Coal price forecasting using complete ensemble empirical mode decomposition and stacking‐based ensemble learning with semisupervised data processing

Globally, coal is a critical energy source, and the profits of related enterprises are highly related to changes in the coal price. A robust coal purchasing cost forecasting method may enhance the coal purchasing strategies of coal‐consuming enterprises and obtain key information for reducing global carbon emissions. However, forecasting the price of coal is a challenging task due to the noise and high random fluctuation of coal price data. To overcome these obstacles, this research proposes a novel forecasting method combining data decomposition, semisupervised feature engineering, and ensemble learning to forecast coal prices. Initially, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) method is employed to decompose the coal price series to reduce the complexity. Second, considering the fluctuation of coal price is influenced by various factors (such as transportation cost and coal mine production), the proposed system incorporates an adaptive data fusion module to fuse data from multiple sources. Finally, a stacking‐based ensemble learning model is adopted in the method to increase the forecasting accuracy by combining the forecasting results of multiple models. The Bohai‐Rim Steam‐Coal Price Index was used to validate the proposed method, and the result of the case study shows that the proposed method provides superior performance than the other nine baseline models in all measured indices. The outcomes of ablation tests indicate the precision of each algorithm is improved by combining CEEMDAN, which proves that the decomposition algorithm is necessary.


| INTRODUCTION
As a critical energy source, changes in the coal price considerably affect the cost and operating profit of coalconsuming enterprises.An information-technologybased accurate, and robust forecasting method of coal price fluctuations can provide essential information on coal procurement strategies for coal-consuming enterprises and necessary warning for coal procurement managers.
Limited studies have focused on coal price forecasting for the Chinese market because coal price fluctuations in China are not solely influenced by market rules; this phenomenon can be attributed to the unique dual-track system of electricity and coal prices Ding et al. 1 Therefore, this study reviewed the literature on various types of energy price forecasting to ensure sufficient and adequate references.Existing energy price forecasting literature can be categorized into four classes: (1) moving average and autoregressive (AR)-based models, (2) treestructure-based models, (3) neural-network-based models, and (4) support vector-machine-based models.Research on energy price forecasting based on these four categories is summarized as follows: Moving average, AR, and their related derivative models are simple and require limited computing power for training.Baumeister and Kilian 2 forecasted the monthly price of West Texas Intermediate (WTI) based on the vector autoregression algorithm.Girish 3 developed a hybrid model for forecasting hourly electricity prices in India by combining the autoregressive integrated moving average (ARIMA) and the generalized autoregressive conditional heteroskedasticity algorithm.Gao et al. 4 forecasted the daily WTI price through an ARIMA-based composite model.This model can achieve excellent results for projects with few input features and stable forecasting data.However, this algorithm exhibits inferior long-term forecasting than those of other types of algorithms Lu et al. 5 As one of the few machine learning methods that can be easily explained, tree-based models have also been tried to be applied to the forecasting of energy prices.Zhou et al. 6 performed daily forecasting of oil prices by the eXtreme Gradient Boosting (XGBoost) algorithm and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) method.The treebased model has proven to be simple, fast to train, insensitive to missing data, and able to demonstrate essential features after training.Nevertheless, tree-based models are sensitive to noise, that is, it is easy to overfit when the data is noisy Lu et al. 5 The neural-network-based model is widely adopted in the forecasting of energy prices because of its excellent flexibility and ability to deal with complex data.Sun et al. 7 used a Spiking Neural Network to forecast the price of carbon emissions trading in Europe.Anamika et al. 8 adopted Feedforward Neural Networks to forecast electricity prices 24 .Zhou et al. 9 used an optimized Long Short-Term Memory (LSTM) network to forecast electricity prices.Li et al. 10 used a Convolutional Neural Network to extract the hidden relationship between online media and oil prices and then forecast the oil price trend.Wu et al. 11 combined Ensemble Empirical Mode Decomposition and LSTM neural network for daily oil price forecasting.Windler et al. 12 employed Deep Feedforward Neural Network to forecast electricity prices for Austria and Germany.Aghajani et al. 13 proposed a hybrid forecasting method, which consists of three Multilayer Perceptron with various learning techniques that make up the primary forecasting engine for shortterm forecasting of the market-clearing price of energy.Jin et al. 14 combine Empirical Mode Decomposition (EMD) with the LSTM method to forecast the stock market price with sentiment analysis.Yujun et al. 15 forecasted the stock price by combining the variational mode decomposition and LSTM method.Yin and Wang 16 established three models for forecasting WTI crude oil price in 2022 by combining EMD with ANN.EMD can decompose the nonlinear stationary signal into a series of modal functions that reflect the inherent vibration in the original data.Chai et al. 17 introduced a forecasting model based on wavelet neural networks, aiming to facilitate real-time monitoring and precise forecasting of photovoltaic power generation.Fan et al. 18 utilized a generalized regression neural network in combination with empirical wavelet decomposition and the sparrow search algorithm to achieve accurate short-term electric load forecasting.Neural-network-based models have excellent nonlinear fitting ability, and the forecasting accuracy can be improved by optimizing the structure and hyperparameters, whereas these types are less interpretable and easy to overfit Lu et al. 5 Support Vector Machine (SVM) and its derivative algorithm have been tried by some scholars to forecast energy prices due to their prominent ability in solving small sample and nonlinear problems.Yu et al. 19 proposed a method based on least-squares support vector regression with a hybrid optimization searching approach to forecast crude oil prices.Zhu et al. 20 combined EMD and evolutionary least-squares SVM to forecast the daily carbon price for the European Union Emissions Trading System.Zhang et al. 21developed a hybrid model for short-term electricity price forecasting by combining SVM and singular spectrum analysis.
The accuracy of data forecasting is influenced by the data preprocessing method and model selection. 22his paper proposes a novel approach that integrates CEEMDAN-based data decomposition, Semisupervised Learning, and a stacking-based ensemble learning model to enable accurate forecasting of coal purchase costs.The main contributions of the proposed method are as follows: • The CEEMDAN algorithm is employed to decompose intricate coal price data into more manageable Intrinsic Mode Functions (IMFs).It effectively isolates essential elements, such as trends and cycles, thereby reducing the complexity of the original data.• Semisupervised learning is utilized on varied, multidimensional data to enhance features and minimize prediction errors.This methodology effectively tackles issues arising from data inconsistency and sparsity.• A stacking-based ensemble learning approach is adopted, delivering reliable predictions by amalgamating multiple algorithms.The meta-model in this approach extracts collaborative information from the outputs of the base learners, combines their strengths, and garners more comprehensive and abundant feature information than any single model could.
The proposed approach is able to forecast the coal purchase cost by combining data from various sources and is expected to promote the coal-consumption enterprises to formulate a reasonable coal purchasing strategy in the historical process of carbon neutrality.The rest of the present paper is organized as follows: the proposed methodology section demonstrates the proposed method, the empirical study section verifies the methodology by testing it, and the conclusion section summarizes the research.

| METHODOLOGY
This section demonstrates the proposed coal price forecasting method.Section 2.1 illustrates the overview of the forecasting framework, while the remaining subsections describe the feature processing and ensemble learning process, respectively.

| Overview of the proposed methodology
The proposed system consists of a feature processing process and a stacking-based ensemble model training process, as shown in Figure 1.The data will be aligned according to time, decomposed by the CEEMDAN method, and the completion of missing data during the process of feature processing.
The feature processing is significant for coal price forecast because of its high volatility, especially the coal purchase cost of a coal-consuming enterprise may not fully follow the macro market rules due to locational factors, such as special regulation strategy and transportation costs variance.Therefore, the purchase price of coal may vary significantly from one coal-consuming enterprise to another simultaneously.It is more reasonable for each coalconsuming enterprise to use its own coal procurement cost data as the forecasting target than the macro market coal price.Nevertheless, the quality of macro coal price index data is usually higher than that of thermal coal-consuming enterprise procurement data, and its dynamics are more closely related to the long-term trend of coal prices.Therefore, training the model by fusing data from various sources is an attractive strategy, which is expected to enable the trained model to forecast future procurement costs by combining micro and macro trends.The detailed feature processing process is described in Section 2.2.
An ensemble learning model is employed to realize the forecasting according to the processed features.Ensemble learning often provides higher forecasting accuracy and better stability than a single machine learning model with the same data set, for a single machine learning model normally relies on an optimization algorithm (e.g., a neural-network model relies on the gradient descent algorithm, a decision tree model relies on the greedy algorithm to grow the tree).Usually, a single algorithm has limitations caused by its solving process.Through the ensemble learning algorithm, several basic machine learning models can be combined to reduce the errors caused by these limitations.Different coal-consuming enterprises have different geographical locations, coal transportation costs, and purchasing habits.Therefore, it is possible that the coal purchase price of one coalconsuming enterprise is more suitable to be forecasted by a Random Forest model, while that of another thermal coal-consuming enterprise is more suitable to be forecasted by an LSTM model.Benefiting from the framework of ensemble learning, the coal purchase data of a coalconsuming enterprise could be trained by multiple models simultaneously, and the forecasting results of each algorithm would be aggregated through the full connection layer with appropriate weights to different models.

| Feature processing
The procedure of the feature processing is demonstrated in Figure 2. Data from different features may have significant differences in the start time, update frequency, and regular update date.The collected multitypes of data will be aligned based on time, and the data under different features inevitably have missing positions after being aligned.Therefore, it is necessary to fill in the missing data after alignment to prepare the training database.The first step of filling in is to locate these missing data.If the position of missing data is in the middle of a certain series and there are neighboring data in the same feature, the missing data will be marked as Type 1. Considering that the data related to the coal price index can hardly fluctuate violently in a short time, this type of missing data will be completed by interpolation.The data that is still missing after filling in the first type of missing data will be marked as Type 2.
Suppose there are m n × elements in the data set in which a ix to a jx are the Type 2 of missing data, as shown in (1): The data will be decomposed by CEEMDAN in the matrix to reduce the complexity and randomness of each feature, except for Type 2 of missing data (a ix to a jx ).The obtained IMFs and residuals will be added to the database as additional features.A model will be trained based on the supervised learning algorithm, the input data of the model in the training set are data series that are not missing in both the time dimension and the feature dimension (a 1,1 to to a i n −1, , and a j x +1, +1 to a m n , ).The output of the model in the training set is the data that are not missing in Feature X (a x 1, to a i x −1, , and a j x +1, to a m x , ).Finally, the trained model will be used to forecast the missing data (a i x , to a j x , ), and outputs the forecasting of missing data and the corresponding confidence level.
The forecasting data with high confidence will be retained afterward, and these data will be reincorporated into the training set to retrain a model for forecasting and reforecast the data that is still missing.This process will continue until the newly generated data set has no new high-confidence data compared with the previous data set.The data that is still missing will be deleted from the time dimension or feature dimension.The data processing step will end at this stage, and the obtained data set will be decomposed by the CEEMDAN method.
CEEMDAN is a numerical decomposition method derived from EMD. CEEMDAN adds white noise to the residuals after each order of IMF components and calculates the mean IMF components.The original data could be entirely decomposed by CEEMDAN with negligible errors by iterating several times.The modal decomposition process of CEEMDAN is shown below.
Assume the solution procedure for the kth modal component of the EMD decomposition of some dimension as E ( ) k  , and let ω i be the white noise that fits the normal distribution from 0 to 1, and ε k be the amplitude coefficient of the kth white noise.
The X t ε ω t ( ) + ( ) i 0 is decomposed I times by EMD in the first step, and the mean value of this decomposition is calculated to obtain the intrinsic modal function: Therefore, the residual component of the first step is calculated as The white noise of ε ω t ( ) is then added to the residual component, while the EMD method is reapplied to obtain the IMF 2 : The above process is repeated until the value of the residual component is less than two extreme values.The kth residual component can be found by the following equation: Simultaneously, IMF k+1 could be obtained as Equations ( 4) and ( 5) are then cyclically executed until less than two residual extreme values are obtained (indecomposable).The final residual when the decomposition is stopped could be represented as where K is the total number of patterns obtained during the decomposition process, and the original data set X t ( ) could be calculated as The permutation entropy (PE) is utilized to estimate the complexity of the series, which performs well for measuring the complexity of a data set in terms of robustness and rapidness (Table 1).The first step of PE calculation is to transform the target time-series x t to an embedding vector with time delay τ and embedded dimension m: Afterward, the vector X t is rearranged to increasing order, as The equal values in X t would be arranged based on the order in which they appear.There are m! total possible permutations π for a given embedding dimen- sion m.The relative frequency for each possible permutation π can be calculated as follows: The PE value for a series with order m 2  is then estimated by The value of H p is within [0, 1], and a larger H p value for time-series data discovers a higher complexity level.

| Stacking-based ensemble learning
Diverse machine learning algorithms scan feature space with their unique perspectives to discover the most feasible and accurate hypotheses for a given task.Typically, a single algorithm is limited by its unique solution process.The stacking-based ensemble learning achieves the final forecasting by combining the multiple base learners in an integrated framework, thus overcoming the limits.The prediction results derived from the identified data patterns by each base learner with their unique methodology are treated as meta-features, and are subsequently input into the meta-learner.The metalearner is then responsible for discovering the optimum combination of prediction results from the base learners.A fully connected layer composed of multiple neurons with a Rectified Linear Unit (ReLU) is adopted as the meta-learner.Each neuron within this fully connected layer receives the prediction results from all basic learners, subsequently performing further calculations and generating predictions based on these results.The output value for each neuron can be expressed as where, h i signifies the output of the ith neuron, w ij represents the weight of the ith neuron corresponding to the prediction result of the jth base learner, and b i is the bias term for the ith neuron.Following this, the metalearner employs the subsequent formula to calculate a weighted sum of the outputs from each neuron, thereby obtaining the final predicted output: where v k is the weight of the output of the kth neuron, and h k is the output of the kth neuron.In essence, the meta-learner further learns the output of the base learner through a fully connected layer of multineurons and ReLU activation function.In this process, the effective base learners are assigned greater weight, facilitating an optimal combination of the predicted outputs from multiple base learners.
Considering the principles of these methods are available in plenty of published works, they are not repeated in this paper.

| EMPIRICAL STUDY
The Bohai-Rim Steam-Coal Price Index (BSPI) is selected as the forecast target to verify the performance of the proposed method.The BSPI is the first coal commodity price index in China that reflects the free On board closing price level and volatility of power coal at Bohai-Rim ports.Bohai-Rim Port is a collective name that includes Qinhuangdao Port, Tianjin Port, Huanghua Port, Jingtang Port, Guotou Jingtang Port, and Caofeidian Port.The first BSPI index was released on June 28, 2010, and the index is updated every 7 days for most of the year, skipping one cycle during special holidays (National Day and Chinese New Year).Figure 4 shows the data of the BSPI from the first release date to April 6, 2022, which is the evaluation case selected in this study.According to the figure, there is no obvious signal during the transition of the rising/falling trend of the data.For example, from 2012 to 2016, the BSPI index was in a falling direction, while it was in a rising trend from 2016 to 2017.There is no relatively gentle fluctuation range or any signal that hints at the change in trend between the falling and rising.Considering the time-series forecasting needs continuous information, the data were not divided between the training set and the test set by random sampling.The data before January 27, 2021 is selected as the training set, while the data after that is selected as the test set.The supplemented data include the futures price of thermal coal, and Bohai-Rim storage data (the amount of coal transferred in, the amount of coal transferred out, the number of ships in anchorage, the number of ships in advance, and the total inventory).Among them, coal futures prices are updated once a day except holidays, while the Bohai-Rim storage data are updated everyday including holidays.

| Data decomposition
As noted in Section 2, rolling iteration and sequential decomposition are adopted in the test set part to prevent "future information" leak into the training process due to the peculiarities of the CEEMDAN algorithm.Seven data periods are selected for the PE computation to illustrate the fluctuating turbulence level of their IMFs with the delay and order set to 1 and 5, and the results are shown in 1.The PE value of the first IMF of the seven selected data points is greater than 0.2, and it gradually decreases as the decomposition continues.The PE value of all the last IMFs is less than 0.01.These patterns exhibit the reduction of sequence complexity.The two subgraphs in Figure 5 depict two examples of decomposition, including the original data, decomposed IMFs, and residuals from the initial release date of BSPI to August 18, 2021, and February 23, 2022, respectively.It is discovered that the data volatility tends to diminish when the decomposition degree increases.In addition, comparing the component graphs of the data in two time periods reveals that the distribution and trend of each component will change dramatically over time, which further proves the necessity of iterative decomposition.

| Evaluation
Figure 6 is a graphical representation that shows the performance of various models in terms of their actual versus forecasted values.The plot is designed such that the x-axis represents the actual values, while the y-axis represents the forecasted values.The 45°line also known as the perfect line, is significant as it represents the ideal scenario where the forecasted value perfectly matches the actual value for all data points.As shown in Figure 6, the CEEMDAN-Stacking model shows satisfactory precision and stability.An important observation is that the data point of most of represents its forecasting value is closer to the perfect line than other models, which indicates that this model has lower forecasting error.In addition, by comparing the group treated with CEEMDAN the group without CEEMDAN treatment reveals a noticeable difference.The data points of the group without CEEMDAN are observed to be farther from the perfect line.This comparison underlines the utility of CEEMDAN in refining the forecasting performance and reliability of models.The models that are not enhanced by CEEMDAN show less consistency and produce a wider range of errors.This phenomenon is more readily discernible when examining the percentage error display diagram of test points as depicted in Figure 7.The error values for most points in the mode with CEEMDAN treatment are notably closer to zero compared with those in the untreated model.This observation suggests that the application of CEEMDAN effectively enhances the forecasting performance of the model, subsequently reducing the magnitude of forecasting errors.
The effectiveness of the model is further examined using statistical measures including Mean Absolute Percentage Error (MAPE), Root-Mean-Square Error (RMSE), and the Coefficient of Determination (R 2 ).The formulas used to compute these metrics are shown in Equations ( 15)- (18), and the results are quantitatively displayed in Figures 8 and 9.
According to Figures 8 and 9, the stacking model demonstrates strong performance across all indicators in both the CEEMDAN and non-CEEMDAN groups.Within the non-CEEMDAN group, the stacking model surpasses all competing models, boasting the highest R 2 score (approximately 0.941) and the smallest error index (1.51%MAPE, 325.71 MSE, and 18.05 RMSE).These results suggest that, within this group, the stacking model is more dependable and precise in forecasting target variables compared to other models.In the CEEMDAN group, the performance of the CEEMDAN-enhanced stacking model remains impressive and even exhibits improved performance, achieving the highest R 2 score (approximately 0.96) and the lowest error index (1.16%MAPE, 231.0 MSE, and 15.2 RMSE).This indicates that the integration of stacking and CEEMDAN further enhances the model's forecasting accuracy.The consistently strong performance of the stacking model can be attributed to its unique capacity to leverage the strengths of multiple base models, thereby mitigating the risk of underperformance due to the shortcomings of any individual model.This advantage is particularly beneficial in complex forecasting tasks where different models can capture various facets of the data.In addition, the performance with CEEMDAN consistently outperforms their non-CEEMDAN counterparts across all models, including Stacking, XGBoost, BPNN, gated recurrent unit (GRU), Recurrent Neural Network (RNN), and LSTM.This phenomenon is consistent with the finding of a perfect line and error diagram, which reveals that the benefit of CEEMDAN is not specific to any single model but is generalizable across different types of models.The adoption of the CEEMDAN helps separate the original data into multidimensional characteristics, thereby eliminating the impact of noise in the original data on the training.All the models trained with the data processed by CEEMDAN perform better than using the original data directly, as demonstrated in Table 2 for the improvement ratio for different models.
According to Table 2, the CEEMDAN technique has varying effects on different models.Remarkably, the XGBoost model shows the greatest improvement across all metrics, with a minimum enhancement of 24.46% in R 2 and a peak of 58.92% in MSE.The BPNN and RNN also exhibit significant improvement, particularly in their MSE values, indicating a substantial reduction in errors.On the other hand, the enhancements for the GRU and LSTM models are relatively minor, with their R 2 values only slightly rising around 2%.The Stacking model falls in the middle, with a moderate MSE improvement of 29.08%.These results suggest that the effectiveness of the CEEMDAN technique is model dependent, being notably beneficial for models, like, XGBoost and BPNN, but less impactful on GRU and LSTM models.Further investigation would be required to understand the underlying reasons for such variability and explore potential optimization for different model types.Furthermore, the CEEMDAN technique is designed to handle nonlinear and nonstationary data, thus the Stacking model shows less improvement after applying CEEMDAN as compared to the other models could potentially indicate that the Stacking model is less influenced by the dynamics of the data.
In summary, the CEEMDAN-Stacking model suggested in this research outperforms the baseline models in terms of both accuracy and stability of forecasting, which is a dependable approach for coal price forecasting.

| CONCLUSION
This study proposes a coal price forecasting system to help coal-consuming enterprises realize coal purchasing cost forecasting.This coal price forecasting system includes feature processing processes and Stacked-based ensemble learning.The data from various sources are fused by combining CEEMDAN data decomposition, data alignment, and semisupervised learning in the feature processing part to overcome the problems of data misalignment caused by different data sources in the industry.Stacking-based ensemble learning module improves the universality and forecasting accuracy of the system by combining various models.The models included in stacking-based ensemble learning in this research include XGBoost, KNN, LightGBM, XT, and BPNN.The forecasting results of these models are combined by a full connection layer, which enables the proposed method to combine the advantages of each method.
The proposed system is verified by forecasting the BSPI index.The data before January 20, 2021 are selected as the training data of the model, and the data after that is used as the test data.The comparison of the test data sets shows that the proposed method obtains the best scores in RMSE, MAPE, and R 2 indexes compared with benchmark models, and the result emphasizes the CEEMDAN method in improving the accuracy and trustworthiness of the models.
However, there are some limitations in this research: the characteristics of stacking-based ensemble learning determine that many kinds of models need to be trained during the training process, which increases the training cost.The models can be sorted according to their contribution to accuracy in industrial applications and remove the less essential models to reduce the training cost.Moreover, this study has primarily focused on analyzing and predicting coal prices based on historical data and patterns extracted by the models.However, the influence of external factors, such as national policy changes, cannot be ignored.These factors significantly impact the dynamics of coal prices and present a complex challenge due to their often nonquantifiable nature.In future work, it might be beneficial to incorporate techniques to better account for these policy changes.For instance, one approach could involve identifying key dates corresponding to the announcement or implementation of significant policy changes, and studying the subsequent effects on coal prices.

F I G U R E 2
Procedure of feature processing.CEEMDAN, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise.

| 1361
Numerous resources demonstrated that stacking-based ensemble learning is capable of reducing data-related deviation and variance errors and realizing the reduction of generalization errors.The choice of base learner and metalearner has always been a concern in stacking ensemble frameworks.Designing the most suitable base learner combination and meta-learner to prevent overfitting with reasonable training cost is a challenging task.The present research employed independent validation set to reduce the training cost, considering the importance of cost control in industrial production.The designed stacking frame in this study is demonstrated in Figure3.The input data set is divided into training, validation, and test sets.The training set is then sent to various algorithms to initiate the training of the basic model and meta-model.Common techniques for preventing overfitting in stacking-based ensemble learning include k-fold cross-validation and independent data validation.k-Fold cross-validation uses rolling iteration to switch training and validation data so that the model can obtain more training data, but it will significantly increase the training cost.The models utilized in the proposed Stacking approach include XGBoost, K-Nearest Neighbors (KNNs), Light Gradient Boosting Machine (LightGBM), eXtreme randomized Trees (XT), and Backpropagation Neural Network (BPNN).

F
I G U R E 4 BSPI data.BSPI, Bohai-Rim Steam-Coal Price Index.F I G U R E 5 Data decomposition of BSPI based on CEEMDAN algorithm.BSPI and its IMFs from (A) June 29, 2010 to July 14, 2021 and (B) June 29, 2010 to February 23, 2021.BSPI, Bohai-Rim Steam-Coal Price Index; CEEMDAN, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise; IMF, Intrinsic Mode Function.F I G U R E 6 Perfect line plot of the test set.BPNN, Backpropagation Neural Network; CEEMDAN, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise; GRU, gated recurrent unit; LSTM, Long Short-Term Memory; RNN, Recurrent Neural Network; XGBoost, eXtreme Gradient Boosting.

F I G U R E 7
Percentage error of test set.BPNN, Backpropagation Neural Network; CEEMDAN, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise; GRU, gated recurrent unit; LSTM, Long Short-Term Memory; RNN, Recurrent Neural Network; XGBoost, eXtreme Gradient Boosting.
T A B L E 1 IMF permutation entropy (PE) of BSPI data in different periods.
T A B L E 2Abbreviations