Forecasting Electricity Price Index with Machine Learning Models and Strategies

Forecasting Electricity Price Index with Machine Learning Models and Strategies | 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 Forecasting Electricity Price Index with Machine Learning Models and Strategies Sevda Kuşkaya, Faik Bilgili This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6298557/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 Electricity consumption is recognized as one of the fundamental indicators of economic activities. Accurate forecasting of electricity prices is therefore critical for economic planning and sustainable development. This research investigates the effectiveness of 19 different machine learning algorithms/models in forecasting the US electricity prices. It provides a comprehensive analysis by evaluating approaches that both include and exclude seasonality factors. Key findings of the study are as follows: (I) Linear Regression and CatBoost Regressor models delivered the best results in terms of accuracy and computational efficiency. (ii) The Linear Regression model using the TimeSeriesSplit strategy exhibited a high agreement with actual electricity price trends. (iii) Linear regression outperformed other models in metrics such as mean absolute error (MAE) and root mean squared logistic error (RMSLE). This study demonstrates that machine learning models can serve as effective tools for forecasting electricity prices and provide valuable recommendations for stakeholders in the energy sector. Especially when appropriate strategies for temporal data structures are applied, these models can offer reliable predictions. Eventually, this paper highlights that machine learning models are an important tool for stakeholders and policymakers in the energy sector, helping to predict electricity price fluctuations and contributing to the decision-making process. Artificial Intelligence and Machine Learning Econometrics Macroeconomics Applied Statistics City Management and Urban Policy Machine Learning ML Algorithm Electricity Price Index Forecasting Prediction Accuracy Metrics. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Forecasting electricity price indices is closely related to sustainable development and economic growth. The energy sector is at the center of sustainable development goals and includes many objectives such as increasing energy access, promoting clean fuels, reducing energy subsidies and limiting air pollution (Wen et al., 2023). At the same time, electricity consumption and prices are directly related to economic growth, and this relationship is particularly pronounced in developing countries (Shahbaz et al., 2017). Electricity consumption is recognized as an indicator of economic activity. Therefore, accurate forecasting of electricity prices is critical for economic planning and sustainable development (Fan et al., 2020). Forecasting electricity prices is crucial for understanding the dynamics of energy markets and shaping energy policies. These forecasts can be used to adjust energy production and consumption models, support energy policy decisions, and optimize economic load dispatch (Fan et al., 2020). Moreover, this forecasting can help to develop energy efficiency strategies and diminish emission levels. Also, accurate forecasting of electricity prices creates a safer environment for investors by reducing uncertainty in energy markets, which in turn supports sustainable economic growth (Osório et al., 2018; Wen, et al. 2023). In this respect, electricity consumption and prices are directly related to economic growth, and this relationship is particularly pronounced in developing countries (Shahbaz et al., 2017). The energy sector is at the centre of sustainable development goals and includes many objectives such as increasing energy access, promoting clean fuels, reducing energy subsidies and limiting air pollution (Wen et al., 2023). Electricity consumption is recognized as an indicator of economic activity. Since electricity consumption is considered an indicator of economic activity, accurate forecasting of electricity prices is critical for economic planning and sustainable development (Fan et al., 2020). At the same time, this forecast also facilitates the integration of renewable energy sources, enabling more efficient use of renewable energy resources and contributing to the development of sustainable energy policies (Abbasi et al., 2021). In this context, the energy sector plays a critical role in both economic growth and sustainable development. Electricity price is an important factor in the electricity market, it can ensure the stable operation of the market, and electricity price forecasting has become the focus of attention of scholars from different countries (Kuo and Huang, 2018). Accurately predicting the future trends of electricity prices is of great importance for energy policymaking, cost management and long-term strategic planning. In this study, monthly data for the US economy for the period 1986-2020 are analyzed (forecast) and future electricity prices are projected for the period 2021-2026. Ex-ante forecasts are based on data obtained from the Federal Reserve Economic Data (FRED). Accordingly, machine learning (ML) models provide powerful tools/analyses for predicting and forecasting future price movements based on historical data. Within the scope of the study, forecasts will be made using various ML models. The ML methods to be used are: CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor, Extra Trees Regressor, Decision Tree Regressor, K Neighbors Regressor, Light Gradient Boosting Machine, AdaBoost Regressor, Orthogonal Matching Pursuit, Linear Regression, Ridge Regression, Least Angle Regression, Bayesian Ridge, Huber Regressor, Elastic Net, Lasso Regression, Lasso Least Angle Regression, Dummy Regressor and Passive Aggressive Regressor. The ML models used in the study are of great importance in predicting the future trends of electricity prices. Each model has different algorithms, data processing strategies, and data processing and the ability to predict and forecast, which means that each model may perform differently under certain data types and conditions. Among the models used in this study, advanced tree-based models such as CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor and Light Gradient Boosting Machine offer the possibility to learn complex relationships and interactions within the data. In addition, linear models such as Linear Regression, Ridge Regression and Bayesian Ridge help to understand underlying trends and relationships by providing simpler and more interpretable results. Especially for time series data such as electricity prices, it is critical to be able to accurately predict future trends by learning from historical data. By comparing the performance of each model, it is possible to identify the model or models that can make predictions with the highest accuracy and reliability. This paper aims to provide important findings in forecasting electricity prices in the energy sector. Accurately predicting the future trends of electricity prices plays a critical role in energy policymaking, economic planning and investment decisions. Electricity prices affect a wide range of economic activities, from industrial production to household consumption. Therefore, understanding the future movements of electricity prices is of strategic importance to ensure security of energy supply, manage costs and achieve sustainable development goals. The various ML models used in the analysis aim to provide valuable information to decision-makers and policymakers by offering innovative approaches to obtain the most accurate and reliable forecasts/predictions. Moreover, the findings of the study will both contribute to the academic literature and provide important information that can be used in practical applications. In this context, the study consists of four sections. After the introduction, there are sections on data and methodology, analysis findings, evaluation and discussion, and conclusions and recommendations. Data and Methodology In the analysis, monthly data from the U.S. economy for the period 1986–2020 was used to forecast electricity prices for the 2021–2026 period. These forecasts were conducted using data obtained from the Federal Reserve Economic Data (FRED). The graphical representation of the data is presented in Figure 1. Data Source: FRED Economic Data, Average Price: Electricity per Kilowatt-Hour in U.S. City Average https://fred.stlouisfed.org/series/APU000072610 In this context, machine learning (ML) models provide powerful tools for forecasting future price movements based on historical data. Various ML models were used in this study for forecasting purposes. The models considered in this study include: · CatBoost Regressor · Gradient Boosting Regressor · Random Forest Regressor · Extra Trees Regressor · Decision Tree Regressor · K Neighbors Regressor · Light Gradient Boosting Machine · AdaBoost Regressor · Orthogonal Matching Pursuit · Linear Regression · Ridge Regression · Least Angle Regression · Bayesian Ridge · Huber Regressor · Elastic Net · Lasso Regression · Lasso Least Angle Regression · Dummy Regressor · Passive Aggressive Regressor The monthly time-series data of the U.S. City Average for Electricity Price per Kilowatt-Hour (APU000072610) aims to be forecasted using these 19 ML models. 1.1. Machine Learning Models: 1. CatBoost Regressor: A gradient boosting algorithm developed by Yandex, effective for categorical data and known for reducing overfitting. 2. Gradient Boosting Regressor (GBR): An ensemble model that builds sequential decision trees to minimize prediction errors and is known for high forecasting performance. 3. Random Forest Regressor (RF): An ensemble of decision trees averaging predictions to improve model accuracy and robustness. 4. Extra Trees Regressor (ET): Similar to Random Forest Regressor but uses more randomized splits for individual trees, often yielding faster results. 5. Decision Tree Regressor (DT): A simple and interpretable model that splits data based on feature values for predictions. 6. K Neighbors Regressor (KNN): A non-parametric algorithm that predicts targets based on the average of the nearest data points. 7. Light Gradient Boosting Machine (LIGHTGBM): A highly efficient gradient boosting algorithm optimized for speed and memory usage. 8. AdaBoost Regressor (ADA): Combines multiple weak models (typically decision trees) into a strong model by adjusting weights based on past errors. 9. Orthogonal Matching Pursuit (OMP): A sparse linear regression method that selects a subset of features to make the best linear predictions. 10. Linear Regression (LR): A fundamental, interpretable model that fits a linear relationship between target and features. 11. Ridge Regression (RIDGE): A regularized linear regression method that adds an L2 penalty to reduce overfitting. 12. Least Angle Regression (LAR): A stepwise algorithm that builds the model incrementally by adding features in order of importance. 13. Bayesian Ridge (BR): A probabilistic linear regression model that estimates coefficient distributions for improved generalization. 14. Huber Regressor (HUBER): Combines squared and absolute errors, making it robust to outliers. 15. Elastic Net (EN): Balances feature selection and regularization by combining L1 (Lasso) and L2 (Ridge) penalties. 16. Lasso Regression: Adds an L1 penalty to linear regression, shrinking some coefficients to zero for feature selection. 17. Lasso Least Angle Regression (LLAR): Similar to LAR but includes an L1 penalty for regularization. 18. Dummy Regressor: A baseline model that makes simple predictions, such as using the mean or median of the data. 19. Passive Aggressive Regressor: An online learning algorithm that updates the model only when predictions are incorrect, designed for large-scale data. 1.2. Classification of ML Models: The ML models can be categorized as follows: · Ensemble Learning Models: CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor, Extra Trees Regressor, AdaBoost Regressor, Light Gradient Boosting Machine. · Linear Models: Linear Regression, Ridge Regression, Bayesian Ridge, Elastic Net, Lasso Regression, Lasso Least Angle Regression, Orthogonal Matching Pursuit, Least Angle Regression. · Tree-Based Models: Decision Tree Regressor. · Distance-Based Models: K Neighbors Regressor. · Robust and Regularized Models: Huber Regressor, Passive Aggressive Regressor. · Baseline Model: Dummy Regressor. This classification aids in understanding the diversity of algorithms and selecting the best model based on dataset characteristics and computational constraints. 2. Analysis Results To execute machine learning programs, various fold strategies in machine learning programming (e.g., k-fold, stratified k-fold, group k-fold, and time series) were employed. In this study, the TimeSeriesSplit strategy was primarily used, with the k-fold strategy applied for comparison purposes. TimeSeriesSplit is most suitable for time-series data, as it splits the data sequentially, ensuring that training data precedes test data. This structure prevents future information from leaking into the training set, providing a realistic validation scenario for forecasting. On the other hand, the k-fold strategy randomly splits the data into k folds, potentially mixing past and future data in training and test sets. 2.1. Forecasting Without Considering Seasonality: Using Fold_Strategy = 'TimeSeries' Table 1: Summary of Model Training Setup for Time Series Regression with Fold_Strategy = 'TimeSeries' Description Value 0 Session id 123 1 Target ElectricityP 2 Target type Regression 3 Original data shape (420, 4) 4 Transformed data shape (420, 4) 5 Transformed train set shape (384, 4) 6 Transformed test set shape (36, 4) 7 Numeric features 2 8 Preprocess True 9 Imputation type simple 10 Numeric imputation mean 11 Categorical imputation mode 12 Transform target True 13 Transform target method yeo-johnson 14 Fold Generator TimeSeriesSplit 15 Fold Number 3 16 CPU Jobs -1 17 Use GPU False 18 Log Experiment False 19 Experiment Name reg-default-name 20 USI (Unique Session Identifier) 2b3 Table 1 provides an overview of the data preprocessing and model training setup, likely implemented using a library like PyCaret or similar frameworks. Key highlights include: 1. Target Variable: "ElectricityP" indicates the target to be predicted. 2. Fold Strategy: The TimeSeriesSplit strategy was employed to align with the sequential nature of time-series data. 3. Data Shape: The training set comprises 384 rows, while the test set contains 36 rows, maintaining the original dimensions of the dataset. 2.2 Comparison of Regression Model Performance Table 2. Comparison of Regression Model Performance Metrics for Electricity Price Series Abbreviation Model MAE MSE RMSE RMSLE MAPE TT (Sec) catboost CatBoost Regressor 0.0081 0.0002 0.0103 0.0093 0.0690 1.1033 gbr Gradient Boosting Regressor 0.0083 0.0002 0.0105 0.0095 0.0706 0.0567 rf Random Forest Regressor 0.0083 0.0002 0.0106 0.0095 0.0715 0.1300 et Extra Trees Regressor 0.0087 0.0002 0.0109 0.0098 0.0736 0.1100 dt Decision Tree Regressor 0.0088 0.0002 0.0111 0.0100 0.0766 0.0300 knn K Neighbors Regressor 0.0089 0.0002 0.0111 0.0100 0.0775 0.0333 lightgbm Light Gradient Boosting Machine 0.0092 0.0002 0.0112 0.0101 0.0779 0.0600 ada AdaBoost Regressor 0.0108 0.0002 0.0130 0.0117 0.0914 0.0733 omp Orthogonal Matching Pursuit 0.0114 0.0002 0.0141 0.0127 0.1055 0.0333 lr Linear Regression 0.0117 0.0002 0.0147 0.0132 0.1069 2.7833 ridge Ridge Regression 0.0117 0.0002 0.0147 0.0132 0.1069 1.9533 lar Least Angle Regression 0.0117 0.0002 0.0147 0.0132 0.1069 0.0367 br Bayesian Ridge 0.0117 0.0002 0.0147 0.0132 0.1069 0.0333 huber Huber Regressor 0.0125 0.0003 0.0169 0.0150 0.1132 0.0467 en Elastic Net 0.0228 0.0008 0.0248 0.0224 0.1850 0.0367 lasso Lasso Regression 0.0233 0.0008 0.0253 0.0228 0.1899 2.1667 llar Lasso Least Angle Regression 0.0233 0.0008 0.0253 0.0228 0.1899 0.0400 dummy Dummy Regressor 0.0233 0.0008 0.0253 0.0228 0.1899 0.0267 par Passive Aggressive Regressor 0.0908 0.0095 0.0915 0.0861 0.8129 0.0300 Key observations: · Best Model: CatBoost Regressor achieves the lowest Mean Absolute Error (MAE) of 0.0081, indicating its high accuracy. · Training Time: Models like Gradient Boosting Regressor and Extra Trees Regressor exhibit faster training times compared to CatBoost. · Linear Regression: While computationally efficient, its performance lags behind advanced tree-based models in terms of prediction accuracy. 2.3 Forecasted Electricity Prices for the 2021–2026 Period: Table 3. Forecasted Electricity Prices (2021-01 to 2026-01) Month year Series Forecast Value 0 1 2021 421 0.135273 1 2 2021 422 0.135813 2 3 2021 423 0.135720 3 4 2021 424 0.135684 4 5 2021 425 0.137136 .. … … … … 56 9 2025 477 0.142297 57 10 2025 478 0.137968 58 11 2025 479 0.135854 59 12 2025 480 0.135880 60 1 2026 481 0.135273 Note: [61 rows x 5 columns] 2.4. Forecasting Using Fold_Strategy = 'k-fold' Although TimeSeriesSplit was preferred for time-series data, the k-fold strategy was also applied for comparison purposes in this study. Table 4. Summary of Model Training Setup for Time Series Regression with Fold_Strategy = 'k-fold' Description Value 0 Session id 123 1 Target ElectricityP 2 Target type Regression 3 Original data shape (420, 4) 4 Transformed data shape (420, 4) 5 Transformed train set shape (384, 4) 6 Transformed test set shape (36, 4) 7 Numeric features 2 8 Preprocess True 9 Imputation type simple 10 Numeric imputation mean 11 Categorical imputation mode 12 Transform target True 13 Transform target method yeo-johnson 14 Fold Generator KFold 15 Fold Number 3 16 CPU Jobs -1 17 Use GPU False 18 Log Experiment False 19 Experiment Name reg-default-name 20 USI (Unique Session Identifier) 0632 The k-fold strategy divides data into k equal subsets, randomly mixing past and future data within training and test sets. While this approach increases model diversity during training, it may allow future data to influence training stages, leading to potential data leakage. Table 5. Comparison of Regression Model Performance Metrics with Fold_Strategy = 'k-fold' Abbreviation Model MAE MSE RMSE RMSLE MAPE TT(Sec) gbr Gradient Boosting Regressor 0.0128 0.0002 0.0146 0.0132 0.1244 0.0767 catboost CatBoost Regressor 0.0129 0.0002 0.0146 0.0132 0.1262 1.1633 ada AdaBoost Regressor 0.0130 0.0002 0.0151 0.0136 0.1237 0.0767 lightgbm Light Gradient Boosting Machine 0.0134 0.0003 0.0153 0.0138 0.1252 0.0633 rf Random Forest Regressor 0.0134 0.0003 0.0155 0.0140 0.1292 0.1433 et Extra Trees Regressor 0.0135 0.0002 0.0150 0.0135 0.1317 0.1267 knn K Neighbors Regressor 0.0138 0.0003 0.0158 0.0142 0.1325 0.0333 dt Decision Tree Regressor 0.0146 0.0003 0.0168 0.0151 0.1436 0.0300 ridge Ridge Regression 0.0193 0.0004 0.0201 0.0183 0.1961 0.0333 lar Least Angle Regression 0.0193 0.0004 0.0201 0.0183 0.1961 0.0367 omp Orthogonal Matching Pursuit 0.0193 0.0004 0.0201 0.0183 0.1961 0.0300 lr Linear Regression 0.0193 0.0004 0.0201 0.0183 0.1961 0.0367 br Bayesian Ridge 0.0193 0.0004 0.0201 0.0183 0.1961 0.0333 huber Huber Regressor 0.0202 0.0005 0.0210 0.0192 0.2050 0.0467 lasso Lasso Regression 0.0204 0.0007 0.0213 0.0192 0.1790 0.0367 llar Lasso Least Angle Regression 0.0204 0.0007 0.0213 0.0192 0.1790 0.0300 en Elastic Net 0.0217 0.0007 0.0225 0.0203 0.1929 0.0333 dummy Dummy Regressor 0.0280 0.0009 0.0289 0.0262 0.2693 0.0300 par Passive Aggressive Regressor 0.0701 0.0070 0.0707 0.0663 0.6194 0.0333 Observations: · The Gradient Boosting Regressor outperformed others in this setup with the lowest MAE (0.0128). · Models like CatBoost Regressor maintained competitive performance but required longer training times. · Compared to TimeSeriesSplit , models trained with k-fold strategy showed slightly less reliability due to potential data leakage. Table 6. Forecasted Electricity Prices for the 2021–2026 Period Using k-fold Strategy Month Year Series Forecast value 0 1 2021 421 0.135902 1 2 2021 422 0.135902 2 3 2021 423 0.135902 3 4 2021 424 0.135902 4 5 2021 425 0.136380 .. … … … … 56 9 2025 477 0.141396 57 10 2025 478 0.136966 58 11 2025 479 0.135521 59 12 2025 480 0.135521 60 1 2026 481 0.135902 Note: [61 rows x 5 columns] 3. Incorporating Seasonality in Forecasting Analysis To improve the accuracy of forecasts, seasonality parameters were integrated into the models. Seasonality reflects the cyclic patterns inherent in electricity prices. Table 7: Summary of Model Training Setup with TimeSeriesSplit Strategy Incorporating Seasonality Description Value 0 Session id 123 1 Target ElectricityP 2 Target type Regression 3 Original data shape (420, 6) 4 Transformed data shape (420, 17) 5 Transformed train set shape (384, 17) 6 Transformed test set shape (36, 17) 7 Numeric features 3 8 Categorical features 2 9 Preprocess True 10 Imputation type simple 11 Numeric imputation mean 12 Categorical imputation mode 13 Maximum one-hot encoding 25 14 Encoding method None 15 Transform target True 16 Transform target method yeo-johnson 17 Fold Generator TimeSeriesSplit 18 Fold Number 3 19 CPU Jobs -1 20 Use GPU False 21 Log Experiment False 22 Experiment Name reg-default-name 23 USI (Unique Session Identifier) e4d7 By incorporating seasonality through transformations like sine and cosine functions, models captured cyclical trends in electricity prices more effectively. Table 8: Comparison of Regression Model Performance Metrics with Seasonality Consideration Abbreviation Model MAE MSE RMSE RMSLE MAPE TT (Sec) lr Linear Regression 0.0079 0.0002 0.0101 0.0091 0.0777 2.8633 ridge Ridge Regression 0.0079 0.0002 0.0101 0.0091 0.0775 1.9267 lar Least Angle Regression 0.0079 0.0002 0.0101 0.0091 0.0777 0.0733 br Bayesian Ridge 0.0079 0.0002 0.0101 0.0091 0.0776 0.0600 huber Huber Regressor 0.0079 0.0002 0.0100 0.0091 0.0780 0.0733 gbr Gradient Boosting Regressor 0.0081 0.0002 0.0104 0.0093 0.0693 0.0933 et Extra Trees Regressor 0.0083 0.0002 0.0104 0.0094 0.0700 0.1467 rf Random Forest Regressor 0.0084 0.0002 0.0106 0.0096 0.0715 0.1600 dt Decision Tree Regressor 0.0085 0.0002 0.0108 0.0097 0.0732 0.0600 catboost CatBoost Regressor 0.0086 0.0002 0.0108 0.0097 0.0726 1.2867 knn K Neighbors Regressor 0.0089 0.0002 0.0111 0.0100 0.0768 0.0967 lightgbm Light Gradient Boosting Machine 0.0091 0.0002 0.0112 0.0101 0.0776 0.0867 ada AdaBoost Regressor 0.0110 0.0002 0.0132 0.0119 0.0920 0.1033 omp Orthogonal Matching Pursuit 0.0114 0.0002 0.0141 0.0127 0.1055 0.0567 en Elastic Net 0.0228 0.0008 0.0248 0.0224 0.1850 0.0633 lasso Lasso Regression 0.0233 0.0008 0.0253 0.0228 0.1899 2.1667 llar Lasso Least Angle Regression 0.0233 0.0008 0.0253 0.0228 0.1899 0.0667 dummy Dummy Regressor 0.0233 0.0008 0.0253 0.0228 0.1899 0.0533 par Passive Aggressive Regressor 0.0908 0.0095 0.0915 0.0861 0.8129 0.0533 Key Takeaways: · Models with seasonality outperformed those without, highlighting the importance of capturing cyclical trends. · Linear Regression achieved strong performance, emphasizing its reliability when paired with seasonal adjustments. · Advanced models like Gradient Boosting Regressor and CatBoost Regressor maintained their competitive edge. Table 9. Forecasted Electricity Prices (2021–2026) with Seasonality Considered Date Year Month Series Sin_ay Cos_ay Forecast Value 2021-01-01 2021 1 420 5.000000e-01 8.660254e-01 0.153708 2021-02-01 2021 2 421 8.660254e-01 5.000000e-01 0.152718 2021-03-01 2021 3 422 1.000000e+00 6.123234e-17 0.153471 2021-04-01 2021 4 423 8.660254e-01 -5.000000e-01 0.153120 2021-05-01 2021 5 424 5.000000e-01 -8.660254e-01 0.156245 … … … … … … … 2025-09-01 2025 9 476 -1.000000e+00 -1.836970e-16 0.223228 2025-10-01 2025 10 477 -8.660254e-01 5.000000e-01 0.192464 2025-11-01 2025 11 478 -5.000000e-01 8.660254e-01 0.182693 2025-12-01 2025 12 479 -2.449294e-16 1.000000e+00 0.183032 2026-01-01 2026 1 480 5.000000e-01 8.660254e-01 0.188493 Note: [61 rows x 5 columns] Evaluation and Discussion The results of the study demonstrate the effectiveness of using machine learning (ML) techniques to forecast U.S. electricity prices based on historical data from January 1986 to December 2020. By comparing the performance of 19 different ML models using both TimeSeriesSplit and k-fold strategies , significant differences in forecasting capabilities were observed. Key insights from the evaluation include: (i) TimeSeriesSplit Analysis: TimeSeriesSplit proved highly suitable for time-series data, respecting the sequential nature of observations and ensuring reliable predictions. · The CatBoost Regressor performed exceptionally well, achieving superior accuracy in terms of Mean Absolute Percentage Error (MAPE). · Despite its simplicity, the Linear Regression model provided forecasts closely aligned with actual trends during the out-of-sample prediction period (2021:1–2026:1). (ii) Comparison with k-fold Strategy: While the k-fold strategy offered diversity in model training, it showed limitations due to the risk of future data influencing training (data leakage). · Models like Gradient Boosting Regressor and CatBoost Regressor maintained competitive performance metrics under the k-fold approach. · However, the reliability of forecasts was marginally lower compared to models trained using the TimeSeriesSplit strategy , especially for time-sensitive data. (iii) Incorporating Seasonality: Accounting for seasonality significantly improved the accuracy of forecasts, underscoring the cyclical nature of electricity prices. · When variables like sine and cosine transformations were included, models effectively captured seasonal patterns, resulting in predictions that closely matched observed data. · Both Linear Regression and Gradient Boosting Regressor performed remarkably well when seasonality adjustments were integrated. Key Findings: 1. Top Performing Models: o The CatBoost Regressor and Linear Regression models emerged as the most effective in terms of accuracy and computational efficiency. o Linear Regression , though simple, demonstrated robust performance with minimal errors, particularly when combined with the TimeSeriesSplit strategy . 2. Importance of Strategy Alignment: Selecting fold strategies that align with the sequential nature of the data (e.g., TimeSeriesSplit ) was crucial for preserving the integrity of the forecasting process and enhancing model performance. 3. Role of Seasonality: Incorporating seasonality using cyclical transformations (e.g., sine and cosine) improved model performance, enabling better alignment with real-world data patterns. 4. Recommendations for Future Work: o Explore hybrid model approaches that combine the strengths of different algorithms (e.g., blending tree-based models with linear models). o Integrate additional external variables such as economic indicators or weather data to enhance the granularity of forecasts. Summary of Practical Implications: The findings emphasize the potential of machine learning models, particularly when paired with suitable strategies and seasonality considerations, as reliable tools for electricity price forecasting. This has significant implications for stakeholders in the energy sector, including policymakers, investors, and operational planners. Accurate forecasts can aid in: · Policy Development: Informing energy policy decisions with reliable price trends. · Economic Planning: Optimizing cost management and investment strategies. · Sustainability Goals: Supporting renewable energy integration and emission reduction initiatives. Conclusion and Recommendations This study aimed to forecast U.S. electricity prices for the 2021–2026 period using 19 different machine learning (ML) models. It compared predictions both with and without incorporating seasonality and utilized various fold strategies, such as TimeSeriesSplit and k-fold , to ensure comprehensive analysis. The effectiveness of the models was validated through metrics such as Mean Absolute Error (MAE) , Root Mean Squared Logarithmic Error (RMSLE) , and others. Key Results: 1. Top Performers: o The CatBoost Regressor and Linear Regression models stood out as the most effective models overall. o Linear Regression provided the best results in terms of simplicity, computational efficiency, and alignment with actual trends when paired with the TimeSeriesSplit strategy . 2. Impact of Seasonality: o Models incorporating seasonality through sine and cosine transformations captured the cyclical behavior of electricity prices, enhancing forecast reliability. o The Linear Regression model , combined with seasonality adjustments, aligned closely with observed data trends for the 2021–2026 period. 3. Performance Comparison: o Models trained using TimeSeriesSplit outperformed those using k-fold , emphasizing the importance of choosing strategies suited to the sequential nature of time-series data Practical Contributions: The study highlights the potential of machine learning models in addressing critical challenges in electricity price forecasting. Accurate forecasts can: · Support energy policy development by offering insights into future price fluctuations. · Aid in economic planning through optimized cost management and strategic decision-making. · Facilitate sustainable development goals , such as integrating renewable energy and reducing market uncertainties. Recommendations for Future Research and Practice: 1. Model Selection and Strategy Alignment: Future studies should prioritize fold strategies tailored to time-series data, such as TimeSeriesSplit , to maintain data integrity and improve prediction accuracy. 2. Enhancing Model Performance: o Incorporating seasonality through cyclical transformations should become standard practice when dealing with data exhibiting cyclical patterns. o Hybrid approaches combining advanced models like CatBoost with simpler models such as Linear Regression could enhance robustness and interpretability. 3. Exploring External Factors: Including additional external variables (e.g., economic indicators, weather data) may provide deeper insights and increase forecast precision. 4. Practical Implementation: Policymakers and stakeholders in the energy sector are encouraged to adopt machine learning tools for forecasting, as these models offer reliable predictions that can drive informed decision-making. Final Note This study demonstrates that machine learning models, particularly those aligned with temporal data structures and enhanced by seasonal adjustments, are invaluable tools for forecasting electricity prices. The findings underscore their relevance for stakeholders, offering reliable insights for decision-making and paving the way for future research that leverages advanced analytical techniques in the energy sector. References Abbasi, K., Abbas, J., & Tufail, M. (2021). Revisiting electricity consumption, price, and real GDP: A modified sectoral level analysis from Pakistan. 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ISBN: 9781003145714. https://doi.org/10.4324/9781003145714 Mohanty, S., Nanjundan, P., & Kar, T. (Eds.). (2024). Artificial Intelligence in Forecasting Tools and Techniques. CRC Press, Routledge, Taylor & Francis. ISBN: 9781032506159. https://doi.org/10.1201/9781003399292 Müller, A. C., & Guido, S. (2016). Introduction to Machine Learning with Python: A Guide for Data Scientists. 1st Edition, O'Reilly Media. ISBN: 9781449369415. https://www.amazon.com/Introduction-Machine-Learning-Python-Scientists/dp/1449369413 Osório, G., Lotfi, M., Shafie-Khah, M., Campos, V., & Catalão, J. (2018). Hybrid Forecasting Model for Short-Term Electricity Market Prices with Renewable Integration. Sustainability, 11(1), 57. https://doi.org/10.3390/SU11010057 Pustejovsky, J., & Stubbs, A. (2012). Natural Language Annotation for Machine Learning: A Guide to Corpus-Building for Applications. 1st Edition, O'Reilly Media. ISBN: 9781449306663. https://www.amazon.com/Natural-Language-Annotation-Machine-Learning/dp/1449306667 Shahbaz, M., Sarwar, S., Chen, W., & Malik, M. (2017). Dynamics of Electricity Consumption, Oil Price and Economic Growth: Global Perspective. Energy Policy, 108, 256–270. https://doi.org/10.1016/j.enpol.2017.06.006 Srivastava, P. K., & Yadav, K. A. (Eds.). (2024). Methodologies, Frameworks, and Applications of Machine Learning. IGI Global. ISBN: 9798369310625. https://www.amazon.com/Methodologies-Frameworks-Applications-Machine-Learning/dp/B0CNK7Z7ZY Wen, M., Zhou, C., & Konstantin, M. (2023). Deep Neural Network for Predicting Changing Market Demands in the Energy Sector for a Sustainable Economy. Energies, 16(5), 2407. https://doi.org/10.3390/en16052407 Additional Declarations The authors declare no competing interests. Supplementary Files ElectricityP2024.xlsx FED Electricty price Datasource.docx Data source Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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Average)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6298557/v1/3bb25b8ed7d170abbe8d88a5.png"},{"id":79403759,"identity":"de17d6f0-7bcd-4540-ac28-4777b18a06fc","added_by":"auto","created_at":"2025-03-28 03:23:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":89834,"visible":true,"origin":"","legend":"\u003cp\u003eElectricity Price Forecasts with CatBoost Regressor (Actual Data: January 1986–December 2020, Forecast Period: January 2021–January 2026)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6298557/v1/ab727d2f71eb8e56ee91d6d2.png"},{"id":79403787,"identity":"96c4fb20-8016-416f-a334-b04cdc97f246","added_by":"auto","created_at":"2025-03-28 03:23:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":92075,"visible":true,"origin":"","legend":"\u003cp\u003eElectricity Price Forecasts with Gradient Boosting Regressor (Actual Data: January 1986–December 2020, Forecast Period: January 2021–January 2026)\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6298557/v1/5720de43cb73b3807223af43.png"},{"id":79403769,"identity":"9c2498ce-7a13-4f0a-89af-9dd6866fb2ab","added_by":"auto","created_at":"2025-03-28 03:23:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":77579,"visible":true,"origin":"","legend":"\u003cp\u003eElectricity Price Forecasts with Linear Regression Incorporating Seasonality (Actual Data: January 1986–December 2020, Forecast Period: January 2021–January 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price\u003c/p\u003e","description":"","filename":"ElectricityP2024.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-6298557/v1/fa6afbc64788315238ed2b8d.xlsx"},{"id":79403739,"identity":"0e98a193-bfb3-47de-ac0c-b4698b2a1960","added_by":"auto","created_at":"2025-03-28 03:23:21","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":13465,"visible":true,"origin":"","legend":"\u003cp\u003eData source\u003c/p\u003e","description":"","filename":"Datasource.docx","url":"https://assets-eu.researchsquare.com/files/rs-6298557/v1/de3b9ae0de38e3607f20c55a.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eForecasting Electricity Price Index with Machine Learning Models and Strategies\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eForecasting electricity price indices is closely related to sustainable development and economic growth. The energy sector is at the center of sustainable development goals and includes many objectives such as increasing energy access, promoting clean fuels, reducing energy subsidies and limiting air pollution (Wen et al., 2023). At the same time, electricity consumption and prices are directly related to economic growth, and this relationship is particularly pronounced in developing countries (Shahbaz et al., 2017). Electricity consumption is recognized as an indicator of economic activity. \u0026nbsp; Therefore, accurate forecasting of electricity prices is critical for economic planning and sustainable development (Fan et al., 2020).\u003c/p\u003e\n\u003cp\u003eForecasting electricity prices is crucial for understanding the dynamics of energy markets and shaping energy policies. These forecasts can be used to adjust energy production and consumption models, support energy policy decisions, and optimize economic load dispatch (Fan et al., 2020). Moreover, this forecasting can help to develop energy efficiency strategies and diminish emission levels. Also, accurate forecasting of electricity prices creates a safer environment for investors by reducing uncertainty in energy markets, which in turn supports sustainable economic growth (Osório et al., 2018; Wen, et al. 2023). In this respect, electricity consumption and prices are directly related to economic growth, and this relationship is particularly pronounced in developing countries (Shahbaz et al., 2017). The energy sector is at the centre of sustainable development goals and includes many objectives such as increasing energy access, promoting clean fuels, reducing energy subsidies and limiting air pollution (Wen et al., 2023). Electricity consumption is recognized as an indicator of economic activity. \u0026nbsp;Since electricity consumption is considered an indicator of economic activity, accurate forecasting of electricity prices is critical for economic planning and sustainable development (Fan et al., 2020). At the same time, this forecast also facilitates the integration of renewable energy sources, enabling more efficient use of renewable energy resources and contributing to the development of sustainable energy policies (Abbasi et al., 2021). \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this context, the energy sector plays a critical role in both economic growth and sustainable development. Electricity price is an important factor in the electricity market, it can ensure the stable operation of the market, and electricity price forecasting has become the focus of attention of scholars from different countries (Kuo and Huang, 2018). Accurately predicting the future trends of electricity prices is of great importance for energy policymaking, cost management and long-term strategic planning.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this study, monthly data for the US economy for the period 1986-2020 are analyzed (forecast) and future electricity prices are projected for the period 2021-2026. \u0026nbsp;Ex-ante forecasts are based on data obtained from the Federal Reserve Economic Data (FRED). Accordingly, machine learning (ML) models provide powerful tools/analyses for predicting and forecasting future price movements based on historical data. Within the scope of the study, forecasts will be made using various ML models. The ML methods to be used are: CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor, Extra Trees Regressor, Decision Tree Regressor, K Neighbors Regressor, Light Gradient Boosting Machine, AdaBoost Regressor, Orthogonal Matching Pursuit, Linear Regression, Ridge Regression, Least Angle Regression, Bayesian Ridge, Huber Regressor, Elastic Net, Lasso Regression, Lasso Least Angle Regression, Dummy Regressor and Passive Aggressive Regressor.\u003c/p\u003e\n\u003cp\u003eThe ML models used in the study are of great importance in predicting the future trends of electricity prices. Each model has different algorithms, data processing strategies, and data processing and the ability to predict and forecast, which means that each model may perform differently under certain data types and conditions. Among the models used in this study, advanced tree-based models such as CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor and Light Gradient Boosting Machine offer the possibility to learn complex relationships and interactions within the data. In addition, linear models such as Linear Regression, Ridge Regression and Bayesian Ridge help to understand underlying trends and relationships by providing simpler and more interpretable results. Especially for time series data such as electricity prices, it is critical to be able to accurately predict future trends by learning from historical data. By comparing the performance of each model, it is possible to identify the model or models that can make predictions with the highest accuracy and reliability. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis paper aims to provide important findings in forecasting electricity prices in the energy sector. Accurately predicting the future trends of electricity prices plays a critical role in energy policymaking, economic planning and investment decisions. Electricity prices affect a wide range of economic activities, from industrial production to household consumption. Therefore, understanding the future movements of electricity prices is of strategic importance to ensure security of energy supply, manage costs and achieve sustainable development goals. The various ML models used in the analysis aim to provide valuable information to decision-makers and policymakers by offering innovative approaches to obtain the most accurate and reliable forecasts/predictions. Moreover, the findings of the study will both contribute to the academic literature and provide important information that can be used in practical applications.\u003c/p\u003e\n\u003cp\u003eIn this context, the study consists of four sections. After the introduction, there are sections on data and methodology, analysis findings, evaluation and discussion, and conclusions and recommendations.\u003c/p\u003e"},{"header":"Data and Methodology","content":"\u003cp\u003eIn the analysis, monthly data from the U.S. economy for the period 1986\u0026ndash;2020 was used to forecast electricity prices for the 2021\u0026ndash;2026 period. These forecasts were conducted using data obtained from the Federal Reserve Economic Data (FRED). The graphical representation of the data is presented in Figure 1.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Source:\u003c/strong\u003e FRED Economic Data, Average Price: Electricity per Kilowatt-Hour in U.S. City Average https://fred.stlouisfed.org/series/APU000072610\u003c/p\u003e\n\u003cp\u003eIn this context, machine learning (ML) models provide powerful tools for forecasting future price movements based on historical data. Various ML models were used in this study for forecasting purposes. The models considered in this study include:\u003c/p\u003e\n\u003cp\u003e\u0026middot; CatBoost Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Gradient Boosting Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Random Forest Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Extra Trees Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Decision Tree Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; K Neighbors Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Light Gradient Boosting Machine\u003c/p\u003e\n\u003cp\u003e\u0026middot; AdaBoost Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Orthogonal Matching Pursuit\u003c/p\u003e\n\u003cp\u003e\u0026middot; Linear Regression\u003c/p\u003e\n\u003cp\u003e\u0026middot; Ridge Regression\u003c/p\u003e\n\u003cp\u003e\u0026middot; Least Angle Regression\u003c/p\u003e\n\u003cp\u003e\u0026middot; Bayesian Ridge\u003c/p\u003e\n\u003cp\u003e\u0026middot; Huber Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Elastic Net\u003c/p\u003e\n\u003cp\u003e\u0026middot; Lasso Regression\u003c/p\u003e\n\u003cp\u003e\u0026middot; Lasso Least Angle Regression\u003c/p\u003e\n\u003cp\u003e\u0026middot; Dummy Regressor\u003c/p\u003e\n\u003cp\u003e\u0026middot; Passive Aggressive Regressor\u003c/p\u003e\n\u003cp\u003eThe monthly time-series data of the U.S. City Average for Electricity Price per Kilowatt-Hour (APU000072610) aims to be forecasted using these 19 ML models.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e1.1. Machine Learning Models:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eCatBoost Regressor:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A gradient boosting algorithm developed by Yandex, effective for categorical data and known for reducing overfitting.\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eGradient Boosting Regressor (GBR):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;An ensemble model that builds sequential decision trees to minimize prediction errors and is known for high forecasting performance.\u003c/p\u003e\n\u003cp\u003e3. \u003cstrong\u003eRandom Forest Regressor (RF):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;An ensemble of decision trees averaging predictions to improve model accuracy and robustness.\u003c/p\u003e\n\u003cp\u003e4. \u003cstrong\u003eExtra Trees Regressor (ET):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Similar to Random Forest Regressor but uses more randomized splits for individual trees, often yielding faster results.\u003c/p\u003e\n\u003cp\u003e5. \u003cstrong\u003eDecision Tree Regressor (DT):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A simple and interpretable model that splits data based on feature values for predictions.\u003c/p\u003e\n\u003cp\u003e6. \u003cstrong\u003eK Neighbors Regressor (KNN):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A non-parametric algorithm that predicts targets based on the average of the nearest data points.\u003c/p\u003e\n\u003cp\u003e7. \u003cstrong\u003eLight Gradient Boosting Machine (LIGHTGBM):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A highly efficient gradient boosting algorithm optimized for speed and memory usage.\u003c/p\u003e\n\u003cp\u003e8. \u003cstrong\u003eAdaBoost Regressor (ADA):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Combines multiple weak models (typically decision trees) into a strong model by adjusting weights based on past errors.\u003c/p\u003e\n\u003cp\u003e9. \u003cstrong\u003eOrthogonal Matching Pursuit (OMP):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A sparse linear regression method that selects a subset of features to make the best linear predictions.\u003c/p\u003e\n\u003cp\u003e10. \u003cstrong\u003eLinear Regression (LR):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A fundamental, interpretable model that fits a linear relationship between target and features.\u003c/p\u003e\n\u003cp\u003e11. \u003cstrong\u003eRidge Regression (RIDGE):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A regularized linear regression method that adds an L2 penalty to reduce overfitting.\u003c/p\u003e\n\u003cp\u003e12. \u003cstrong\u003eLeast Angle Regression (LAR):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A stepwise algorithm that builds the model incrementally by adding features in order of importance.\u003c/p\u003e\n\u003cp\u003e13. \u003cstrong\u003eBayesian Ridge (BR):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A probabilistic linear regression model that estimates coefficient distributions for improved generalization.\u003c/p\u003e\n\u003cp\u003e14. \u003cstrong\u003eHuber Regressor (HUBER):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Combines squared and absolute errors, making it robust to outliers.\u003c/p\u003e\n\u003cp\u003e15. \u003cstrong\u003eElastic Net (EN):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Balances feature selection and regularization by combining L1 (Lasso) and L2 (Ridge) penalties.\u003c/p\u003e\n\u003cp\u003e16. \u003cstrong\u003eLasso Regression:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Adds an L1 penalty to linear regression, shrinking some coefficients to zero for feature selection.\u003c/p\u003e\n\u003cp\u003e17. \u003cstrong\u003eLasso Least Angle Regression (LLAR):\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Similar to LAR but includes an L1 penalty for regularization.\u003c/p\u003e\n\u003cp\u003e18. \u003cstrong\u003eDummy Regressor:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;A baseline model that makes simple predictions, such as using the mean or median of the data.\u003c/p\u003e\n\u003cp\u003e19. \u003cstrong\u003ePassive Aggressive Regressor:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;An online learning algorithm that updates the model only when predictions are incorrect, designed for large-scale data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e1.2. Classification of ML Models:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe ML models can be categorized as follows:\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eEnsemble Learning Models:\u003c/strong\u003e CatBoost Regressor, Gradient Boosting Regressor, Random Forest Regressor, Extra Trees Regressor, AdaBoost Regressor, Light Gradient Boosting Machine.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eLinear Models:\u003c/strong\u003e Linear Regression, Ridge Regression, Bayesian Ridge, Elastic Net, Lasso Regression, Lasso Least Angle Regression, Orthogonal Matching Pursuit, Least Angle Regression.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eTree-Based Models:\u003c/strong\u003e Decision Tree Regressor.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eDistance-Based Models:\u003c/strong\u003e K Neighbors Regressor.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eRobust and Regularized Models:\u003c/strong\u003e Huber Regressor, Passive Aggressive Regressor.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eBaseline Model:\u003c/strong\u003e Dummy Regressor.\u003c/p\u003e\n\u003cp\u003eThis classification aids in understanding the diversity of algorithms and selecting the best model based on dataset characteristics and computational constraints.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.\u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eAnalysis Results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo execute machine learning programs, various fold strategies in machine learning programming (e.g., k-fold, stratified k-fold, group k-fold, and time series) were employed. In this study, the \u003cstrong\u003eTimeSeriesSplit strategy\u003c/strong\u003e was primarily used, with the \u003cstrong\u003ek-fold strategy\u003c/strong\u003e applied for comparison purposes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e is most suitable for time-series data, as it splits the data sequentially, ensuring that training data precedes test data. This structure prevents future information from leaking into the training set, providing a realistic validation scenario for forecasting. On the other hand, the k-fold strategy randomly splits the data into k folds, potentially mixing past and future data in training and test sets.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.1. Forecasting Without Considering Seasonality: Using Fold_Strategy = \u0026apos;TimeSeries\u0026apos;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1:\u003c/strong\u003e Summary of Model Training Setup for Time Series Regression with Fold_Strategy = \u0026apos;TimeSeries\u0026apos;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValue\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eSession id\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e123\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTarget\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eElectricityP\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTarget type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eRegression\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eOriginal data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed train set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(384, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed test set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(36, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eNumeric features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003ePreprocess\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eImputation type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003esimple\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eNumeric imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emean\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eCategorical imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emode\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransform target\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransform target method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eyeo-johnson\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eFold Generator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTimeSeriesSplit\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eFold Number\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eCPU Jobs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eUse GPU\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eLog Experiment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eExperiment Name\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003ereg-default-name\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eUSI (Unique Session Identifier)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e2b3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTable 1 provides an overview of the data preprocessing and model training setup, likely implemented using a library like PyCaret or similar frameworks.\u003c/p\u003e\n\u003cp\u003eKey highlights include:\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eTarget Variable:\u003c/strong\u003e \u0026quot;ElectricityP\u0026quot; indicates the target to be predicted.\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eFold Strategy:\u003c/strong\u003e The \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e strategy was employed to align with the sequential nature of time-series data.\u003c/p\u003e\n\u003cp\u003e3. \u003cstrong\u003eData Shape:\u003c/strong\u003e The training set comprises 384 rows, while the test set contains 36 rows, maintaining the original dimensions of the dataset.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2 Comparison of Regression Model Performance\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u003c/strong\u003e Comparison of Regression Model Performance Metrics for Electricity Price Series\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAbbreviation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSLE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAPE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTT (Sec)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003ecatboost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eCatBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0081\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0093\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0690\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1.1033\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003egbr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eGradient Boosting Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0083\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0105\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0706\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0567\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003erf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eRandom Forest Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0083\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0715\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.1300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eet\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eExtra Trees Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0087\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0109\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0098\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0736\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.1100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003edt\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eDecision Tree Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0088\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0766\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eknn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eK Neighbors Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0089\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0775\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003elightgbm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eLight Gradient Boosting Machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0092\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0779\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eada\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eAdaBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0914\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0733\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eomp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eOrthogonal Matching Pursuit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0127\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1055\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003elr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eLinear Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e2.7833\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eridge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1.9533\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003elar\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eLeast Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0367\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003ebr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eBayesian Ridge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003ehuber\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eHuber Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0169\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0467\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003een\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eElastic Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0248\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1850\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0367\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003elasso\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eLasso Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e2.1667\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003ellar\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eLasso Least Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0400\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003edummy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003eDummy Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0267\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003epar\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27px;\"\u003e\n \u003cp\u003ePassive Aggressive Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0908\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0915\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.0861\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.8129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eKey observations:\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eBest Model:\u003c/strong\u003e CatBoost Regressor achieves the lowest \u003cstrong\u003eMean Absolute Error (MAE)\u003c/strong\u003e of 0.0081, indicating its high accuracy.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eTraining Time:\u003c/strong\u003e Models like Gradient Boosting Regressor and Extra Trees Regressor exhibit faster training times compared to CatBoost.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eLinear Regression:\u003c/strong\u003e While computationally efficient, its performance lags behind advanced tree-based models in terms of prediction accuracy.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.3 Forecasted Electricity Prices for the 2021\u0026ndash;2026 Period:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3.\u003c/strong\u003e Forecasted Electricity Prices (2021-01 to 2026-01)\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMonth\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eyear\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSeries\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eForecast Value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e421\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135273\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e422\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135813\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135720\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e424\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135684\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e425\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.137136\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 118px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e..\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 112px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 121px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 124px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 129px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026hellip;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e477\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.142297\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.137968\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135854\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e480\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135880\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 118px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 121px;\"\u003e\n \u003cp\u003e2026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e481\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e0.135273\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNote: [61 rows x 5 columns]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.4. Forecasting Using Fold_Strategy = \u0026apos;k-fold\u0026apos;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAlthough \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e was preferred for time-series data, the \u003cstrong\u003ek-fold strategy\u003c/strong\u003e was also applied for comparison purposes in this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4.\u003c/strong\u003e Summary of Model Training Setup for Time Series Regression with Fold_Strategy = \u0026apos;k-fold\u0026apos;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValue\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eSession id\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e123\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTarget\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eElectricityP\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTarget type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eRegression\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eOriginal data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed train set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(384, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransformed test set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(36, 4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eNumeric features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003ePreprocess\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eImputation type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003esimple\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eNumeric imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emean\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eCategorical imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emode\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransform target\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eTransform target method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eyeo-johnson\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eFold Generator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eKFold\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eFold Number\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eCPU Jobs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eUse GPU\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eLog Experiment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eExperiment Name\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003ereg-default-name\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 54px;\"\u003e\n \u003cp\u003eUSI (Unique Session Identifier)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e0632\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe \u003cstrong\u003ek-fold strategy\u003c/strong\u003e divides data into k equal subsets, randomly mixing past and future data within training and test sets. While this approach increases model diversity during training, it may allow future data to influence training stages, leading to potential data leakage.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 5.\u003c/strong\u003e Comparison of Regression Model Performance Metrics with Fold_Strategy = \u0026apos;k-fold\u0026apos;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAbbreviation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSLE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAPE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTT(Sec)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003egbr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eGradient Boosting Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0146\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1244\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0767\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ecatboost\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eCatBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0146\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1262\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1.1633\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eada\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eAdaBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0151\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0136\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1237\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0767\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003elightgbm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eLight Gradient Boosting Machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0153\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0138\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1252\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0633\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003erf\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eRandom Forest Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0155\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1292\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.1433\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eet\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eExtra Trees Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1317\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.1267\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eknn\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eK Neighbors Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0138\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0158\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0142\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1325\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003edt\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eDecision Tree Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0146\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0168\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0151\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1436\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eridge\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0201\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1961\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003elar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eLeast Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0201\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1961\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0367\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eomp\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eOrthogonal Matching Pursuit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0201\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1961\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003elr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eLinear Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0201\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1961\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0367\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ebr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eBayesian Ridge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0193\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0201\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1961\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ehuber\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eHuber Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0202\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0210\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.2050\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0467\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003elasso\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eLasso Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0204\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0213\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1790\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0367\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ellar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eLasso Least Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0204\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0213\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1790\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003een\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eElastic Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0217\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0225\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0203\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.1929\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003edummy\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003eDummy Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0289\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0262\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.2693\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u003cstrong\u003epar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 34px;\"\u003e\n \u003cp\u003ePassive Aggressive Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 6px;\"\u003e\n \u003cp\u003e0.0701\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8px;\"\u003e\n \u003cp\u003e0.0070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.0707\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0663\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.6194\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.0333\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eObservations:\u003c/p\u003e\n\u003cp\u003e\u0026middot; The \u003cstrong\u003eGradient Boosting Regressor\u003c/strong\u003e outperformed others in this setup with the lowest \u003cstrong\u003eMAE\u003c/strong\u003e (0.0128).\u003c/p\u003e\n\u003cp\u003e\u0026middot; Models like \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e maintained competitive performance but required longer training times.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Compared to \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e, models trained with k-fold strategy showed slightly less reliability due to potential data leakage.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 6.\u003c/strong\u003e Forecasted Electricity Prices for the 2021\u0026ndash;2026 Period Using k-fold Strategy\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003eMonth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003eYear\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003eSeries\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003eForecast value\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e421\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135902\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e422\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135902\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135902\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e424\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135902\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e425\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.136380\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e..\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e477\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.141396\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.136966\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135521\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e480\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135521\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e2026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 127px;\"\u003e\n \u003cp\u003e481\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e0.135902\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eNote: [61 rows x 5 columns]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3. Incorporating Seasonality in Forecasting Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo improve the accuracy of forecasts, \u003cstrong\u003eseasonality parameters\u003c/strong\u003e were integrated into the models. Seasonality reflects the cyclic patterns inherent in electricity prices.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 7:\u003c/strong\u003e Summary of Model Training Setup with TimeSeriesSplit Strategy Incorporating Seasonality\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValue\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eSession id\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e123\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTarget\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eElectricityP\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTarget type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eRegression\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eOriginal data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTransformed data shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(420, 17)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTransformed train set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(384, 17)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTransformed test set shape\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e(36, 17)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eNumeric features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eCategorical features\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003ePreprocess\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eImputation type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003esimple\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eNumeric imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emean\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eCategorical imputation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003emode\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMaximum one-hot encoding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eEncoding method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eNone\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTransform target\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTrue\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eTransform target method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eyeo-johnson\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eFold Generator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eTimeSeriesSplit\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eFold Number\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eCPU Jobs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003e-1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eUse GPU\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eLog Experiment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003eFalse\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eExperiment Name\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003ereg-default-name\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eUSI (Unique Session Identifier)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 35px;\"\u003e\n \u003cp\u003ee4d7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eBy incorporating seasonality through transformations like sine and cosine functions, models captured cyclical trends in electricity prices more effectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 8:\u003c/strong\u003e Comparison of Regression Model Performance Metrics with Seasonality Consideration\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eAbbreviation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eModel\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSLE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAPE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eTT (Sec)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003elr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLinear Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0777\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e2.8633\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eridge\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0775\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e1.9267\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003elar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLeast Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0777\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0733\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ebr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eBayesian Ridge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0776\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ehuber\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eHuber Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0780\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0733\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003egbr\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eGradient Boosting Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0081\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0093\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0693\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0933\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eet\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eExtra Trees Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0083\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0094\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1467\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003erf\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eRandom Forest Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0084\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0096\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0715\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003edt\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eDecision Tree Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0085\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0097\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0732\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0600\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ecatboost\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eCatBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0097\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0726\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e1.2867\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eknn\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eK Neighbors Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0089\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0768\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0967\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003elightgbm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLight Gradient Boosting Machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0776\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0867\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eada\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eAdaBoost Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0110\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0119\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1033\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eomp\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eOrthogonal Matching Pursuit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0141\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0127\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1055\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0567\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003een\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eElastic Net\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0248\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1850\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0633\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003elasso\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLasso Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e2.1667\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ellar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLasso Least Angle Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0667\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003edummy\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eDummy Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0233\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.1899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0533\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003epar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003ePassive Aggressive Regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0908\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0095\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0915\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0861\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.8129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0533\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eKey Takeaways:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026middot; Models with seasonality outperformed those without, highlighting the importance of capturing cyclical trends.\u003c/p\u003e\n\u003cp\u003e\u0026middot; \u003cstrong\u003eLinear Regression\u003c/strong\u003e achieved strong performance, emphasizing its reliability when paired with seasonal adjustments.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Advanced models like \u003cstrong\u003eGradient Boosting Regressor\u003c/strong\u003e and \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e maintained their competitive edge.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 9.\u003c/strong\u003e Forecasted Electricity Prices (2021\u0026ndash;2026) with Seasonality Considered\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDate\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eYear\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMonth\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSeries\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSin_ay\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCos_ay\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eForecast Value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2021-01-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e420\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e5.000000e-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e8.660254e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.153708\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2021-02-01 \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e421\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e8.660254e-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e5.000000e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.152718\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2021-03-01 \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e422\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e1.000000e+00 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e6.123234e-17 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.153471\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2021-04-01 \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e8.660254e-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e-5.000000e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.153120\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2021-05-01 \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e424\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e5.000000e-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e-8.660254e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.156245\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e\u0026hellip;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2025-09-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e476\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e-1.000000e+00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e-1.836970e-16 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.223228\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2025-10-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e477\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e-8.660254e-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e5.000000e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.192464\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2025-11-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e-5.000000e-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e8.660254e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.182693\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2025-12-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e479\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e-2.449294e-16 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e1.000000e+00 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.183032\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e2026-01-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 65px;\"\u003e\n \u003cp\u003e480\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e5.000000e-01 \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e8.660254e-01 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 83px;\"\u003e\n \u003cp\u003e0.188493\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eNote: [61 rows x 5 columns]\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"Evaluation and Discussion","content":"\u003cp\u003eThe results of the study demonstrate the effectiveness of using machine learning (ML) techniques to forecast U.S. electricity prices based on historical data from January 1986 to December 2020. By comparing the performance of 19 different ML models using both \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e and \u003cstrong\u003ek-fold strategies\u003c/strong\u003e, significant differences in forecasting capabilities were observed. Key insights from the evaluation include:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(i) TimeSeriesSplit Analysis:\u003c/strong\u003e \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e proved highly suitable for time-series data, respecting the sequential nature of observations and ensuring reliable predictions.\u003c/p\u003e\n\u003cp\u003e· The \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e performed exceptionally well, achieving superior accuracy in terms of Mean Absolute Percentage Error (MAPE).\u003c/p\u003e\n\u003cp\u003e· Despite its simplicity, the \u003cstrong\u003eLinear Regression model\u003c/strong\u003e provided forecasts closely aligned with actual trends during the out-of-sample prediction period (2021:1–2026:1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(ii) Comparison with k-fold Strategy:\u003c/strong\u003e While the \u003cstrong\u003ek-fold strategy\u003c/strong\u003e offered diversity in model training, it showed limitations due to the risk of future data influencing training (data leakage).\u003c/p\u003e\n\u003cp\u003e· Models like \u003cstrong\u003eGradient Boosting Regressor\u003c/strong\u003e and \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e maintained competitive performance metrics under the k-fold approach.\u003c/p\u003e\n\u003cp\u003e· However, the reliability of forecasts was marginally lower compared to models trained using the \u003cstrong\u003eTimeSeriesSplit strategy\u003c/strong\u003e, especially for time-sensitive data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(iii) Incorporating Seasonality:\u0026nbsp;\u003c/strong\u003eAccounting for seasonality significantly improved the accuracy of forecasts, underscoring the cyclical nature of electricity prices.\u003c/p\u003e\n\u003cp\u003e· When variables like sine and cosine transformations were included, models effectively captured seasonal patterns, resulting in predictions that closely matched observed data.\u003c/p\u003e\n\u003cp\u003e· Both \u003cstrong\u003eLinear Regression\u003c/strong\u003e and \u003cstrong\u003eGradient Boosting Regressor\u003c/strong\u003e performed remarkably well when seasonality adjustments were integrated.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eKey Findings:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e1. \u003cstrong\u003eTop Performing Models:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eo The \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e and \u003cstrong\u003eLinear Regression\u003c/strong\u003e models emerged as the most effective in terms of accuracy and computational efficiency.\u003c/p\u003e\n\u003cp\u003eo \u003cstrong\u003eLinear Regression\u003c/strong\u003e, though simple, demonstrated robust performance with minimal errors, particularly when combined with the \u003cstrong\u003eTimeSeriesSplit strategy\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003e2. \u003cstrong\u003eImportance of Strategy Alignment:\u003c/strong\u003e\u003cbr\u003eSelecting fold strategies that align with the sequential nature of the data (e.g., \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e) was crucial for preserving the integrity of the forecasting process and enhancing model performance.\u003c/p\u003e\n\u003cp\u003e3. \u003cstrong\u003eRole of Seasonality:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Incorporating seasonality using cyclical transformations (e.g., sine and cosine) improved model performance, enabling better alignment with real-world data patterns.\u003c/p\u003e\n\u003cp\u003e4. \u003cstrong\u003eRecommendations for Future Work:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eo Explore hybrid model approaches that combine the strengths of different algorithms (e.g., blending tree-based models with linear models).\u003c/p\u003e\n\u003cp\u003eo Integrate additional external variables such as economic indicators or weather data to enhance the granularity of forecasts.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSummary of Practical Implications:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe findings emphasize the potential of machine learning models, particularly when paired with suitable strategies and seasonality considerations, as reliable tools for electricity price forecasting. This has significant implications for stakeholders in the energy sector, including policymakers, investors, and operational planners. Accurate forecasts can aid in:\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003ePolicy Development:\u003c/strong\u003e Informing energy policy decisions with reliable price trends.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eEconomic Planning:\u003c/strong\u003e Optimizing cost management and investment strategies.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eSustainability Goals:\u003c/strong\u003e Supporting renewable energy integration and emission reduction initiatives.\u003c/p\u003e\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"},{"header":"Conclusion and Recommendations","content":"\u003cp\u003eThis study aimed to forecast U.S. electricity prices for the 2021–2026 period using 19 different machine learning (ML) models. It compared predictions both with and without incorporating seasonality and utilized various fold strategies, such as \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e and \u003cstrong\u003ek-fold\u003c/strong\u003e, to ensure comprehensive analysis. The effectiveness of the models was validated through metrics such as \u003cstrong\u003eMean Absolute Error (MAE)\u003c/strong\u003e, \u003cstrong\u003eRoot Mean Squared Logarithmic Error (RMSLE)\u003c/strong\u003e, and others.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eKey Results:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003e1. \u003cstrong\u003eTop Performers:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eo The \u003cstrong\u003eCatBoost Regressor\u003c/strong\u003e and \u003cstrong\u003eLinear Regression\u003c/strong\u003e models stood out as the most effective models overall.\u003c/p\u003e\u003cp\u003eo \u003cstrong\u003eLinear Regression\u003c/strong\u003e provided the best results in terms of simplicity, computational efficiency, and alignment with actual trends when paired with the \u003cstrong\u003eTimeSeriesSplit strategy\u003c/strong\u003e.\u003c/p\u003e\u003cp\u003e2. \u003cstrong\u003eImpact of Seasonality:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eo Models incorporating seasonality through sine and cosine transformations captured the cyclical behavior of electricity prices, enhancing forecast reliability.\u003c/p\u003e\u003cp\u003eo The \u003cstrong\u003eLinear Regression model\u003c/strong\u003e, combined with seasonality adjustments, aligned closely with observed data trends for the 2021–2026 period.\u003c/p\u003e\u003cp\u003e3. \u003cstrong\u003ePerformance Comparison:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eo Models trained using \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e outperformed those using \u003cstrong\u003ek-fold\u003c/strong\u003e, emphasizing the importance of choosing strategies suited to the sequential nature of time-series data\u003c/p\u003e\u003cp\u003e\u003cstrong\u003ePractical Contributions:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eThe study highlights the potential of machine learning models in addressing critical challenges in electricity price forecasting. Accurate forecasts can:\u003c/p\u003e\u003cp\u003e· Support \u003cstrong\u003eenergy policy development\u003c/strong\u003e by offering insights into future price fluctuations.\u003c/p\u003e\u003cp\u003e· Aid in \u003cstrong\u003eeconomic planning\u003c/strong\u003e through optimized cost management and strategic decision-making.\u003c/p\u003e\u003cp\u003e· Facilitate \u003cstrong\u003esustainable development goals\u003c/strong\u003e, such as integrating renewable energy and reducing market uncertainties.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eRecommendations for Future Research and Practice:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003e1. \u003cstrong\u003eModel Selection and Strategy Alignment:\u003c/strong\u003e\u003cbr\u003eFuture studies should prioritize fold strategies tailored to time-series data, such as \u003cstrong\u003eTimeSeriesSplit\u003c/strong\u003e, to maintain data integrity and improve prediction accuracy.\u003c/p\u003e\u003cp\u003e2. \u003cstrong\u003eEnhancing Model Performance:\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eo Incorporating \u003cstrong\u003eseasonality\u003c/strong\u003e through cyclical transformations should become standard practice when dealing with data exhibiting cyclical patterns.\u003c/p\u003e\u003cp\u003eo Hybrid approaches combining advanced models like \u003cstrong\u003eCatBoost\u003c/strong\u003e with simpler models such as \u003cstrong\u003eLinear Regression\u003c/strong\u003e could enhance robustness and interpretability.\u003c/p\u003e\u003cp\u003e3. \u003cstrong\u003eExploring External Factors:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Including additional external variables (e.g., economic indicators, weather data) may provide deeper insights and increase forecast precision.\u003c/p\u003e\u003cp\u003e4. \u003cstrong\u003ePractical Implementation:\u003c/strong\u003e\u003cbr\u003e\u0026nbsp;Policymakers and stakeholders in the energy sector are encouraged to adopt machine learning tools for forecasting, as these models offer reliable predictions that can drive informed decision-making. \u0026nbsp;\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eFinal Note\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eThis study demonstrates that machine learning models, particularly those aligned with temporal data structures and enhanced by seasonal adjustments, are invaluable tools for forecasting electricity prices. The findings underscore their relevance for stakeholders, offering reliable insights for decision-making and paving the way for future research that leverages advanced analytical techniques in the energy sector.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAbbasi, K., Abbas, J., \u0026amp; Tufail, M. (2021). Revisiting electricity consumption, price, and real GDP: A modified sectoral level analysis from Pakistan. \u003cem\u003eEnergy Policy, 149,\u003c/em\u003e 112087. https://doi.org/10.1016/j.enpol.2020.112087\u003c/li\u003e\n \u003cli\u003eFan, G., Wei, X., Li, Y., \u0026amp; Hong, W. (2020). Forecasting electricity consumption using a novel hybrid model. \u003cem\u003eSustainable Cities and Society, 61,\u003c/em\u003e 102320. https://doi.org/10.1016/j.scs.2020.102320\u003c/li\u003e\n \u003cli\u003eFRED, Federal Reserve Bank of St. Louis (2024). U.S. Bureau of Labor Statistics, Average Price: Electricity per Kilowatt-Hour in the U.S. City Average [APU000072610]. Retrieved from FRED, Federal Reserve Bank of St. Louis.\u003cbr\u003ehttps://fred.stlouisfed.org/series/APU000072610, November 5, 2024.\u003c/li\u003e\n \u003cli\u003eJung, J.-K., Patnam, M., \u0026amp; Ter-Martirosyan, A. (2018). \u003cem\u003eAn Algorithmic Crystal Ball: Forecasts Based on Machine Learning.\u003c/em\u003e International Monetary Fund. ISBN: 9781484380635. https://www.imf.org/en/Publications/WP/Issues/2018/11/01/An-Algorithmic-Crystal-Ball-Forecasts-based-on-Machine-Learning-46288\u003c/li\u003e\n \u003cli\u003eKazantsev, G., Creamer, G., \u0026amp; Aste, T. (Eds.). (2021). \u003cem\u003eMachine Learning and AI in Finance.\u003c/em\u003e Taylor \u0026amp; Francis. ISBN: 9781003145714. https://doi.org/10.4324/9781003145714\u003c/li\u003e\n \u003cli\u003eMohanty, S., Nanjundan, P., \u0026amp; Kar, T. (Eds.). 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(2012). \u003cem\u003eNatural Language Annotation for Machine Learning: A Guide to Corpus-Building for Applications.\u003c/em\u003e 1st Edition, O\u0026apos;Reilly Media. ISBN: 9781449306663. https://www.amazon.com/Natural-Language-Annotation-Machine-Learning/dp/1449306667\u003c/li\u003e\n \u003cli\u003eShahbaz, M., Sarwar, S., Chen, W., \u0026amp; Malik, M. (2017). Dynamics of Electricity Consumption, Oil Price and Economic Growth: Global Perspective. \u003cem\u003eEnergy Policy, 108,\u003c/em\u003e 256\u0026ndash;270. https://doi.org/10.1016/j.enpol.2017.06.006\u003c/li\u003e\n \u003cli\u003eSrivastava, P. K., \u0026amp; Yadav, K. A. (Eds.). (2024). \u003cem\u003eMethodologies, Frameworks, and Applications of Machine Learning.\u003c/em\u003e IGI Global. ISBN: 9798369310625. https://www.amazon.com/Methodologies-Frameworks-Applications-Machine-Learning/dp/B0CNK7Z7ZY\u003c/li\u003e\n \u003cli\u003eWen, M., Zhou, C., \u0026amp; Konstantin, M. (2023). Deep Neural Network for Predicting Changing Market Demands in the Energy Sector for a Sustainable Economy. \u003cem\u003eEnergies, 16(5),\u003c/em\u003e 2407. https://doi.org/10.3390/en16052407\u003c/li\u003e\n\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":"Machine Learning, ML Algorithm, Electricity Price Index, Forecasting, Prediction Accuracy Metrics.","lastPublishedDoi":"10.21203/rs.3.rs-6298557/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6298557/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eElectricity consumption is recognized as one of the fundamental indicators of economic activities. Accurate forecasting of electricity prices is therefore critical for economic planning and sustainable development. This research investigates the effectiveness of 19 different machine learning algorithms/models in forecasting the US electricity prices. It provides a comprehensive analysis by evaluating approaches that both include and exclude seasonality factors. Key findings of the study are as follows: (I) Linear Regression and CatBoost Regressor models delivered the best results in terms of accuracy and computational efficiency. (ii) The Linear Regression model using the TimeSeriesSplit strategy exhibited a high agreement with actual electricity price trends. (iii) Linear regression outperformed other models in metrics such as mean absolute error (MAE) and root mean squared logistic error (RMSLE).\u003c/p\u003e \u003cp\u003eThis study demonstrates that machine learning models can serve as effective tools for forecasting electricity prices and provide valuable recommendations for stakeholders in the energy sector. Especially when appropriate strategies for temporal data structures are applied, these models can offer reliable predictions. Eventually, this paper highlights that machine learning models are an important tool for stakeholders and policymakers in the energy sector, helping to predict electricity price fluctuations and contributing to the decision-making process.\u003c/p\u003e","manuscriptTitle":"Forecasting Electricity Price Index with Machine Learning Models and Strategies","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-28 03:23:06","doi":"10.21203/rs.3.rs-6298557/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":"5626b3cb-198f-4912-a58e-7ee332108360","owner":[],"postedDate":"March 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":46151368,"name":"Artificial Intelligence and Machine Learning"},{"id":46151369,"name":"Econometrics"},{"id":46151370,"name":"Macroeconomics"},{"id":46151371,"name":"Applied Statistics"},{"id":46151372,"name":"City Management and Urban Policy"}],"tags":[],"updatedAt":"2025-03-28T03:23:06+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-28 03:23:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6298557","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6298557","identity":"rs-6298557","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}