Electricity price forecast in wholesale markets using conformal prediction: Case study in Mexico

In recent years, machine and deep learning models have attracted significant attention for electricity price forecast in global wholesale electricity markets. Yet, a predominant focus on point forecast in most parts of literature limits the practical application of these models due to the absence of uncertainty quantification. In this study, we first perform an analysis of the electricity price trends in the Mexican wholesale electricity market to determine the influence of key variables. Using independent component analysis and wavelet coherence analysis, we were able to identify primary determinants influencing locational marginal electricity prices. Subsequently, we applied four different models covering the most important algorithms proposed in the literature for electricity price forecast. Our findings revealed that the most accurate forecasting results were achieved using a deep learning‐based method with a decision tree‐based model trailing closely. Finally, we incorporate conformal prediction for uncertainty quantification by calculating the prediction intervals with a target coverage level of 95%. The conformal prediction intervals provide a more comprehensive view of the possible future scenarios, enhancing economic efficiency, risk management, and decision‐making processes. This is particularly important because of the dynamic nature of electricity markets, where prices are strongly influenced by multiple factors.

about consumption patterns, investment in renewable energy, and potential cost savings, this task has been revealed to be particularly difficult as multiple challenges have to be overcome.The first major issue is the tunning of any proposed forecast model as electricity price is affected by multiple factors like fuel prices, energy demand, currency exchange rates, and renewable sources just to name a few, thus it reveals necessary to perform a careful analysis of the impact of each variable on the electricity price to make a selection and simplify any model that could be proposed for forecast.Another challenge for EPF is the availability and quality of data.Although most energy markets generate a vast amount of data, including historical price data, weather data, economic indicators, and consumer demand data they are often incomplete, inconsistent, and prone to measurement errors.In addition, data from different sources may be incompatible, making it difficult to integrate and analyze.Thus, to overcome these challenges, researchers have explored various techniques such as data cleaning, data normalization, and feature engineering to improve the quality and compatibility of data.
One more important issue is the difficulty in comparing the performance of the multiple models proposed in the literature because the different conditions of each electrical market causing that any proposed forecast model should be adapted to those conditions.For example, most of the studies and models proposed for EPF in the literature are focused on the European and USA markets with both markets sharing some important characteristics like being based on a mix of regulated and competitive structures and also being competitive markets for the generation and sale of electricity.3][4] FDA is valued for its enhanced flexibility and depth in analyzing seasonal patterns, thus augmenting traditional time series methodologies and fostering a deeper understanding of the data.For instance, research documented in 4 applied FDA within the Spanish electricity market to devise model-based procedures for constructing prediction regions for daily demand curves and electricity prices, utilizing bootstrap algorithms and integrating both endogenous and exogenous functional variables, alongside exogenous scalar variables, within a functional response regression model.
Similarly, 2 introduced a functional autoregressive model for short-term price forecasting in electricity markets, which, by employing functional final prediction error (FFPE) for automatic selection of model dimensionality and lag structure, demonstrated superior efficacy over nonfunctional forecasting techniques in the Italian electricity market (IPEX).
Another strategy to mitigate the limitations of point forecast methods involves adopting conformal prediction (CP) to establish prediction intervals or regions, thereby quantifying forecasting uncertainty-a critical element in market participants' decision-making.Notably, the application of CP in EPF remains largely underexplored [5][6][7] with its potential for the Mexican wholesale market yet to be investigated.
In general, two schemes of electricity markets can be identified.The first scheme is the pool-type where trading, dispatch, and transmission are managed by the system operator whereas the second scheme is a power exchange type where trading and initial dispatch are managed by an institution independent from transmission system operator. 8Concerning the electricity price bidding the day-ahead (DA) and the real time (RT) markets are usually employed.In both bidding schemes, the electricity price is calculated using algorithms where the forecasted demand is satisfied by considering the supply biddings from market participants.Finally, the electricity price is calculated for each node of the network being defined as locational marginal price (LMP) or for a whole zone of the network zonal price (ZP) depending in the market regulations.
In Mexico, the wholesale electricity market is particularly influenced by the USA electricity market, thus a LMP nodal pricing in the day-ahead scheme is calculated by the National Energy Control Center (CENACE) using an algorithm. 9he Mexican electricity market supplies over 47 million users 10 and since 1992 has undergone significant changes, moving from a state-dominated, vertically integrated market to a more open and competitive market.Figure 1 shows a timeline with the major changes in the electrical market.
The electricity sector in Mexico is regulated by the Federal Electricity Commission (CFE) and the Energy Regulatory Commission (CRE).The CFE is responsible for electricity generation, transmission, and distribution, while the CRE oversees market regulation and promotes competition.Additionally, it is divided into two segments: the basic service segment and the free market segment.The basic service segment includes residential and small commercial customers and is served by the CFE.The free-market segment includes large commercial and industrial customers and is open to competition.| 525 Before 2013, the electricity market in Mexico was dominated by the CFE, which held a virtual monopoly on electricity generation, transmission, and distribution.However, in 2013, the Mexican government enacted a major energy reform, aimed at increasing competition and private investment in the energy sector.This reform opened up the electricity market to private companies, allowing them to participate in electricity generation, transmission, and distribution.
One of the major changes in the Mexican electricity market in the last decade was the promotion of renewable energy sources.The Mexican government set a target of generating 35% of the country's electricity from clean energy sources by 2024.To achieve this target, the government implemented various policies and incentives to promote renewable energy, including a Clean Energy Certificates (CEL) scheme and net metering regulations.Another significant change in the Mexican electricity market was the implementation of a wholesale electricity market (WEM) in 2016.The WEM is a platform where electricity producers and buyers can trade electricity, promoting competition and reducing electricity costs.The WEM is also designed to facilitate the integration of renewable energy sources into the grid.
However, in 2021 major changes to the electricity industry law were proposed.Specifically, it was proposed that the state-owned utility CFE has priority over private companies in the dispatch of electricity to the grid.This would mean that when there is excess capacity, the CFE would be given priority to sell its electricity before private companies.The CEL scheme was proposed to be modified and the government will have the authority to cancel or modify permits for private companies to generate and sell electricity, if their operations are deemed to jeopardize the reliability and safety of the national electricity system.To date, these modifications have not been implemented because of multiple legal battles and political debates over the issue.
The electrical market in Mexico provides energy to over 47 million users throughout the country.The system is divided into 10 main regions, 11 as depicted in Figure 2.Each region consists of multiple cities and connection nodes, which are defined as PNodes.
In this work, we conduct a pioneering and comprehensive analysis of the WEM in Mexico, employing a combination of advanced analytical techniques.These include independent component analysis, which uncovers hidden factors affecting market prices, and wavelet coherence analysis, offering insights into the frequency-based relationships within the data.Our approach integrates diverse forecasting models, such as boost tree-based methods (light gradient boosting machine [LGBM]), seasonal autoregressive integrated moving average (SARIMA), lasso estimated autoregressive (LEAR) models, and cutting-edge deep learning techniques (LSTM).This multifaceted methodology not only provides unique insights but also significantly enhances our ability to tackle the market's volatility and Major changes in the Mexican electrical market from 1992 to date.specific characteristics more effectively than prior studies.The comparative analysis of these methods reveals their individual and combined strengths, presenting a novel perspective on the dynamics of Mexico's electricity market.

| MATERIALS AND METHODS
The electricity day-ahead price data set for the Mexican market was obtained from the CENACE website. 12This organization is responsible for calculating the LMP and the distributed nodes price (DNP).Both prices are calculated in a day-ahead and real-time scheme for all connection nodes.While the data set covers the period from 2016 to the present day, the first 2 years (2016 and 2017) were found to contain numerous inconsistencies.As a result, we chose to use a subset of the data set that spans the timeframe from 2018 to 2023 for this work.
In this study, the LMP for region 3 was retrieved using the prices reported for node 03ACU-69.This connection node was selected because it belongs to the area (West) with the highest number of electricity users, according to the 2021 SENER report 13 and can be considered highly representative of the Mexican electricity market, as shown in Table 1.
F I G U R E 2 Mexican electrical system is divided into 10 control areas and each control area has multiple connection nodes (PNodes).For this work, the node 03ACU-69 located in area 3 (west region) was selected as is one of the most populated areas in Mexico.
Data set wrangling must be performed to adapt them for proper analysis with machine learning models.This involves removing irrelevant columns and filtering the datasets according to the specified connection node (03ACU-69).After this, a resampling was performed to obtain a daily-based timeframe.
Because electricity prices can be affected by multiple external variables like fuel prices, energy demand (ED), currency exchange rates, and renewable sources to name a few, a variable selection has to be made based on the impact of each one of them on the LMP.In our case 11 exogenous variables that could affect LMP were considered namely, natural gas price (NGP), ED, wind energy power, photovoltaic power, coal-fired power, combined cycle power, internal combustion power, hydroelectric power (HEP), nucleoelectric power, conventional thermoelectric power, and turbo gas power.
However, using all variables in the forecasting proposed models can be highly computationally expensive and probably the majority of those variables do not have a significant influence on electricity price behavior.Therefore, it was necessary to identify the most influential variables (features) on the target (LMP) and to do so we used an independent component analysis (ICA) 14 along with a wavelet coherence analysis (WCA). 15or EPF a great number of models have been proposed in the literature that in general can be classified into classical, 16,17 deep learning/machine learning, 18 or hybrid models. 19In our case, we selected four different models representing those with the best results reported in the literature.The first selected model was the SARIMA.The second model was a LEAR method while the third tested model was a LGBM method.Finally, the fourth model was a hybrid model namely a multivariate long short-term memory (MVLSTM) network with previous filtering of the data set using Discrete Wavelet Transform (DWT).
In this study, one model from each category was selected for EPF as described in Table 2.
The metrics used for comparison and evaluation of the different models were the mean absolute error (MAE), relative mean absolute error (rMAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (sMAPE).The equations for calculation of each metric are shown below: Using conformal prediction to calculate prediction intervals (PIs) as opposed to relying solely on typical point forecasts can provide several advantages from an economic and decision-making perspective like the possibility to have a more precise risk management for investors and stakeholders and for energy producers the knowing of possible future prices range can help them to take better decisions about electricity production.In our case, we take advantage that conformal PIs offer an additional dimension for model comparison.Two models might provide similar point forecasts, but one might consistently give narrower prediction intervals, indicating higher precision.In this work, PIs were calculated using the ensemble batch prediction intervals (EnbPI) method with a target coverage level of 95%.This method uses bootstrap ensemble estimators to construct sequential prediction intervals as described in Xu and Xie. 20he computational algorithm unfolds through a series of meticulously structured steps, beginning with data preparation and cleaning, and culminating in the evaluation of forecasting accuracy.Initially, essential Python libraries are loaded to facilitate model construction and data analysis.This is followed by the importation of raw data from CSV files, the removal of noninfluential columns, the conversion of date formats, and the establishment of time-based indices for the data set.A custom Python function is then crafted for the calculation of statistical metrics, setting the stage for the division of the data set into training and testing subsets.This division is critical for preventing lookahead bias and ensuring the model's performance is assessed under unseen conditions.
Subsequently, the algorithm advances to the model selection phase, where a choice is made from among several forecasting models, including SARIMA, LGBM, LEAR, and LSTM networks.Depending on the model selected, specific preprocessing steps are undertaken, such as wavelet decomposition for LSTM models or the creation of lag-type features for LGBM, aimed at enhancing model accuracy by capturing autocorrelation and the influence of past prices.
The core of the algorithm lies in training the chosen model with the prepared data set and employing the trained model to make predictions on the test set.Postprediction steps involve scaling the predicted data back to its original dimensions, if necessary, and visualizing the forecast results alongside actual data for comparative analysis.Additionally, the algorithm incorporates the calculation of prediction intervals using the MAPIE library, offering a quantitative measure of forecast uncertainty.The culmination of the process is the computation and evaluation of statistical metrics for both prediction points and intervals, such as MAE, root mean squared error (RMSE), and MAPE, among others.These metrics serve as a benchmark for assessing the model's predictive performance and the reliability of its forecasts.
A detailed flowchart of this comprehensive process is illustrated in Figure 3, providing a visual representation that enhances understanding of the methodological framework employed in this study.

| RESULTS
The results obtained from ICA and WCA are presented.

| ICA
The ICA analysis can extract useful information from the target time series by decomposing it and identifying the contribution of each one of the features time series.ICA can be also used as a dimensionality reduction algorithm as it allows to ignore or retain a particular time series of interest.ICA can be considered as an extension of the principal component analysis (PCA) technique.However, PCA optimizes the covariance matrix while ICA optimizes higher-order statistics such as kurtosis.Hence, PCA finds uncorrelated components while ICA finds independent components.
The theory of ICA is detailed explained in Maciejowska et al. 8 Here, we summarize for our case of multiple time series (features) influencing on one time series (target).Consider two time series TS 1 and TS 2 that can be represented as: Where N is the number of time steps of the series.The time series can then be mixed as: (7) where a and b are the mixing coefficients while ×1 is one mixture of TS1 and TS2.On the other hand, c and d are also mixing coefficients with values different to the previously described (a and b) whereas ×2 is a different mixture of TS1 and TS2 thus each time series has different consequence on target.Both mixtures can be expressed as: where X is the target time series, s is features time series vector and A is the mixing coefficients matrix.The results obtained from the ICA analysis are reported in the correlogram depicted in Figure 4.
ICA analysis was performed using FastICA library for Python and all the time series were previously scaled and differentiated to have deseasonalized data as required.
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This analysis revealed that NGP, ED, and HEP have the highest correlation on LMP.Furthermore, among those three variables is NGP who by far has the stronger correlation with LMP.This is quite significative as, based on these findings, it can be proposed that a forecast models can consider a fewer number of variables to obtain a good precision for EPF.Even more, it can be assumed that using NGP as the sole exogenous variable could produce a good LMP forecasting accuracy and this will be our approach for the remaining analysis.

| WCA
WCA helps to reveal the strength and direction of the relationship between LMP and each one of the exogenous variables.This analysis can be particularly useful for analyzing nonstationary and nonlinear relationships that may not be easily detected using other methods.
The detailed explanation of WCA was presented by Liu et al. 9 where they considered that given two time series X(t) and Y(t), with wavelet transforms WX(s,τ) and WY(s,τ), the cross-wavelet spectrum can be defined as: XY (10)   While the complex-valued wavelet coherency can be described by: F I G U R E 3 Flowchart of the methodological framework employed in this study for electricity price forecasting.
And the real valued wavelet coherency can be described by: To gain a deeper understanding of the relationships between the selected exogenous variable and the LMP, a WCA analysis was conducted.Figure 5 shows the wavelet coherence spectrum along with the global wavelet spectrum.
This analysis confirms the strong correlation between LMP and NGP for a 107-day period between mid-2020 thru 2022.The correlation is visible for almost all the analyzed period of time.
Once the exogenous variable was properly identified, the forecast can be performed using each one of the proposed models described previously in Table 2.However, before any model could be applied the LMP and NGP datasets have to be split by defining the training period from January 01, 2020 through December 31, 2021, while the test period was defined from January 01, 2022 through December 31, 2022, as shown in Figure 6 and the outliers were processed by imputing the mean value of the adjacent values.Two important spikes around October 2020 and march 2021 are clearly visible, as reported in the literature 21 those spikes are caused by big differences between demand and supply which are rapidly reflected in day-ahead spot prices in electricity markets.
For the particular case of hybrid model the training data set was preprocessed by decomposing the data set using a DWT before it can be used in the model.In this study, we evaluated only three wavelet types namely Daubechies, Symlets, and Coiflets, as they are the most commonly used for time series decomposition.To identify the appropriate mother wavelet to be used for decomposition, it is necessary to calculate the maximum amount of energy extracted from the time series by the wavelet while minimizing the Shannon entropy.Therefore, the three proposed wavelets were compared using the energy-to-Shannon Entropy ratio (ESR), defined by Equations ( 6), (7), and ( 8).
In this case, a fifth order with five levels of decomposition was selected for each wavelet, as these conditions show a good balance between detail signal conservation and signal smoothing.Table 3 shows the results for the three main mother wavelets proposed.
The highest value of the energy-shannon entropy ratio (ESR) was obtained for the Daubechies wavelet, and therefore this is the one that will be used for wavelet transformation.It can be noticed that this result is consistent with those observed by Chang et al. 19 The results of this decomposition are the coefficients identified as approximation (cA) and detailed (cD).Figures 7  and 8 show the decomposition results of the electricity and natural gas series, respectively.
After the decomposition of both time series, the signals were reconstructed by eliminating the highest frequency component (cD1), based on the consideration that this component does not have a significant amount of information and only represents noise.Finally, both reconstructed signals are ready to be used as training datasets for the hybrid model.

| Forecasting with SARIMAX model
In the case of classical statistical category, a SARIMAX model was used to forecast the LMP.The results are shown in Figure 9 with PIs shown as the gray area.The  4. In this case, the 82% PIs coverage level obtained is well below the 95% target proposed.

| Forecasting with LEAR model
The second model used for EPF was the LEAR model as multiple research groups have reported good precision. 22,23n our case, as observed from the curve comparison between EPF and test data set plotted in Figure 10 and the evaluation metrics described in Table 5, the model does not show a very good precision because a substantial difference between forecast data and test data is observed for the most part of the year and it is only towards the last F I G U R E 8 Discrete wavelet decomposition of natural gas price data set using fifth order Daubechies wavelet.
trimester of the year when this difference is reduced.This discrepancy is further confirmed by the high rMAE and sMAPE values obtained.This poor performance of the model could be explained by an overfitting effect of the LEAR model due to the limited quantity of data available for model training (only 2 years) thus causing that the model performs well on the training data but poorly on unseen test data.Additionally, the 84% PIs coverage is rather poor regarding the 95% required.
The error metrics obtained for the LEAR model are shown in Table 5.

| Forecasting with LGBM model
The LGBM, or Light Gradient Boosting Machine, represents our third model choice for EPF.As a decision tree-based gradient boosting framework, LGBM facilitates efficient and effective learning through its hierarchical tree structure, where internal nodes signify features, branches denote decision rules, and leaf nodes indicate outcomes.The model excels in handling both numerical and categorical data with minimal preprocessing, offering intuitive visualization and interpretation.However, it requires careful tuning to mitigate overfitting and adapt to data set imbalances.
Hyperparameter tuning was conducted using the Optuna package for Python, a framework designed for automating hyperparameter optimization.This process involves setting a range of values for each parameter to find the optimal configuration that enhances model performance.The parameters tuned included: n_estimators: Defined as the number of trees constructed, influencing the model's complexity and accuracy the initial range can be set between 50 and 200.Given the variability in electricity price time series, we chose an initial range from 100 to 10,000 to accommodate different data complexities.Learning_rate: Determines the model's learning speed and generally test range is defined between 0.001 and 0.1, in our case we set the range from 0.001 to 0.2 to balance between convergence speed and training stability.max_depth: Controls tree depth with an initial range of 3-10 might be appropriate, here we allowed for a broad range from 1 to 50 to enable model adaptability across various pattern complexities.num_leaves: Specifies the maximum leaf count per tree it can be considered an initial range of 10-50 to  | 535 limit the complexity of the model, in our work we set a range from 800 to 4000, allowing the model to capture intricate patterns in complex time series.max_bin: Affects how continuous features are binned and an initial range of 10-100 might be sufficient, our range was set between 1 and 500 to precisely model data variability.min_child_samples: Sets the minimum data points required to form a leaf with an initial range between 5 and 20, in our case we set the range from 1 to 600, adjusting for data volume and variability to prevent overfitting.
Optimal hyperparameters, as identified through this tuning process, significantly improved our model's forecasting accuracy, with the best configurations detailed in Table 6.
The curve obtained from the model was compared to test data set and plotted in Figure 11.In this case, the LGBM model revealed a better performance compared to the LEAR model that can be explained by the fact that gradient boost trees models are relatively robust to small training samples thanks to its built-in regularization and optimization techniques which helps to prevent overfitting.
The results obtained from LGBM for rMAE and sMAPE metrics (shown in Table 7) are considerably better than those obtained from SARIMAX and LEAR models.Also, the 94% coverage level obtained for PIs is quite close to the target.

Metric Value
Mean Hyperparameter tuning was systematically conducted using the GridSearchCV library from the scikit-learn package, with initial settings for key parameters as follows: the LSTM layer a range between 32 and 512 LSTM units is usually suggested, and in our case we selected a range from 32 to 250, to capture the time series' complexity adequately.Dense units: Denoting neurons in the post-LSTM dense layers a suggested range might be 32-512 dense units, we set a range from 2 to 50, aimed at striking a balance between learning complex representations and mitigating overfitting.Dropout: A regularization strategy to prevent overfitting, with a dropout fraction range of 0.1-0.5, to optimize the model's generalization ability.
Optimal hyperparameters, as derived from this tuning process, are documented in Table 8, showcasing the model's calibrated performance.
A significantly improvement is observed in Figure 12 when forecasted plot is compared to test data set.These observations are confirmed in Table 9 where calculated rMAE and sMAPE metrics confirm a substantial reduction of forecast error.The 99% PIs coverage level

Metric Value
Mean obtained with this model is superior to the 95% target defined.
For ease of comparison, we summarize in Table 10 the statistical metrics calculated for each of the tested models.
In summary, Table 10 shows that the best performance for EPF in the case of the wholesale mexican market was obtained using the MVLSTM-DWT model followed by LGBM model.However, LSTM-based model has some serious drawbacks with respect to LGBM model like requiring a large amount of training data, is computationally expensive and can be challenging to interpret the results.

| CONCLUSION
Overall, this work provides important insights into the mexican electricity market and offers a comprehensive analysis of different EPF models.By utilizing advanced statistical tools and machine learning algorithms, the study demonstrates the potential of using hybrid models for EPF.The findings suggest that NGP would be sufficient for electricity price forecast in the mexican market resulting in a simpler model for deployment thus significantly reducing the computational costs.In particular, we found that MVLSTM-DWT and LGBM model outperformed the 'classical' models in terms of accuracy and uncertainty.This research offers significant insights for policymakers, energy traders, the academic community, and other key stakeholders, enhancing their understanding of the impact of exogenous variables on electricity prices.The methodologies introduced herein hold promise for application across diverse wholesale electricity markets, potentially streamlining existing forecasting models by accommodating varying market dynamics.Looking forward, a promising path for further investigation involves the application of functional data  analysis to our time series data.This approach, inspired by its success in enhancing forecasting accuracy in other markets as documented for example in Liebl 3 and Pelaez et al., 4 warrants examination for its potential to similarly augment results in the context of electricity price forecasting.For the sake of transparency and to facilitate future research, the codebase for each model developed in this study, alongside the curated data set, has been made publicly available.Interested parties are encouraged to access these resources through our GitHub repository, "Electricity_Price_Forecast," which can be found at (https://github.com/jorgetorre70/Electricity_| 539 TS , TS , …, TS ) (TS , TS , …, TS ) ,

F
I G U R E 4 Correlogram obtained from independent component analysis analysis showing the estimate correlation factor of each feature on locational marginal price (LMP).

F I G U R E 5
Wavelet coherence and global wavelet spectra obtained for electricity price versus natural gas price.DE LA TORRE ET AL.| 531

T A B L E 3 7
Energy-to-shanon entropy ratio (ESR).Discrete wavelet decomposition of electricity price data set using fifth order Daubechies wavelet.DE LA TORRE ET AL. | 533 pdq and PDQ hyperparameters were tuned using autoarima package for Python with initial values derived from an analysis of the autocorrelation function (ACF) and partial autocorrelation function (PACF).The best fitting values for these hyperparameters were (1, 1, 1), (1, 1, 1, 7).The error and PIs metrics obtained for this model are shown in Table

F I G U R E 9
Locational marginal price (LMP) forecast compared to test data set using SARIMAX model.Dotted line indicates actual measured values, solid line represents predicted data and gray area shows the predicted interval using conformal prediction method.T A B L E 4 Error metrics for SARIMAX model.
The DWT Multivariate LSTM (MVLSTM-DWT) model, examined next for EPF, leverages deep learning to simulate

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I G U R E 10 Electricity price forecasting compared to test data set using lasso estimated auto-regressive (LEAR) model.Solid line indicates actual measured data and ticked line represents predicted data.T A B L E 5 Error metrics for lasso estimated auto-regressive model.
Batch size: Essential for determining the gradient calculation and weight update frequency a range of 16-256 is generally recommended, we set it to a range from 8 to 200 to balance between training speed and gradient accuracy.Epochs: Indicative of the complete data set's training cycles a typical range of 10-100 is recommended, we chosen a range from 10 to 200, tailored to the model's complexity and the data set's size.LSTM units: Reflecting the count of memory cells in

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I G U R E 11 Electricity price forecasting (EPF) compared to test data set using LightGBM model.Solid line indicates actual measured data and ticked line represents predicted data.T A B L E 7 Error metrics for light gradient boosting machine model.

T A B L E 8 2 F
Tuned hyperparameters for multivariate long shortterm memory-discrete wavelet transform model.I G U R E 12 Electricity price forecasting (EPF) compared to test data set using multivariate long short-term memory-discrete wavelet transform model.Solid line indicates actual measured data and ticked line represents predicted data.
Net electrical consumption in Mexico by area in 2021.Proposed models for electricity price forecast.
T A B L E 1 Tuned hyperparameters for light gradient boosting machine model.
T A B L E 9 Error metrics for multivariate long short-term memory-discrete wavelet transform model.
T A B L E 10 Error metrics comparison for all forecast models.