A carbon price prediction method and device, and a storage medium

Abstract

The present disclosure provides a carbon price prediction method, device and storage medium, comprising: obtaining historical carbon price data; and determining a first carbon price sequence of the change of carbon price with time according to the historical carbon price data; adding white noise data to the first carbon price sequence, and using the CEEMDAN algorithm to iteratively calculate the intrinsic mode function and the residual; wherein in each iteration calculation process, the noise level coefficient of the white noise data added in the next iteration calculation is determined according to the residual of the previous iteration calculation; the feature extraction and feature selection are performed on each intrinsic mode function to determine a first multi-dimensional feature vector of the historical carbon price data; and the first multi-dimensional feature vector is input into an extreme learning machine model to obtain a prediction result of the carbon price. The present disclosure uses the CEEMDAN algorithm to dynamically adjust the noise level to eliminate the residual noise and the parasitic mode, eliminates the error accumulation of the traditional "decomposition-reconstruction-prediction" mode, and improves the multi-modal prediction accuracy.

Description

Technical Field

[0001] This disclosure relates to the field of carbon market forecasting technology, and in particular to a carbon price forecasting method, apparatus and storage medium. Background Technology

[0002] With the development of deep learning technology, deep learning-based hybrid prediction models have become a core research direction in the field of carbon price prediction, and numerous research results have shown some effectiveness. However, current research still has the following shortcomings:

[0003] 1. The hybrid carbon price prediction model using the "decomposition-reconstruction-prediction" mode still has residual noise and parasitic mode interference in the data decomposition stage;

[0004] 2. When predicting multiple modes, there is an error accumulation problem;

[0005] 3. Existing models are unable to accurately determine the differences in the importance of various elements in historical carbon price data during the prediction process.

[0006] Based on the above problems, there is an urgent need to provide a carbon price forecasting method to improve the accuracy of carbon price forecasting. Summary of the Invention

[0007] This disclosure provides a carbon price prediction method, apparatus, and storage medium to address the problem that existing hybrid carbon price prediction models suffer from insufficient accuracy due to residual noise and parasitic mode interference, error accumulation, and inaccurate judgment of the importance of various elements in historical carbon price data.

[0008] In view of the above problems, firstly, the present disclosure provides a carbon price prediction method, including:

[0009] Obtain historical carbon price data; and based on the historical carbon price data, determine a first carbon price sequence that reflects the change of carbon prices over time.

[0010] White noise data is added to the first carbon price series, and the intrinsic mode function and residuals are iteratively calculated using the CEEMDAN algorithm. In each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration.

[0011] For each of the intrinsic mode functions, feature extraction and feature filtering are performed to determine the first multidimensional feature vector of historical carbon price data;

[0012] The first multidimensional feature vector is input into the extreme learning machine model to obtain the carbon price prediction result.

[0013] In conjunction with the first aspect, in one possible implementation, white noise data is added to the first carbon price series, and the intrinsic mode function and residuals are iteratively calculated using the CEEMDAN algorithm, including:

[0014] Adding white noise data to the first carbon price series, the formula for calculating the intrinsic mode function and residual pair in the first iteration of the CEEMDAN algorithm is expressed as follows:

[0015] r1 = <M(X+β0E1(ω i ))>

[0016] IMF1 = X - r1

[0017] Where X represents the first carbon price series, ω i Let represent the i-th white noise data, i = 1, 2, ..., L, β0 represent the initial noise level coefficient, β0 > 0, E1 represent the first EMD decomposition operation, M represent the local mean operation, <> represent the average operation, r1 represent the residual obtained from the first iteration, and IMF1 represent the intrinsic mode function obtained from the first iteration.

[0018] The formula for calculating the intrinsic mode functions and residuals using the CEEMDAN algorithm in the nth iteration is expressed as follows:

[0019] r n = <M(r n-1 +β n-1 E n (ω i ))>

[0020] IMF n =r n -r n-1

[0021] Where n≥2.

[0022] In conjunction with the first aspect, in one possible implementation, the iterative calculation is stopped if the residual obtained in the nth iteration is a monotonic function.

[0023] In conjunction with the first aspect, in one possible implementation, during each iteration of the calculation, the noise level coefficient for adding white noise data in the next iteration is determined based on the residual from the previous iteration, expressed by the following formula:

[0024]

[0025] Where β0 represents the initial noise level coefficient, ||·|| 2 It represents the signal energy.

[0026] In conjunction with the first aspect, in one possible implementation, the step of performing feature extraction and feature filtering on each of the intrinsic mode functions to determine the first multidimensional feature vector of historical carbon price data includes:

[0027] For each of the intrinsic mode functions, feature extraction is performed to determine a first feature; wherein, the first feature includes: time-domain features and frequency-domain features;

[0028] Calculate the Pearson correlation coefficient between the first feature and the first carbon price sequence to obtain a second feature whose corresponding Pearson correlation coefficient value is greater than a first preset value.

[0029] The LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data.

[0030] In conjunction with the first aspect, in one possible implementation, the LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data, expressed by the formula:

[0031]

[0032] Among them, y i x represents the i-th value in the first carbon price sequence; ij w represents the value of the j-th second feature corresponding to the i-th intrinsic mode function; j Let L represent the weight coefficient of the j-th second feature; L represent the loss function; λ represent the regularization strength parameter; N represent the number of intrinsic mode functions; and M represent the number of second features.

[0033] In conjunction with the first aspect, in one possible implementation, it further includes:

[0034] Identify the primary factors influencing carbon prices;

[0035] Feature screening is performed on the first carbon price influencing factors to determine the second multidimensional feature vector of the carbon price influencing factors;

[0036] The first multidimensional feature vector and the second multidimensional feature vector are input into the extreme learning machine model to obtain the carbon price prediction result.

[0037] In conjunction with the first aspect, in one possible implementation, the step of screening the first carbon price influencing factors to determine the second multidimensional feature vector of the carbon price influencing factors includes:

[0038] Calculate the Pearson correlation coefficient between the first carbon price influencing factor and the first carbon price sequence, and obtain the second carbon price influencing factor whose corresponding Pearson correlation coefficient value is greater than the second preset value among the first carbon price influencing factors;

[0039] The LASSO algorithm was used to screen the second carbon price influencing factors and determine the second multidimensional feature vector of the historical carbon price influencing factors.

[0040] Secondly, a carbon price forecasting device is provided, comprising:

[0041] A preprocessing module is used to acquire historical carbon price data and, based on the historical carbon price data, determine a first carbon price sequence that shows the change of carbon prices over time.

[0042] The intrinsic mode function determination module is used to add white noise data to the first carbon price sequence and iteratively calculate the intrinsic mode function and residuals using the CEEMDAN algorithm; wherein, in each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration.

[0043] The feature extraction module is used to extract and filter features for each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data.

[0044] The prediction module is used to input the first multidimensional feature vector into the extreme learning machine model to obtain the predicted carbon price.

[0045] Thirdly, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, performs the steps of the carbon price prediction method as described in the first aspect or any possible embodiment in conjunction with the first aspect.

[0046] The beneficial effects of the embodiments disclosed herein include:

[0047] The carbon price prediction method, apparatus, and storage medium provided in this disclosure include: acquiring historical carbon price data; determining a first carbon price sequence that changes over time based on the historical carbon price data; adding white noise data to the first carbon price sequence and iteratively calculating intrinsic mode functions and residuals using the CEEMDAN algorithm; wherein, in each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration; performing feature extraction and feature filtering on each intrinsic mode function to determine a first multidimensional feature vector of the historical carbon price data; and inputting the first multidimensional feature vector into an extreme learning machine model to obtain the carbon price prediction result. The carbon price prediction method provided in this disclosure uses the CEEMDAN algorithm to introduce white noise to assist decomposition, effectively alleviating the mode aliasing problem. Dynamically adjusting the noise level can specifically eliminate residual noise and parasitic modes. During the iterative decomposition process, the noise parameters are adaptively adjusted based on the residuals, breaking the error accumulation chain of the traditional "decomposition-reconstruction-prediction" model and improving the accuracy of multimodal prediction. The first multidimensional feature vector construction process incorporates a feature selection mechanism to avoid interference from irrelevant data in the prediction, thereby improving the ability to identify the importance of each element in historical carbon price data. The stochastic hidden layer parameter settings and fast training characteristics of the extreme learning machine model enhance its ability to fit the nonlinear fluctuations of carbon prices, thus improving the accuracy of carbon price prediction. Attached Figure Description

[0048] Figure 1 A flowchart of the carbon price prediction method provided in the embodiments of this disclosure;

[0049] Figure 2 A structural diagram of the carbon price prediction device provided in an embodiment of this disclosure. Detailed Implementation

[0050] This disclosure provides a carbon price prediction method, apparatus, and storage medium. Preferred embodiments of this disclosure are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit this disclosure. Furthermore, the embodiments and features described herein can be combined with each other unless otherwise specified.

[0051] This disclosure provides a carbon price prediction method, such as... Figure 1 As shown, it includes:

[0052] S101. Obtain historical carbon price data; and based on the historical carbon price data, determine the first carbon price sequence that changes over time.

[0053] S102. Add white noise data to the first carbon price series and use the CEEMDAN algorithm to iteratively calculate the intrinsic mode function and residuals; wherein, in each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration.

[0054] S103. Perform feature extraction and feature filtering on each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data;

[0055] S104. Input the first multidimensional feature vector into the extreme learning machine model to obtain the carbon price prediction result.

[0056] In this disclosure, as global attention to climate change continues to increase, the carbon trading market is gradually becoming an important mechanism for regulating greenhouse gas emissions. Accurate carbon price forecasting is crucial for policymakers, market participants, and related enterprises. In recent years, the rapid development of deep learning technology has provided new ideas and methods for carbon price forecasting. However, despite significant progress made by deep learning-based hybrid forecasting models in the field of carbon price forecasting, some problems remain to be solved. Deep learning technology, by constructing complex neural network models, can automatically learn complex patterns and relationships from large amounts of data. In carbon price forecasting, deep learning models can use historical carbon price data to predict future carbon price trends. These models can not only capture short-term fluctuations in carbon prices but also analyze long-term trends, providing decision support for market participants. In recent years, researchers have proposed various deep learning-based hybrid forecasting models. These models typically adopt a "decomposition-reconstruction-prediction" approach, that is, first decomposing the complex carbon price sequence into multiple modes (or components), then predicting each mode separately, and finally reconstructing the prediction results into the final carbon price forecast value. This method can effectively handle the non-stationarity and complexity of carbon price sequences and improve prediction accuracy. While deep learning-based hybrid prediction models have achieved significant success in carbon price forecasting, current research still has some shortcomings that limit further development and application. In the "decomposition-reconstruction-prediction" model, data decomposition is a crucial step. Through decomposition, complex carbon price sequences are broken down into multiple simpler modes, each representing features within a specific frequency range of the original signal. However, in practical applications, residual noise and parasitic mode interference still exist in the data decomposition stage. Despite the introduction of noise processing mechanisms during decomposition, residual noise may still remain. This noise interferes with mode extraction, making the decomposition results inaccurate. For example, when dealing with high-frequency carbon price fluctuations, residual noise may cause the decomposed modes to contain spurious high-frequency components, thus affecting subsequent prediction accuracy. Parasitic modes refer to unwanted mode components generated during the decomposition process. These modes are unrelated to the true features of the original signal but may be incorrectly extracted. For example, the decomposition algorithm may mistake noise for a true component of the signal, thus generating parasitic modes. These parasitic modes interfere with the analysis of the true signal, reducing the reliability of the model. In hybrid prediction models, each mode makes predictions independently, and the results are then reconstructed into a final carbon price forecast. However, in this process, the prediction errors of each mode can accumulate, affecting the final prediction accuracy. For example, if a carbon price series is decomposed into three modes, with prediction errors of 1%, 2%, and 3% for each mode, these errors may overlap during reconstruction, leading to a significant increase in the final prediction error.The lack of assessment of the importance of each modality during the forecasting process means that existing models cannot accurately identify the differences in importance of various elements in historical carbon price data, resulting in inaccurate forecasting results.

[0057] In this embodiment of the disclosure, historical carbon price data for a preset time span, such as daily / weekly closing prices, is obtained through a public data interface or database of the carbon trading market. This data is then sorted by timestamp to form one-dimensional time-series data X = [x1, x2, ..., x...]. n ], where x iThis represents the carbon price data at the i-th time point. The one-dimensional time series data is preprocessed to remove outliers, such as extreme price limits, and missing values ​​are filled using linear interpolation. The original distribution characteristics of the trend, periodic, and random fluctuation components of carbon prices over time are preserved, resulting in the first carbon price sequence. White noise data is added to the first carbon price sequence. White noise is a special type of random signal used to assist the decomposition process, reducing the influence of parasitic modes and residual noise. Its power spectral density is uniformly distributed across all frequencies, and white noise has the same energy at any frequency, with each frequency component being independent. Due to the nonlinear and non-stationary characteristics of the first carbon price sequence, the CEEMDAN algorithm is used to iteratively calculate its intrinsic mode functions and residuals. The CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) algorithm is an improved method based on Empirical Mode Decomposition (EMD), which can solve the mode aliasing and decomposition instability problems existing in traditional EMD methods. The EMD method reveals the intrinsic characteristics of the first carbon price series by decomposing a complex signal into a series of Intrinsic Mode Functions (IMFs) and residuals. However, EMD is prone to mode aliasing when processing non-stationary signals, that is, first carbon price series of different frequencies are incorrectly assigned to the same IMF. To solve this problem, white noise data is introduced, and the stability and accuracy of the decomposition are improved through multiple iterations and averaging. Intrinsic Mode Functions are one of the core concepts of the EMD method. An IMF can be a signal component that meets specific conditions, representing the local characteristics of a specific frequency range in the first carbon price series. Specifically, an IMF must meet the following two conditions: (1) In the first carbon price series, the difference between the number of extreme points (maximum and minimum points) and the number of zero-crossing points does not exceed 1. (2) The mean of the upper envelope (the curve fitted through the maximum point) and the lower envelope (the curve fitted through the minimum point) of the first carbon price series is zero. By decomposing the first carbon price series into multiple IMFs, the intrinsic structure and dynamic changes of the signal can be better understood. For example, in the first carbon price series, each IMF can correspond to the characteristics of carbon price fluctuations at different time scales, thus providing a basis for subsequent prediction and analysis. In the CEEMDAN algorithm, the residual refers to the part remaining after gradually extracting the IMFs from the first carbon price series during the decomposition process. The residual typically contains low-frequency components or trend terms from the first carbon price series. As the decomposition process proceeds, the residual gradually decreases until no more components satisfying the IMF conditions can be extracted. The processing of the residual is crucial for understanding the long-term trend and short-term fluctuations of the signal.In the CEEMDAN algorithm, white noise is introduced to increase the randomness of the signal, thereby reducing mode aliasing. However, the level of white noise (i.e., noise intensity) has a significant impact on the accuracy of the decomposition results. If the white noise level is too high, it may drown out the true components of the signal; if the white noise level is too low, it cannot effectively reduce mode aliasing. Therefore, choosing a reasonable white noise level is crucial for the CEEMDAN algorithm. In the analysis of the first carbon price series, a strategy of dynamically adjusting the white noise level is adopted. Specifically, in each iteration, the level of white noise data to be added in the next iteration is determined based on the residual calculated in the previous iteration. As the decomposition process progresses, the high-frequency components of the first carbon price series are gradually extracted, and the low-frequency components in the residual gradually emerge. Therefore, dynamically adjusting the white noise level according to the characteristics of the residual can better adapt to the needs of the first carbon price series at different decomposition stages. In the first iteration, a suitable initial white noise level is selected. This level usually needs to be determined based on the characteristics of the first carbon price series and experience. In each iteration, white noise data is added to the current residual, and then EMD decomposition is performed to extract the new IMF and residual. Based on the newly calculated residual characteristics, the level of white noise added in the next iteration is adjusted. If there are still significant high-frequency components in the residuals, the white noise level is increased appropriately; if the residuals mainly contain low-frequency components, the white noise level is decreased appropriately. This process is repeated until the residuals can no longer extract components that satisfy the IMF conditions. Through this dynamic adjustment strategy, the CEEMDAN algorithm can flexibly adjust the white noise level at different decomposition stages, thereby improving the accuracy and stability of the decomposition results. By gradually adding adaptive noise during the first carbon price series decomposition process, the influence of white noise data on the decomposition results is effectively reduced, solving not only the mode aliasing problem in traditional EMD but also overcoming the problem of residual noise propagation from high to low frequencies in EEMD. In each iteration, the noise level of the white noise data is adjusted and added to the residuals instead of being directly added to the first carbon price series. This gradual addition method can more accurately control the influence of residual noise. Introducing white noise data into the residuals of each IMF order can also effectively reduce the generation of parasitic modes, significantly improving the accuracy and stability of the first carbon price series decomposition.

[0058] Furthermore, historical carbon price data often contains redundant information in carbon price forecasting. Directly using this data for forecasting may lead to model overfitting, reducing the accuracy and generalization ability of the forecast. Therefore, feature extraction and feature selection become crucial steps in improving forecasting performance. Feature extraction refers to extracting variables that can effectively characterize the data from historical carbon price data, while feature selection involves choosing the most valuable parts for the forecast target from these extracted features. Intrinsic Mode Functions (IMFs) are the result of Empirical Mode Decomposition (EMD), which decomposes the first carbon price sequence into multiple simpler modal components. Each IMF can correspond to the carbon price fluctuation characteristics at different time scales, thus providing a basis for feature extraction. Useful features are extracted from each IMF. These features can include: mean, variance, maximum, minimum, energy, and entropy: the mean reflects the central trend of the IMF, while the variance represents its degree of volatility. For example, in an IMF, a high mean and a small variance may mean that the mode has a stable and high-value contribution to carbon prices. Maximum and minimum values ​​can provide information about the range of carbon price fluctuations. For example, a large gap between the maximum and minimum values ​​of an IMF indicates that this mode has a significant impact on short-term carbon price fluctuations. Energy can measure the importance of an IMF in the signal, while entropy reflects its complexity. An IMF with higher energy may have a greater impact on the overall trend of carbon prices, while an IMF with higher entropy may contain more detailed information. Although multiple features are extracted from each IMF, not all features are equally important for predicting carbon prices. Therefore, these features need to be screened to remove redundant and irrelevant features, improving the efficiency and accuracy of the model. For example, the LASSO algorithm can be used to screen features by taking multiple extracted features as input. The LASSO algorithm can automatically evaluate the importance of each feature to the prediction target and compress the coefficients of unimportant features to zero. In this way, a screened feature set can be obtained, which includes the features most valuable for carbon price prediction. The screened features are converted into feature vectors, thus obtaining the first multidimensional feature vector of historical carbon price data. After feature extraction and screening, the screened first multidimensional feature vector is input into an Extreme Learning Machine (ELM) model to predict future carbon prices. Extreme Learning Machine (ELM) is a fast learning algorithm based on feedforward neural networks. Compared with traditional neural network training methods (such as backpropagation), ELM has advantages such as fast training speed and strong generalization ability. It predicts the target variable by randomly initializing the weights and biases from the input layer to the hidden layer, and then calculating the weights from the hidden layer to the output layer using the least squares method. The first multidimensional feature vector, after feature extraction and feature selection, is used as the input to the ELM model.The ELM model learns the relationship between a first multidimensional feature vector and carbon prices, and predicts future carbon prices based on the input first multidimensional feature vector. For example, if an 8-dimensional feature vector is obtained through feature extraction and filtering, this 8-dimensional feature vector is input into the ELM model, and the model will output a predicted value, i.e., the carbon price prediction result at a certain point in the future or within a certain period of time, based on its internal learning mechanism.

[0059] In this embodiment, the CEEMDAN algorithm is employed, introducing white noise to assist decomposition, effectively mitigating the mode aliasing problem. Dynamically adjusting the noise level can specifically eliminate residual noise and parasitic modes. During the iterative decomposition process, noise parameters are adaptively adjusted based on the residuals, breaking the error accumulation chain of the traditional "decomposition-reconstruction-prediction" model and improving the accuracy of multimodal prediction. A feature selection mechanism is incorporated into the construction of the first multidimensional feature vector to avoid interference from irrelevant data, improving the ability to identify the importance of various elements in historical carbon price data. The stochastic hidden layer parameter settings and rapid training characteristics of the extreme learning machine model enhance the fitting ability to nonlinear fluctuations in carbon prices, thereby improving the accuracy of carbon price prediction.

[0060] In another embodiment of this disclosure, step S102 above, which involves adding white noise data to the first carbon price sequence and iteratively calculating the intrinsic mode function and residuals using the CEEMDAN algorithm, includes:

[0061] Adding white noise data to the first carbon price series, the formula for calculating the intrinsic mode function and residuals in the first iteration of the CEEMDAN algorithm is expressed as follows:

[0062] r1 = <M(X+β0E1(ω i ))>

[0063] IMF1 = X - r1

[0064] Where X represents the first carbon price series, ω i Let represent the i-th white noise data, i = 1, 2, ..., L, β0 represent the initial noise level coefficient, β0 > 0, E1 represent the first EMD decomposition operation, M represent the local mean operation, <> represent the average operation, r1 represent the residual obtained from the first iteration, and IMF1 represent the intrinsic mode function obtained from the first iteration.

[0065] The formula for calculating the intrinsic mode functions and residuals using the CEEMDAN algorithm in the nth iteration is expressed as follows:

[0066] r n = <M(r n-1 +β n-1 E n (ω i ))>

[0067] IMF n =r n -r n-1

[0068] Where n≥2.

[0069] In this embodiment of the disclosure, in the analysis of the first carbon price sequence, the CEEMDAN algorithm can effectively extract the intrinsic mode function (IMF) and residuals in the sequence by adding white noise data and performing multiple iterations.

[0070] For the first iteration, the formula is expressed as:

[0071] r1 = <M(X+β0E1(ω i ))>

[0072] IMF1 = X - r1

[0073] Add white noise data β0E1(ω) to the first carbon price series X i ), where ω i Let E1 represent the i-th white noise data point, i = 1, 2, ..., L, and β0 represent the initial noise level coefficient, where β0 > 0. After adding white noise, EMD decomposition is performed to obtain the residual r1 and intrinsic mode function (IMF1) calculated in the first iteration. E1 represents the first EMD decomposition operation, M represents the local mean operation, <> represents the averaging operation, r1 represents the residual obtained in the first iteration, and IMF1 represents the intrinsic mode function obtained in the first iteration.

[0074] For the nth iteration, the formula is expressed as:

[0075] r n = <M(r n-1 +β n-1 E n (ω i ))>

[0076] IMF n =r n -r n-1

[0077] Where n ≥ 2. The residual r obtained in the (n-1)th iteration is... n-1 Add white noise data β n-1 E n (ω i ), where β n-1 β represents the noise level coefficient in the (n-1)th iteration. n-1 >0. After adding white noise, EMD decomposition is performed to obtain the residual r calculated in the nth iteration. nand intrinsic mode function (IMF) n Calculate all IMFs and obtain N modes {IMF1, IMF2, ..., IMF}. n The CEEMDAN algorithm iterates through the carbon price series to gradually extract different frequency components. Each IMF corresponds to the carbon price fluctuation characteristics at different time scales, effectively revealing the intrinsic structure and dynamic changes of the carbon price series, thus providing a foundation for subsequent prediction and analysis.

[0078] In another embodiment of this disclosure, the iterative calculation is stopped when the residual obtained in the nth iteration is a monotonic function.

[0079] In this embodiment, the termination condition for iterative calculation is to determine whether the residual is a monotonic function. This ensures that the CEEMDAN algorithm stops after extracting all meaningful intrinsic mode functions (IMFs), avoiding unnecessary calculations and ensuring the accuracy and stability of the decomposition results. A monotonic function can be a function whose value increases or decreases monotonically with the increase of the independent variable. In the CEEMDAN algorithm, the residual r... n It is a time series, if the residual r n If the residual r increases or decreases monotonically over the entire time period, then the residual r can be considered to be... n It no longer contains meaningful fluctuations and has instead converged to a stable baseline. In this case, continuing iterative decomposition is no longer meaningful, so iteration can be stopped.

[0080] In another embodiment of this disclosure, during each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual of the previous iteration, as expressed by the formula:

[0081]

[0082] Where β0 represents the initial noise level coefficient, ||·|| 2 It represents the signal energy.

[0083] In this embodiment, white noise data is introduced to increase the randomness of the first carbon price sequence, thereby reducing mode aliasing and the generation of parasitic modes. However, the level of white noise (i.e., the intensity of the noise) has a significant impact on the accuracy of the decomposition results. Therefore, appropriately selecting the white noise level is crucial for the CEEMDAN algorithm. During each iteration, the noise level coefficient for the next iteration, based on the residual from the previous iteration, is dynamically adjusted to further improve the stability and accuracy of the decomposition. The noise level coefficient for the next iteration, determined based on the residual from the previous iteration, is expressed by the following formula:

[0084]

[0085] Where β0 represents the initial noise level coefficient, ||·|| 2 It represents the signal energy.

[0086] In the first iteration, a suitable initial noise level coefficient β0 is selected. The initial noise level coefficient β0 is typically determined based on the characteristics and experience of the first carbon price sequence. For example, if the signal-to-noise ratio of the first carbon price sequence is low, a larger initial noise level coefficient may be needed to better separate the signal and noise. The white noise level coefficient β0 for the next iteration is adjusted based on the residual energy. n If the residual energy is large, it indicates that the residual still contains a significant amount of high-frequency components, and the white noise level coefficient can be appropriately increased. If the residual energy is small, it indicates that the residual mainly contains low-frequency components, and the white noise level coefficient can be appropriately decreased. Dynamically adjusting the noise level coefficient of the white noise data added in the next iteration based on the residual calculated in the previous iteration can effectively reduce noise interference and error accumulation. By using different white noise levels in different decomposition stages, the intrinsic mode functions of the signal can be extracted more accurately, improving the decomposition accuracy.

[0087] In another embodiment of this disclosure, step S103 above, which involves feature extraction and feature filtering for each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data, includes:

[0088] Step 1: Extract features from each intrinsic mode function to determine the first feature; wherein, the first feature includes: time domain features and frequency domain features;

[0089] Step 2: Calculate the Pearson correlation coefficient between the first feature and the first carbon price series, and obtain the second feature whose corresponding Pearson correlation coefficient value is greater than the first preset value.

[0090] Step 3: Use the LASSO algorithm to filter the second feature and determine the first multidimensional feature vector of historical carbon price data.

[0091] In this embodiment, feature extraction and feature selection can extract the most valuable information from the intrinsic mode functions (EMFs) and transform them into a concise first multidimensional feature vector. This not only improves the quality of the features but also reduces the number of features, thereby improving the efficiency and accuracy of the prediction model. For step 1 above, for each EMF obtained by the CEEMDAN algorithm, feature extraction is performed from two key perspectives: the time domain and the frequency domain. Time-domain features focus on the direct performance of the data over time, such as calculating the mean to reflect the average level of carbon prices; calculating the variance to measure the volatility of carbon prices; determining the peak value to capture extreme changes in carbon prices; and calculating the zero-crossing rate to understand how frequently carbon prices cross zero on the time axis. Frequency-domain features involve converting the time-domain signal to the frequency domain for analysis. Methods such as Fourier transform are used to obtain the distribution characteristics of carbon price data at different frequencies, such as spectral analysis to analyze the energy proportion of specific frequency components and uncover the implicit periodic patterns in the data. This results in a first feature that includes both time-domain and frequency-domain features, comprehensively characterizing the properties of each EMF. Regarding step 2 above, the Pearson correlation coefficient is used to measure the degree of linear correlation between two variables, with a value ranging from -1 to 1. The Pearson correlation coefficient is calculated between each extracted first feature and the original first carbon price series. If the coefficient value is close to 1 or -1, it indicates that the feature has a strong linear correlation with the carbon price series; if the coefficient value is close to 0, it indicates a weak correlation. By setting a first preset value, such as 0.3, features with a Pearson correlation coefficient value |r|>0.3 are selected to obtain the second features. This quickly filters out features with little impact on carbon prices and insignificant correlations, retaining key features closely related to carbon price changes, effectively reducing data dimensionality, reducing subsequent computation, and avoiding interference from irrelevant features in carbon price prediction results. Regarding step 3 above, the LASSO (Least Absolute Shrinkage and Selection Operator) algorithm is a regression analysis method for feature selection and regularization. Using the second feature as input, the LASSO algorithm adds an L1 regularization term to the loss function of the regression model, compressing the coefficients of some features to 0, thereby achieving the purpose of feature selection. Specifically, during the optimization process, the LASSO algorithm automatically evaluates the contribution of each secondary feature to carbon prices, discarding features with smaller contributions and retaining only those features that are significant for carbon price prediction. After screening by the LASSO algorithm, the final feature combination is converted into a first multidimensional feature vector of historical carbon price data. This first multidimensional feature vector focuses on the most valuable feature information, which can more accurately reflect the pattern of carbon price changes, providing high-quality input data for subsequent carbon price prediction models and improving the accuracy of carbon price prediction.By extracting multi-dimensional features in the time and frequency domains, we can comprehensively uncover the changing patterns of carbon price data at different levels, providing a rich information foundation for subsequent predictions. Preliminary screening using the Pearson correlation coefficient quickly eliminates features with low correlation to carbon prices, reducing data dimensionality, improving computational efficiency, and avoiding interference from redundant information in carbon price prediction results. In further screening, the LASSO algorithm not only eliminates unimportant features but also optimizes and combines features, enhancing the representativeness of the feature vector and the accuracy and stability of the prediction model. The first multi-dimensional feature vector obtained after feature screening accurately focuses on key information, better adapts to the prediction model, and significantly improves the accuracy and reliability of carbon price predictions.

[0092] In another embodiment of this disclosure, the LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data, as expressed by the formula:

[0093]

[0094] Among them, y i x represents the i-th value in the first carbon price sequence; ij w represents the value of the j-th second feature corresponding to the i-th intrinsic mode function; j Let L represent the weight coefficient of the j-th second feature; L represent the loss function; λ represent the regularization strength parameter; N represent the number of intrinsic mode functions; and M represent the number of second features.

[0095] In this embodiment, the LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data, as expressed by the formula:

[0096]

[0097] Among them, y i x represents the i-th value in the first carbon price sequence; ij w represents the value of the j-th second feature corresponding to the i-th intrinsic mode function; j The weight coefficient of the j-th second feature is represented by ; N represents the number of intrinsic mode functions; M represents the number of second features; L represents the loss function, which includes two parts:

[0098] The first part is the mean square error term: It is used to measure how well the second feature fits the first carbon price sequence, so that the second feature is as close as possible to the first carbon price sequence;

[0099] The second part consists of L1 regularization terms: The weight coefficients used to penalize features are made to make the coefficients of unimportant features approach zero. The regularization strength parameter λ controls the weight of the regularization term; a larger λ will cause more second features to be compressed to zero. The weight coefficient w of each second feature is then examined. j If the weight coefficient of a certain second feature approaches zero, for example, less than a preset threshold, then the second feature is considered unimportant and can be removed. The retained second features are then converted into a first multidimensional feature vector, which has a significant impact on the prediction of carbon prices.

[0100] In another embodiment of this disclosure, it further includes:

[0101] Step 1: Obtain the first factors affecting carbon prices;

[0102] Step 2: Perform feature screening on the first carbon price influencing factors to determine the second multidimensional feature vector of the carbon price influencing factors;

[0103] Step 3: Input the first multidimensional feature vector and the second multidimensional feature vector into the extreme learning machine model to obtain the carbon price prediction result.

[0104] In this embodiment, historical carbon price data characteristics and first carbon price influencing factors are comprehensively considered to avoid the limitations of a single data source, more comprehensively reflect the internal mechanism and external drivers of carbon price fluctuations, and improve the reliability of prediction results. Regarding step 1 above, the first carbon price influencing factors are obtained. Carbon price fluctuations are influenced by a combination of factors. At the market level, changes in energy prices (such as coal and natural gas prices) directly affect enterprises' carbon emission costs, thereby affecting the supply and demand relationship and carbon prices in the carbon market. Macroeconomic conditions (such as GDP growth rate and inflation rate) reflect the overall economic development; during periods of economic prosperity, increased enterprise production activities lead to higher carbon emission demand, driving up carbon prices. At the policy level, government policies on carbon quota allocation and carbon trading market regulation directly determine the operating rules and resource allocation of the carbon market, playing a crucial guiding role in carbon price trends. Furthermore, technological innovation is also a significant factor. Breakthroughs in new energy technologies and the development of carbon capture and storage technologies can reduce enterprises' emission reduction costs and change market expectations regarding carbon emission rights, thus affecting carbon prices. Through literature review, industry report analysis, expert interviews, and other methods, factors that may influence carbon prices were extensively collected, resulting in the first set of carbon price influencing factors, providing a rich data foundation for subsequent analysis. Regarding step 2 above, after obtaining the first set of carbon price influencing factors, since not all factors have a significant impact on carbon prices, and some factors may have overlapping information, feature screening of these factors is necessary. For example, correlation analysis can be used to calculate the degree of association between each influencing factor and carbon prices, eliminating factors with weak correlations and selecting those with a certain impact on carbon prices. The final identified key factors and their characteristics constitute the second multidimensional feature vector of carbon price influencing factors. This second multidimensional feature vector focuses on the core factors that significantly affect carbon prices, presenting key information about carbon price influencing factors in a more concise and efficient manner. Regarding step 3 above, the first and second multidimensional feature vectors are input into an extreme learning machine model to obtain the predicted carbon price. Extreme Learning Machine (ELM) is a highly efficient machine learning model that integrates a first multidimensional feature vector obtained by processing historical carbon price data with a second multidimensional feature vector obtained after filtering the first influencing factors of carbon price. These two vectors are then used as input data for the ELM model. During training, the ELM model automatically learns the complex nonlinear relationship between the first and second multidimensional feature vectors and carbon prices. ELM possesses powerful nonlinear fitting capabilities, effectively capturing the complex internal patterns and combined effects of external influencing factors in carbon price changes. After inputting the first and second multidimensional feature vectors into the trained ELM model, it can quickly output corresponding carbon price predictions, providing timely and accurate references for relevant decision-making.

[0105] In another embodiment of this disclosure, step 2 above, which involves screening the first carbon price influencing factors and determining the second multidimensional feature vector of the carbon price influencing factors, includes:

[0106] Step 1: Calculate the Pearson correlation coefficient between the first carbon price influencing factor and the first carbon price series, and obtain the second carbon price influencing factor whose corresponding Pearson correlation coefficient value is greater than the second preset value among the first carbon price influencing factors;

[0107] Step 2: Use the LASSO algorithm to screen the second carbon price influencing factors and determine the second multidimensional feature vector of the historical carbon price influencing factors.

[0108] In this embodiment, the Pearson correlation coefficient first filters out factors with weak linear correlation, and the LASSO algorithm further eliminates nonlinear redundant features. This two-layer screening mechanism ensures that the feature vector focuses on the core influencing factors. For step one, the Pearson correlation coefficient with the first carbon price series is calculated for each of the first carbon price influencing factors (such as energy prices, GDP growth rate, carbon policy indicators, etc.). The Pearson correlation coefficient reflects the strength and direction of the factor's influence on carbon prices by measuring the consistency of linear changes between variables. For example, a rise in coal prices is usually positively correlated with carbon prices. If the Pearson correlation coefficient is greater than a second preset value, for example, |r|>0.3, then the first carbon price influencing factor is a "strongly correlated factor," and thus it is determined as the second carbon price influencing factor. For step two, the min-max normalization method is used to uniformly map the numerical range of the second carbon price influencing factor to the [0,1] interval. For example, an energy price indicator with an original value of [50, 200] yuan is normalized to a dimensionless value of [0, 1], eliminating the interference of different dimensional factors on the LASSO algorithm. An L1 regularization penalty function is introduced into the LASSO algorithm, which makes the coefficients of some features strictly zero, thus achieving feature selection. The LASSO algorithm automatically evaluates the contribution of each second carbon price influencing factor to carbon price prediction: for second carbon price influencing factors with weak predictive effect, their regression coefficients are compressed to 0 and eliminated; the retained second carbon price influencing factors (with non-zero coefficients) are converted into a second multidimensional feature vector. For example, among carbon policy-related factors, the LASSO algorithm retains "carbon quota allocation" while eliminating "policy release frequency," because the former has a more significant non-linear correlation with carbon prices. The final output second multidimensional feature vector of historical carbon price influencing factors is sparse, including only core factors that have a substantial impact on carbon price fluctuations, such as energy prices, macroeconomic indicators, and key policy variables, forming a feature combination that combines predictive effectiveness and explanatory power. LASSO's sparsity processing can effectively combat noise interference in high-dimensional data, compress the feature dimension to the optimal range, and avoid the impact of the "curse of dimensionality" on the extreme learning machine model.

[0109] Based on the same disclosed concept, this disclosure also provides a carbon price prediction device. Since the principle of these devices in solving the problem is similar to that of the aforementioned carbon price prediction method, the implementation of the device can refer to the implementation of the aforementioned method, and the repeated parts will not be described again.

[0110] The carbon price prediction device provided in this disclosure embodiment, such as Figure 2 As shown, it includes:

[0111] The preprocessing module 201 is used to acquire historical carbon price data and determine a first carbon price sequence that changes carbon prices over time based on the historical carbon price data.

[0112] The intrinsic mode function determination module 202 is used to add white noise data to the first carbon price sequence and use the CEEMDAN algorithm to iteratively calculate the intrinsic mode function and residuals; wherein, in each iteration calculation process, the noise level coefficient of the white noise data added in the next iteration calculation is determined based on the residual calculated in the previous iteration.

[0113] Feature extraction module 203 is used to extract and filter features for each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data;

[0114] The prediction module 204 is used to input the first multidimensional feature vector into the extreme learning machine model to obtain the prediction result of carbon price.

[0115] In another embodiment of this disclosure, the intrinsic mode function determination module 202 is used to add white noise data to the first carbon price sequence, and to calculate the intrinsic mode function and residual pair using the CEEMDAN algorithm in the first iteration. The formula is expressed as follows:

[0116] r1 = <M(X+β0E1(ω i ))>

[0117] IMF1 = X - r1

[0118] Where X represents the first carbon price series, ω i Let represent the i-th white noise data, i = 1, 2, ..., L, β0 represent the initial noise level coefficient, β0 > 0, E1 represent the first EMD decomposition operation, M represent the local mean operation, <> represent the average operation, r1 represent the residual obtained from the first iteration, and IMF1 represent the intrinsic mode function obtained from the first iteration.

[0119] The formula for calculating the intrinsic mode functions and residuals using the CEEMDAN algorithm in the nth iteration is expressed as follows:

[0120] r n = <M(r n-1 +β n-1 E n (ω i ))>

[0121] IMF n =r n -r n-1

[0122] Where n≥2.

[0123] In another embodiment of this disclosure, the intrinsic mode function determination module 202 is used to stop the iterative calculation when the residual obtained in the nth iteration is a monotonic function.

[0124] In another embodiment of this disclosure, the intrinsic mode function determination module 202 is used to determine the noise level coefficient of the white noise data added in the next iteration calculation based on the residual of the previous iteration calculation during each iteration calculation process, as expressed by the formula:

[0125]

[0126] Where β0 represents the initial noise level coefficient, ||·|| 2 It represents the signal energy.

[0127] In another embodiment of this disclosure, the feature extraction module 203 is used to extract features from each of the intrinsic mode functions to determine a first feature; wherein the first feature includes: time-domain features and frequency-domain features;

[0128] Calculate the Pearson correlation coefficient between the first feature and the first carbon price sequence to obtain a second feature whose corresponding Pearson correlation coefficient value is greater than a first preset value.

[0129] The LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data.

[0130] In another embodiment of this disclosure, the feature extraction module 203 is used to filter the second feature using the LASSO algorithm to determine the first multidimensional feature vector of historical carbon price data, expressed by the formula:

[0131]

[0132] Among them, y i x represents the i-th value in the first carbon price sequence; ij w represents the value of the j-th second feature corresponding to the i-th intrinsic mode function; j Let L represent the weight coefficient of the j-th second feature; L represent the loss function; λ represent the regularization strength parameter; N represent the number of intrinsic mode functions; and M represent the number of second features.

[0133] In another embodiment of this disclosure, the preprocessing module 201 is further configured to obtain a first carbon price influencing factor;

[0134] The feature extraction module 203 is used to perform feature screening on the first carbon price influencing factors and determine the second multidimensional feature vector of the carbon price influencing factors.

[0135] The prediction module 204 is used to input the first multidimensional feature vector and the second multidimensional feature vector into the extreme learning machine model to obtain the prediction result of carbon price.

[0136] In another embodiment of this disclosure, the feature extraction module 203 is used to calculate the Pearson correlation coefficient between the first carbon price influencing factor and the first carbon price sequence, and to obtain the second carbon price influencing factor whose corresponding Pearson correlation coefficient value is greater than the second preset value among the first carbon price influencing factors.

[0137] The LASSO algorithm was used to screen the second carbon price influencing factors and determine the second multidimensional feature vector of the historical carbon price influencing factors.

[0138] Based on the same disclosed concept, embodiments of this disclosure provide a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the carbon price prediction method as described in any of the above embodiments.

[0139] Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments of this disclosure can be implemented in hardware or by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of this disclosure.

[0140] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes in the drawings are not necessarily essential for implementing this disclosure.

[0141] Those skilled in the art will understand that the modules in the apparatus of the embodiments can be distributed in the apparatus of the embodiments as described in the embodiments, or they can be located in one or more devices different from this embodiment with corresponding changes. The modules of the above embodiments can be combined into one module, or they can be further divided into multiple sub-modules.

[0142] The sequence numbers of the embodiments disclosed above are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0143] Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from its spirit and scope. Therefore, if such modifications and variations fall within the scope of the claims of this disclosure and their equivalents, this disclosure is also intended to include such modifications and variations.

Claims

1. A carbon price prediction method, characterized in that, include: Obtain historical carbon price data; and based on the historical carbon price data, determine a first carbon price sequence that reflects the change of carbon prices over time. White noise data is added to the first carbon price series, and the intrinsic mode function and residuals are iteratively calculated using the CEEMDAN algorithm. In each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration. For each of the intrinsic mode functions, feature extraction and feature filtering are performed to determine the first multidimensional feature vector of historical carbon price data; The first multidimensional feature vector is input into the extreme learning machine model to obtain the carbon price prediction result.

2. The method as described in claim 1, characterized in that, Adding white noise data to the first carbon price series, the intrinsic mode function and residuals are iteratively calculated using the CEEMDAN algorithm, including: Adding white noise data to the first carbon price series, the formula for calculating the intrinsic mode function and residual pair in the first iteration of the CEEMDAN algorithm is expressed as follows: r1= <M(X+β0E1(ω i ))> IMF1 = X - r1 Where X represents the first carbon price series, ω i Let represent the i-th white noise data, i = 1, 2, ..., L, β0 represent the initial noise level coefficient, β0 > 0, E1 represent the first EMD decomposition operation, M represent the local mean operation, <> represent the average operation, r1 represent the residual obtained from the first iteration, and IMF1 represent the intrinsic mode function obtained from the first iteration. The formula for calculating the intrinsic mode functions and residuals using the CEEMDAN algorithm in the nth iteration is expressed as follows: r n = <M(r n-1 +b n-1 E n (oh i ))> IMF n =r n -r n-1 Where n≥2.

3. The method as described in claim 2, characterized in that, If the residual obtained in the nth iteration is a monotonic function, the iteration calculation is stopped.

4. The method as described in claim 2, characterized in that, In each iteration of the calculation, the noise level coefficient for adding white noise data in the next iteration is determined based on the residual from the previous iteration. The formula is as follows: Where β0 represents the initial noise level coefficient, ||·|| 2 It represents the signal energy.

5. The method as described in claim 1, characterized in that, The step of extracting and filtering features for each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data includes: For each of the intrinsic mode functions, feature extraction is performed to determine a first feature; wherein, the first feature includes: time-domain features and frequency-domain features; Calculate the Pearson correlation coefficient between the first feature and the first carbon price sequence to obtain a second feature whose corresponding Pearson correlation coefficient value is greater than a first preset value. The LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data.

6. The method as described in claim 5, characterized in that, The LASSO algorithm is used to filter the second feature to determine the first multidimensional feature vector of historical carbon price data, as expressed by the formula: Among them, y i x represents the i-th value in the first carbon price sequence; ij w represents the value of the j-th second feature corresponding to the i-th intrinsic mode function; j Let L represent the weight coefficient of the j-th second feature; L represent the loss function; λ represent the regularization strength parameter; N represent the number of intrinsic mode functions; and M represent the number of second features.

7. The method as described in claim 1, characterized in that, Also includes: Identify the primary factors influencing carbon prices; Feature screening is performed on the first carbon price influencing factors to determine the second multidimensional feature vector of the carbon price influencing factors; The first multidimensional feature vector and the second multidimensional feature vector are input into the extreme learning machine model to obtain the carbon price prediction result.

8. The method as described in claim 7, characterized in that, The step of screening the first carbon price influencing factors to determine the second multidimensional feature vector of the carbon price influencing factors includes: Calculate the Pearson correlation coefficient between the first carbon price influencing factor and the first carbon price sequence, and obtain the second carbon price influencing factor whose corresponding Pearson correlation coefficient value is greater than the second preset value among the first carbon price influencing factors; The LASSO algorithm was used to screen the second carbon price influencing factors and determine the second multidimensional feature vector of the historical carbon price influencing factors.

9. A carbon price prediction device, characterized in that, include: The preprocessing module is used to acquire historical carbon price data; Based on the historical carbon price data, a first carbon price sequence is determined to reflect the change of carbon prices over time. The intrinsic mode function determination module is used to add white noise data to the first carbon price sequence and iteratively calculate the intrinsic mode function and residuals using the CEEMDAN algorithm; wherein, in each iteration, the noise level coefficient of the white noise data added in the next iteration is determined based on the residual calculated in the previous iteration. The feature extraction module is used to extract and filter features for each intrinsic mode function to determine the first multidimensional feature vector of historical carbon price data. The prediction module is used to input the first multidimensional feature vector into the extreme learning machine model to obtain the predicted carbon price.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the carbon price prediction method as described in any one of claims 1 to 8.

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