Strategy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRMSE (Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;Std)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE (Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;Std)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSeasonal Na\u0026iuml;ve\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e316.51 \u0026plusmn; \u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e236.90 \u0026plusmn; \u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSARIMAX\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e315.89\u0026thinsp;\u0026plusmn;\u0026thinsp;130.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e259.71\u0026thinsp;\u0026plusmn;\u0026thinsp;130.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGradient Boosting (GBR)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e88.44\u0026thinsp;\u0026plusmn;\u0026thinsp;29.62\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e66.69\u0026thinsp;\u0026plusmn;\u0026thinsp;19.85\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eInterpretation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe walk-forward evaluation reveals a substantial performance gap between the Gradient Boosting model and baseline approaches. The GBR model achieves a mean RMSE of 88.44 MW, significantly outperforming both SARIMAX (315.89 MW) and the Seasonal Na\u0026iuml;ve benchmark (316.51 MW). This represents an improvement of approximately 72% in forecasting error relative to classical baselines.\u003c/p\u003e \u003cp\u003eAdditionally, SARIMAX exhibits high variability across folds (standard deviation of 130.10 MW), indicating unstable performance under changing temporal conditions. In contrast, the GBR model demonstrates more consistent behavior, with lower variance across evaluation windows.\u003c/p\u003e \u003cp\u003eThese results highlight the limitations of linear statistical models for structured electricity demand forecasting tasks and confirm the effectiveness of feature-driven ensemble learning approaches in capturing nonlinear demand patterns.\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel Performance Analysis\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe results demonstrate that weather-augmented Gradient Boosting models outperform both classical statistical approaches and deep neural forecasting models. This outcome can be attributed to the structured nature of the forecasting dataset.\u003c/p\u003e \u003cp\u003eElectricity demand forecasting in this study relies heavily on engineered tabular features such as lagged demand values, rolling statistics, and calendar variables. Tree-based ensemble models are particularly well suited to this type of feature representation because they can capture nonlinear interactions among predictors.\u003c/p\u003e \u003cp\u003eDeep neural architectures such as DeepAR are optimized for learning temporal dependencies directly from sequential data. However, when extensive feature engineering is already performed, tree-based models often outperform neural networks, particularly when the dataset size is limited.\u003c/p\u003e \u003cp\u003eFurthermore, the results show that weather variables provide increasing predictive value as the forecasting horizon expands. Environmental conditions influence electricity demand patterns in ways that cannot be fully captured through historical demand alone. Incorporating weather variables therefore improves model performance, particularly for longer forecast horizons such as t\u0026thinsp;+\u0026thinsp;24 and t\u0026thinsp;+\u0026thinsp;168.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical Distribution of Model Error (Walk-Forward Folds)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEvaluation Aspect\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue (MW)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePerformance Significance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMean RMSE\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e88.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBaseline expected error across the dataset.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRMSE Standard Deviation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e29.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMeasure of model stability across time windows.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMinimum Fold RMSE\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e56.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeak performance (Best Case Scenario).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMaximum Fold RMSE\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e162.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaximum observed volatility (Worst Case Scenario).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eForecast performance varies substantially across walk-forward folds, with RMSE ranging from 56.34 MW to 162.08 MW.\u003c/p\u003e \u003cp\u003eThis variability reflects changing demand dynamics across different temporal segments of the dataset, including periods of stable demand and periods of high volatility.\u003c/p\u003e \u003cp\u003eWhile the average performance remains strong, the observed variation highlights that forecasting accuracy is context-dependent and influenced by underlying demand patterns.\u003c/p\u003e \u003cp\u003eThis reinforces the importance of walk-forward evaluation, as single-split evaluation would fail to capture this temporal variability.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecast performance across horizons\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHorizon\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e91.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e64.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeather-GBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e91.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e65.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e282.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e218.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e236.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e165.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e85.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e61.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeather-GBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e84.98\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e61.27\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e281.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e215.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e284.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;168\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e84.90\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e62.39\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;168\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeather-GBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e85.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e62.11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;168\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e255.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e196.88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003et\u0026thinsp;+\u0026thinsp;168\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e211.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e148.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eHorizon-wise evaluation shows that gradient boosting models substantially outperform statistical and persistence baselines across all forecasting horizons. At the ultra-short horizon (t\u0026thinsp;+\u0026thinsp;1), plain GBR achieved the lowest RMSE (91.26 MW), while weather-augmented GBR showed comparable performance (91.38 MW). At the day-ahead horizon (t\u0026thinsp;+\u0026thinsp;24), the weather-augmented model produced the best performance (RMSE 84.98 MW). At the week-ahead horizon (t\u0026thinsp;+\u0026thinsp;168), both models remained competitive, with only marginal differences between variants. In contrast, SARIMAX and seasonal na\u0026iuml;ve baselines exhibited substantially higher forecast errors across all horizons.\u003c/p\u003e \u003cp\u003eKey findings:-\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDiebold\u0026ndash;Mariano statistical comparison of forecast errors across horizons\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComparison\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eResult\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeather-GBR vs GBR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003esignificant only at t\u0026thinsp;+\u0026thinsp;168\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGBR vs SARIMAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003esignificant at all horizons\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGBR vs Seasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003esignificant at all horizons\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSARIMAX vs Seasonal Na\u0026iuml;ve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eweak difference at long horizon\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eStatistical significance was evaluated at the 5% level using two-sided Diebold\u0026ndash;Mariano tests under squared-error loss, with fold-level forecast errors treated as independent evaluation samples.\u003c/p\u003e \u003cp\u003eDiebold\u0026ndash;Mariano testing confirms that Gradient Boosting models significantly outperform SARIMAX and seasonal na\u0026iuml;ve baselines across all horizons (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Differences between weather-augmented and non-augmented Gradient Boosting models are statistically insignificant at short and day-ahead horizons but become significant at the week-ahead horizon, indicating increasing importance of meteorological information for longer-range prediction.\u003c/p\u003e"},{"header":"9. Feature Importance Analysis","content":"\u003cp\u003eBecause the weather-augmented Gradient Boosting model achieved the best forecasting performance, feature importance analysis was conducted to understand the variables most responsible for predictive accuracy.\u003c/p\u003e \u003cp\u003eTree-based ensemble models provide natural measures of feature importance based on the contribution of each predictor to reducing prediction error during model training.\u003c/p\u003e \u003cp\u003eFeature importance analysis indicates that the most influential predictors include:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eload_lag_24 (previous day demand)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eload_lag_168 (previous week demand)\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ehour_of_day\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ewind generation proxy variable\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eLagged demand variables dominate short-term forecasts, reflecting strong temporal autocorrelation in electricity consumption patterns. However, weather variables contribute more significantly to longer-horizon forecasts, particularly for the t\u0026thinsp;+\u0026thinsp;24 and t\u0026thinsp;+\u0026thinsp;168 horizons where historical demand alone becomes less informative.\u003c/p\u003e \u003cp\u003eThis analysis confirms that both temporal features and environmental signals play important roles in electricity demand forecasting.\u003c/p\u003e"},{"header":"10. Discussion","content":"\u003cp\u003eThe experimental results demonstrate that feature-driven Gradient Boosting models consistently outperform classical statistical baselines and probabilistic neural forecasting architectures across all evaluated prediction horizons. This performance advantage can be attributed primarily to the structured nature of the forecasting dataset, which combines lagged demand variables, rolling statistics, calendar encodings, and proxy meteorological indicators within a tabular feature representation. Tree-based ensemble models are well suited to exploiting nonlinear interactions among such predictors without requiring strong parametric assumptions regarding temporal structure.\u003c/p\u003e \u003cp\u003eIn contrast, SARIMAX models rely on linear dependence structures and therefore exhibit reduced flexibility when modeling nonlinear demand dynamics influenced by calendar effects and environmental variability. The observed instability of SARIMAX across walk-forward folds, reflected by high error variance, indicates limited robustness under evolving temporal demand regimes. These findings are consistent with prior benchmarking studies reporting that ensemble learning approaches outperform classical time-series models when extensive engineered features are available for electricity demand prediction tasks.\u003c/p\u003e \u003cp\u003eThe probabilistic DeepAR model did not achieve performance comparable to Gradient Boosting variants in this study. Deep neural forecasting architectures typically require larger training corpora to learn stable sequential representations of temporal structure. Because the dataset used in this work consists of approximately one year of hourly observations from a single regional demand series, the available training data are insufficient for fully exploiting the representational capacity of recurrent probabilistic neural networks. Under limited-data conditions, feature-driven ensemble models therefore provide a more efficient forecasting solution.\u003c/p\u003e \u003cp\u003eHorizon-specific evaluation further reveals that meteorological variables contribute increasing predictive value as the forecasting horizon extends. At ultra-short prediction intervals, demand persistence captured through autoregressive lag features dominates predictive performance. However, as the forecasting horizon increases to day-ahead and week-ahead intervals, the predictive influence of recent observations weakens and exogenous environmental signals become more informative. The Diebold\u0026ndash;Mariano statistical comparison confirms that weather augmentation produces significant improvements primarily at the week-ahead horizon, supporting the interpretation that environmental covariates provide complementary predictive structure beyond autoregressive information at longer forecast intervals.\u003c/p\u003e \u003cp\u003ePrediction interval evaluation indicates moderate under-calibration relative to the nominal 80% coverage level, with empirical coverage of 0.759. This result suggests that the probabilistic forecasting framework underestimates uncertainty in periods of elevated demand variability. Such behavior is commonly observed in quantile-based forecasting models when conditional variance structure is not fully captured by available predictors. Although the generated prediction intervals successfully track general demand variability during stable periods, improved calibration techniques such as conformal prediction or post-hoc interval adjustment may further enhance probabilistic reliability in operational deployment settings.\u003c/p\u003e \u003cp\u003eWalk-forward evaluation additionally highlights that forecasting accuracy varies across temporal segments of the dataset. Higher prediction errors occur during periods characterized by rapid demand transitions and peak consumption intervals, where lag-based predictors provide weaker guidance for future demand trajectories. Nevertheless, Gradient Boosting variants maintain stable performance rankings across folds and prediction horizons, indicating robustness to non-stationary consumption behavior commonly observed in real-world electricity demand series. This stability supports the suitability of ensemble learning approaches for operational forecasting environments requiring consistent predictive performance under evolving demand conditions.\u003c/p\u003e \u003cp\u003eOverall, the results demonstrate that model\u0026ndash;data alignment plays a critical role in electricity demand forecasting performance. When forecasting pipelines incorporate structured temporal features and operate under limited-data conditions, ensemble learning approaches provide a practical and computationally efficient alternative to deep probabilistic forecasting architectures while maintaining strong predictive accuracy across multiple operational horizons.\u003c/p\u003e"},{"header":"11. Forecast Uncertainty Analysis","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eInterpretation\u003c/b\u003e \u003c/p\u003e \u003cp\u003ePrediction intervals generated by the probabilistic models exhibit under-coverage relative to the nominal 80% confidence level. This indicates that the predictive uncertainty intervals are narrower than required for well-calibrated probabilistic forecasts.\u003c/p\u003e"},{"header":"12. Forecast Visualization","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eInterpretation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe median forecast tracks the general demand pattern closely and successfully captures daily demand cycles. Forecast uncertainty increases during peak demand periods, reflected by wider prediction intervals.\u003c/p\u003e"},{"header":"13. Forecasting Pipeline Architecture","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eExplanation\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eThe forecasting system combines multiple datasets, transforms them into structured features, and evaluates multiple forecasting models within a reproducible machine learning workflow.\u003c/p\u003e"},{"header":"14. Study Limitations","content":"\u003cp\u003eDespite the promising results, several limitations should be acknowledged.\u003c/p\u003e \u003cp\u003eFirst, the dataset used in this study covers only a single year of hourly observations. A longer historical dataset would likely improve model training, particularly for deep learning models such as DeepAR that require large volumes of sequential data.\u003c/p\u003e \u003cp\u003eSecond, the set of meteorological variables included in the forecasting pipeline is limited. Additional weather features such as humidity, precipitation, and atmospheric pressure may provide further predictive information. Future work will incorporate multi-year datasets to validate temporal generalization of the proposed framework\u003c/p\u003e \u003cp\u003eThird, the forecasting experiments focus on a single geographic region (Ireland). Electricity demand patterns vary across different climates and grid systems, so further research is needed to evaluate whether the findings generalize to other regions.\u003c/p\u003e \u003cp\u003eFinally, probabilistic forecast calibration remains an open challenge. Although prediction intervals were generated using quantile regression and probabilistic modeling, empirical coverage remained below the desired level. Future research should explore calibration techniques to improve uncertainty estimation. Future work will evaluate multi-year datasets to assess temporal transferability across seasonal demand regimes.\u003c/p\u003e"},{"header":"15. Key Challenges","content":"\u003cp\u003eSeveral challenges were encountered during development:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ealigning multiple datasets with different temporal resolutions\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ehandling missing weather observations\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eachieving reliable probabilistic forecast calibration\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003econfiguring deep learning models for limited dataset sizes\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"16. Future Work","content":"\u003cp\u003eFuture research may explore:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003etransformer-based forecasting models\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eimproved probabilistic calibration techniques\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003elarger historical datasets\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003emulti-region electricity forecasting\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eFuture work may also evaluate horizon-specific model calibration using conformal prediction methods.\u003c/p\u003e"},{"header":"17. Conclusion","content":"\u003cp\u003eThis study developed a weather-augmented electricity demand forecasting framework capable of predicting load across multiple horizons. Experimental results demonstrate that gradient boosting models achieve the highest predictive accuracy among the evaluated methods, while weather augmentation provides statistically significant improvements at longer prediction horizons.\u003c/p\u003e \u003cp\u003eThe findings emphasize the importance of environmental variables in electricity demand forecasting and highlight the effectiveness of ensemble machine learning methods for structured tabular time-series forecasting problems. The results suggest that feature-driven ensemble models can outperform both classical statistical methods and deep probabilistic models under limited data regimes, highlighting the importance of model\u0026ndash;data alignment in time-series forecasting tasks.The study contributes a statistically validated evaluation framework for multi-horizon electricity load forecasting that enables consistent comparison between statistical, machine learning, and probabilistic forecasting paradigms under realistic operational conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e\n\u003ch2\u003eAuthor Contributions\u003c/h2\u003e\n\u003cp\u003eMHS conceived the study, designed the methodology, implemented the forecasting models, conducted the experiments, analyzed the results, and prepared the manuscript.\u003c/p\u003e\n\u003ch2\u003eCompeting Interests\u003c/h2\u003e\n\u003cp\u003eMHS declares no competing interests.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe datasets used in this study are publicly available from the ENTSO-E Transparency Platform and NASA POWER. \u003cbr\u003eThe code and processed data supporting this study are available at: https://github.com/MeherabHS/Statistically-Validated-Multi-Horizon-Electricity-Load-Forecasting-with-Weather-Augmented-ML\u003c/p\u003e\n\u003ch2\u003eCode Availability\u003c/h2\u003e\n\u003cp\u003eThe forecasting pipeline, preprocessing scripts, and evaluation framework developed for this study are publicly available in the GitHub repository listed above.\u003c/p\u003e\n\u003ch2\u003eEthics Approval\u003c/h2\u003e\n\u003cp\u003eThis study does not involve human participants or animals and therefore does not require ethical approval.\u003c/p\u003e\n\u003ch2\u003eConsent to Participate\u003c/h2\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003ch2\u003eConsent for Publication\u003c/h2\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003eClinical Trial Number\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHong T, Fan S. 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Data Min Knowl Discov. 2023;37:788\u0026ndash;832.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9285801/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9285801/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eShort-term electricity load forecasting is essential for maintaining grid reliability, supporting generation scheduling, and enabling efficient operation of modern energy systems. This study develops a weather-augmented multi-horizon forecasting framework for electricity demand prediction using hourly load observations from the ENTSO-E Transparency Platform combined with meteorological data obtained from the NASA POWER dataset. Four forecasting approaches are evaluated within a unified benchmarking framework: Seasonal Na\u0026iuml;ve persistence, SARIMAX, Gradient Boosting Regression (GBR), and a weather-augmented GBR variant incorporating exogenous meteorological covariates. In addition, the probabilistic DeepAR neural forecasting model implemented using GluonTS is included as a distributional reference model for uncertainty-aware comparison.\u003c/p\u003e \u003cp\u003eForecast performance is assessed across three operationally relevant prediction horizons (t\u0026thinsp;+\u0026thinsp;1, t\u0026thinsp;+\u0026thinsp;24, and t\u0026thinsp;+\u0026thinsp;168) using an expanding-window rolling-origin walk-forward validation strategy. The feature set includes calendar encodings, autoregressive lag features, rolling demand statistics, and wind-related meteorological indicators. Results demonstrate that Gradient Boosting models consistently outperform statistical and persistence baselines across all forecasting horizons. Horizon-specific Diebold\u0026ndash;Mariano tests further indicate that weather augmentation provides statistically significant improvements primarily at longer prediction intervals. Across 17 walk-forward evaluation folds, the best-performing configuration achieved a mean RMSE of 88.44 MW (\u0026plusmn;\u0026thinsp;29.62) and a mean MAE of 66.69 MW. Probabilistic evaluation produced empirical 80% prediction interval coverage of 0.759, indicating moderate under-calibration relative to nominal uncertainty levels.\u003c/p\u003e \u003cp\u003eThese findings highlight the effectiveness of feature-driven ensemble methods for structured electricity demand forecasting and demonstrate the value of statistically validated multi-horizon benchmarking frameworks for operational load prediction under limited-data conditions.\u003c/p\u003e","manuscriptTitle":"Statistically Validated Multi-Horizon Electricity Load Forecasting with Weather-Augmented Machine Learning under Walk-Forward Evaluation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-06 06:29:32","doi":"10.21203/rs.3.rs-9285801/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a7eb8660-3cb0-44a9-9841-36b9113d6999","owner":[],"postedDate":"April 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-15T10:16:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-06 06:29:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9285801","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9285801","identity":"rs-9285801","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}