Carbon future price prediction method and system based on multilevel feature engineering and bidirectional gating

Abstract

The invention provides a carbon future price prediction method and system based on multi-level feature engineering and bidirectional gating. According to the invention, accurate prediction of the carbon future price is realized through data preprocessing, multi-level feature engineering, BiGRU construction, point prediction and interval prediction. Wherein the multi-level feature engineering integrates original features, statistical features, differential features and similarity features, the similarity features are extracted through a probability density network (PDN) and random walk similarity propagation (SRW), and the long-range dependency capture capability is enhanced. According to the method, the long-range dependency recognition capability of the model is remarkably enhanced through the probability density network and the random walk similarity propagation method, and the probability density network constructs a global similarity matrix by quantifying the distribution similarity between time windows; the node indirect relation is captured through random walk similarity propagation, the similarity features enable the model to utilize historical similar situation information, and ablation experiments prove that the MAE of the model containing the similarity features is reduced by about 6.1%.

Description

Technical Field

[0001] This invention relates to the fields of deep learning and futures prediction technology, and in particular to a carbon futures price prediction method and system based on multi-level feature engineering and two-way gating. Background Technology

[0002] Carbon price forecasting technology refers to the technical methods used to predict the future trend of carbon allowance prices in the carbon emission trading market using mathematical models, statistical methods, or artificial intelligence algorithms. As carbon dioxide is a major greenhouse gas, establishing a carbon trading market mechanism is a key policy tool for addressing climate change, promoting a global low-carbon transition through market mechanisms. The core of the carbon trading market is to convert carbon emission rights into tradable scarce resources, thereby constructing an emission reduction incentive system based on price signals. Carbon price fluctuations directly affect the economic decisions of market participants. However, compared with traditional financial markets, the carbon market exhibits significant immaturity, including high uncertainty, drastic price volatility, and data non-stationarity, all of which pose challenges to accurate price forecasting.

[0003] In existing technologies, time series prediction methods based on complex networks are gradually being applied, such as the PLVG algorithm, phase space coarsening, and probability density recursive networks. These methods map time series data to complex network structures and utilize network topology features to reveal patterns in data fluctuations. However, existing technologies still have the following significant drawbacks: Insufficient feature extraction: Most methods only use the original price series as input and fail to extract features from multiple levels such as statistical characteristics, difference characteristics, and similarity characteristics. The feature expression is simple and cannot fully characterize the short-term dynamics, long-term trends, distribution characteristics and complex dependencies of carbon price series, resulting in limited model expressive power and low prediction accuracy. Information leakage problem of data decomposition method: Traditional data decomposition prediction model decomposes the original carbon price time series and then uses artificial intelligence model to analyze it. This can easily destroy the inherent relationship between different features in the series. Moreover, the decomposed signal may contain information about future time points at the current moment, causing information leakage, which leads to overfitting of model training and a significant drop in prediction performance in practical applications. Insufficient ability to capture long-range dependencies: Traditional statistical models are based on linear assumptions and cannot capture non-linear long-term dependency patterns; even though deep learning models such as LSTM have a certain long-range memory capability, they are still insufficient when dealing with complex global similarity structures and lack effective mechanisms to identify and utilize potential similarity relationships between different time windows in time series. The ability to quantify uncertainty is lacking: existing forecasting methods can only provide a single, definite value for future prices, and cannot describe the potential range of price fluctuations, making it difficult to meet the needs of risk assessment and decision support; while existing interval forecasting methods have weak ability to balance and control between coverage and interval width. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a carbon futures price prediction method and system based on multi-level feature engineering and two-way gating. This invention can improve prediction accuracy, avoid information leakage, enhance the ability to capture long-range dependencies, and provide reliable uncertainty quantification information.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a carbon futures price prediction method based on multi-level feature engineering and two-way gating, comprising the following steps: S1) Preprocess the original carbon price time series; S2) Based on the preprocessed carbon price time series, extract the original features, statistical features, difference features and similarity features, and concatenate the multiple features to form an enhanced feature matrix; S3) Construct a two-layer bidirectional gated recurrent unit network prediction model BiGRU and train it. S4) Use the trained bi-layer bidirectional gated recurrent unit network (BiGRU) prediction model to predict carbon futures price points and output the price point prediction results. S5) Based on the point prediction results, a Gaussian process is used to construct a prediction interval with multiple confidence levels to quantify the uncertainty of price fluctuations.

[0006] Preferably, in step S2), the original feature extraction is performed by directly extracting the features within each time window. The original observations are used as the original feature vector.

[0007] Preferably, in step S2), the extraction of statistical features is as follows: calculate the mean, standard deviation, range, skewness and kurtosis of each window, and concatenate the five statistical features into a statistical feature.

[0008] Preferably, in step S2), the difference features include first-order difference, second-order difference, and fourth-order difference, which respectively capture short-term, medium-term, and long-term dynamic changes.

[0009] Preferably, in step S2), similarity features are generated using a probability density network (PDN) and a random walk similarity propagation (SRW) method.

[0010] Preferably, in step S2), similarity features are extracted, specifically including the following steps: S241) Construct a probability density network and calculate a normalized similarity score. The probability density network is a weighted network constructed by quantifying the distribution similarity between time windows to capture the implicit patterns of carbon price series. Each time window is regarded as a node in the network. S242) Enhance the global consistency of the initial similarity matrix by random walk similarity propagation, capture the indirect relationships between nodes, accumulate the transfer results through multi-step iteration, normalize the weights by combining the weighted out-degree of nodes and the total weight of the network, and eliminate directional bias through symmetry processing to obtain the global similarity matrix; S243) Calculate similarity features for each window based on the generated global similarity matrix.

[0011] Preferably, in step S3), the BiGRU prediction model consists of two GRU networks with opposite propagation directions, which simultaneously learn the forward and backward dependencies of the sequence.

[0012] Preferably, in step S3), the BiGRU prediction model of the two-layer bidirectional gated recurrent unit network consists of, from bottom to top: an input layer, a first bidirectional GRU layer, a Dropout layer, a second bidirectional GRU layer, and a fully connected output layer. The first bidirectional GRU layer and the second bidirectional GRU layer both include a forward GRU sublayer and a backward GRU sublayer.

[0013] Preferably, in step S5), based on the point prediction results, a Gaussian process is used to construct a prediction interval with multiple confidence levels to quantify the uncertainty of price fluctuations, as follows: S51) Assuming prediction error Follows a mean of 0 and a standard deviation of Gaussian distribution ; S52) For a given confidence level The upper and lower bounds of the prediction interval, i.e.: In the formula, The lower bound; The upper boundary; The quantiles of the standard normal distribution; The significance level parameter; S53) The predicted interval coverage probability (PICP), the predicted interval normalized average width (PINAW), and the cumulative width deviation (AWD) are used to evaluate the interval prediction performance.

[0014] Secondly, the present invention also provides a carbon futures price prediction system based on multi-level feature engineering and two-way gating, comprising: The data acquisition and preprocessing module is used to acquire the raw carbon price time series and preprocess it. The multi-level feature engineering module extracts original features, statistical features, difference features, and similarity features based on the preprocessed carbon price time series, and concatenates the multiple features to form an enhanced feature matrix; The prediction model building module is used to build a two-layer bidirectional gated recurrent unit network prediction model BiGRU and train it. The futures price prediction module uses a trained bi-dimensional gated recurrent unit network (BiGRU) prediction model to predict carbon futures prices and outputs the price prediction results. Futures price range prediction is based on point prediction results. A Gaussian process is used to construct prediction ranges with multiple confidence levels to quantify the uncertainty of price fluctuations.

[0015] The beneficial effects of this invention are as follows: 1. This invention integrates original features, statistical features, difference features, and similarity features, and comprehensively extracts data features through multi-level feature engineering. It adopts a non-decomposition feature extraction strategy and directly extracts features from the original sequence through sliding window and multi-level feature calculation, maintaining the temporal integrity and causal relationship of the data, eliminating the risk of overfitting caused by information leakage, and improving the generalization ability of the model. 2. This invention significantly enhances the model's ability to identify long-range dependencies through probability density networks and random walk similarity propagation. The probability density network constructs a global similarity matrix by quantifying the distributional similarity between time windows; random walk similarity propagation captures indirect relationships between nodes. Similarity features enable the model to utilize historical similar context information. Ablation experiments demonstrate that the MAE of the model including similarity features is reduced by approximately 6.1%. 3. At a 95% confidence level, the present invention achieves 98.51% PICP, only 0.2853 PINAW, and 0.0002 AWD, ensuring high coverage while achieving interval compactness and symmetry, providing comprehensive support for risk assessment. 4. This invention employs a dual-layer BiGRU structure to simultaneously capture forward and backward temporal dependencies; compared to BiLSTM, the BiGRU network reduces the number of parameters by 25% and shortens the training time by 15-20%, maintaining its predictive performance advantage while being more suitable for practical application scenarios. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the method of an embodiment of the present invention; Figure 2 This is a comparison chart of EUA carbon price point prediction results in embodiments of the present invention; Figure 3This is a graph showing the prediction results of the present invention at three confidence levels: 85%, 90%, and 95%. Detailed Implementation

[0017] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings: Example 1 like Figure 1 As shown, this embodiment provides a carbon futures price prediction method based on multi-level feature engineering and two-way gating, including the following steps: S1) Preprocessing the original carbon price series; specifically including the following steps: S11), using 3 σ The criteria are used to remove outliers; First, calculate the mean of the carbon price series. and standard deviation ,Right now: ; ; In the formula, For the first Individual carbon price value; The length of the original carbon price time series; Will exceed Data points within a certain range are considered outliers, and these outliers are either removed or replaced using linear interpolation. S12), the length used is L A sliding window is used to segment the time series; Let the original carbon price series be... , No. Each time window is represented as: ,in, Indicates the first The first time window Individual carbon price value; The sliding step size is set to 1, meaning there is a certain distance between adjacent windows. L- One data point overlaps; S13) Divide the split data into training and test sets in an 8:2 ratio.

[0018] S2) Based on the preprocessed carbon price time series, extract original features, statistical features, difference features, and similarity features, and concatenate the multiple features to form an enhanced feature matrix; specifically as follows: S21) Extracting time window L The original observations are used as the original features. ,Right now: ; S22) Extracting statistical features ,Right now: In the formula, This represents the average price level within the window. The standard deviation within the window; The range represents the price range within the window. , These are the maximum and minimum values ​​of all data within the window, respectively; Skewness is used to quantify the asymmetry of price distribution. Positive skewness indicates that the right tail of the distribution is longer, while negative skewness indicates that the left tail is longer. Kurtosis is used to describe the sharpness of the price distribution peaks. The larger the kurtosis, the sharper the distribution and the higher the probability of extreme values. The five statistical indicators together constitute a comprehensive description of the central trend, variability, dispersion, asymmetry and kurtosis of the data within each window, which can capture the morphological characteristics of price distribution and provide rich statistical information for the model.

[0019] S23) Extracting differential features ,Right now: in, , , These are the first-order difference, second-order difference, and fourth-order difference, respectively. First-order difference Measuring instantaneous changes between adjacent observations captures short-term trends, reflects the immediate volatility of prices, and can identify rapid price increases or decreases. ; Second-order differencing captures changes over larger intervals, identifies medium-term change patterns, filters out short-term noise, and reveals price trends on medium-term timescales. ; The fourth-order difference further expands the interval to capture long-term changes, revealing long-term trends and providing insights into the long-term evolution of prices. It can identify persistent upward or downward trends. .

[0020] S24) A global similarity matrix is ​​generated using a probability density network (PDN) and a random walk similarity propagation (SRW) method to extract similarity features. ,Right now: S241) Construct a probability density network and calculate a normalized similarity score. The probability density network is a weighted network constructed by quantifying the distribution similarity between time windows to capture the implicit patterns of carbon price series. Each time window is regarded as a node in the network; specifically as follows: S2411) Calculate the cumulative distribution function (CDF) for each time window. and The probability density function is estimated using kernel density estimation. Then, the cumulative distribution function is obtained by integrating the estimated density function. ;Right now: ; In the formula, For bandwidth parameters; For kernel functions; Indicates the index of the sliding window; This represents the number of sliding windows; S2412), in the interval , Equally spaced sampling points For each sampling point Calculate the CDF difference between the left and right offsets, i.e.: ; ; In the formula, The neighborhood radius parameter; , These represent the left offset CDF difference and the right offset CDF difference, respectively. , Time windows Cumulative distribution function, time window The cumulative distribution function; By comparing the offset differences of CDF at multiple sampling points, the similarity between two window distributions can be finely characterized.

[0021] S2413) Generate similarity scores and identify windows. CDF relative to window Maximum excess of offset CDF and minimum deficiency And adjust it to the effective range: In the formula, , These are the maximum insufficiency on the left side of the normalized data and the maximum insufficiency on the right side of the normalized data, respectively. , These represent the minimum values ​​of the left-offset CDF difference and the right-offset CDF difference, respectively. , These are the maximum left-side overflow and the maximum right-side overflow under normalization, respectively. , These represent the maximum values ​​of the left-offset CDF difference and the right-offset CDF difference, respectively. Then calculate the proportion of the overlapping area: In the formula, , These represent the overlap ratio on the left and the overlap ratio on the right, respectively. Finally, the normalized similarity score is obtained. : in, , The larger the value, the higher the similarity of the distributions between the two windows.

[0022] S242) Enhance the global consistency of the initial similarity matrix through random walk similarity propagation, capturing indirect relationships between nodes, as follows: S2421), based on the initial similarity score matrix Construct a weighted transition matrix ,Right now: In the formula, A Boolean parameter indicating whether to use weighted normalization; Indicates the index of the time window; By using a weighted transfer method, nodes are allocated transfer probabilities proportionally, thus preserving the original similarity weight information; (S2422) Accumulates transition results through multi-step walk iterations. In each iteration, the transition matrix of the random walk is updated, and the result is added to the final similarity matrix. In; that is: ; In the formula, express Step transition matrix; (S2423) Combining the weighted out-degree of nodes and the total network weight, weight normalization is performed, and directional bias is eliminated through symmetry processing to obtain the global similarity matrix. ; In the formula, Represents the normalized similarity matrix ; express The transpose of the matrix; in, Represents a node Weighted out-degree; This represents the total weight of the network.

[0023] S243) Calculate similarity features for each window based on the generated global similarity matrix. ; In this embodiment, for each window, the mean feature of the three most similar windows is calculated, that is: ; In the formula, Indicates the first The top 3 most similar windows of the sliding window; This represents the feature value of the k-th window.

[0024] S25) Concatenate the original features, statistical features, difference features, and similarity features to form an enhanced feature matrix. ,Right now: .

[0025] S3) Construct a two-layer bidirectional gated recurrent unit network prediction model BiGRU, and train the enhanced feature matrix obtained in step S2); In this embodiment, the BiGRU prediction model consists of two GRU networks with opposite propagation directions, which simultaneously learn the forward and backward dependencies of the sequence. The BiGRU prediction model, described above, consists of the following layers from bottom to top: input layer, first bidirectional GRU layer, Dropout layer, second bidirectional GRU layer, and fully connected output layer. The first bidirectional GRU layer and the second bidirectional GRU layer both include a forward GRU sublayer and a backward GRU sublayer.

[0026] S4) The trained two-layer bidirectional gated recurrent unit network (BiGRU) prediction model is used to predict carbon futures price points, and the price point prediction results are output. ;Right now: In this embodiment, the enhanced feature matrix is ​​input into the trained two-layer bidirectional gated recurrent unit network prediction model BiGRU. The specific prediction process includes the following five steps: (1) Input layer processing: receiving the enhanced feature matrix The input data is organized as a three-dimensional tensor with dimensions ( ),in For batch size, The time window length, Total feature dimension; (2) Processing of the first bidirectional GRU layer: This layer contains a forward GRU sublayer and a backward GRU sublayer. The forward GRU sublayer is processed in chronological order. The input sequences are processed sequentially, and the historical dependencies of carbon prices are captured through reset and update gate mechanisms. The data is then processed in reverse order in the GRU sublayer. Process the input sequence, capture future trend information, at each time step The forward and backward hidden states are concatenated.

[0027] (3) Dropout layer processing: The output of the first bidirectional GRU layer is randomly deactivated with dropout probability. (In this embodiment, it is set to 0.2) Randomly set the output of some neurons to zero to prevent the model from overfitting and enhance the generalization ability.

[0028] (4) Second bidirectional GRU layer processing: Receives the output of the Dropout layer as input and further extracts high-level temporal features. This layer also contains forward and backward GRU sub-layers. The forward sub-layer learns the sequence pattern after processing by the first layer, and the backward sub-layer captures deep dependencies from the reverse direction.

[0029] (5) Processing of the fully connected output layer: Extract the last time step of the second bidirectional GRU layer The hidden state, whose state vector integrates forward and backward information throughout the entire time window.

[0030] The entire forecasting process fully captures the forward historical dependence and backward trend information of the carbon price series through a two-layer, two-way structure. Combined with Dropout regularization and multi-level feature engineering, it achieves high-precision forecasting of carbon futures prices. Compared with unidirectional or single-layer structures, this two-layer, two-way architecture can more comprehensively understand the complex dynamic characteristics of the price series, significantly improving forecast accuracy and robustness.

[0031] In addition, this embodiment uses mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) to evaluate the point prediction performance.

[0032] S5) Based on the point prediction results, a Gaussian process is used to construct prediction intervals with multiple confidence levels to quantify the uncertainty of price fluctuations; specifically as follows: S51) Assuming prediction error Follows a mean of 0 and a standard deviation of Gaussian distribution ,Right now: In the formula, Represents the actual carbon price; the standard deviation is estimated using the prediction error from the training or validation set. .

[0033] S52) For a given confidence level The upper and lower bounds of the prediction interval, i.e.: In the formula, The lower bound; The upper boundary; The quantiles of the standard normal distribution; The significance level parameter; A higher confidence level results in a larger quantile, a wider prediction interval, and a higher probability of covering the actual value, but also a lower information content within the interval. This embodiment selects three confidence levels: 85%, 90%, and 95%, to meet the decision-making needs of different risk preferences.

[0034] S53) The predicted interval coverage probability (PICP), the predicted interval normalized average width (PINAW), and the cumulative width deviation (AWD) are used to evaluate the interval prediction performance; the ideal interval should meet the following requirements: PICP Confidence level, PINAW as small as possible, AWD close to 0.

[0035] In this embodiment, the predicted interval coverage probability (PICP) is expressed as: ; In the formula, This indicates an indicator function; it is 1 if the condition is met, and 0 otherwise. Indicates the total number of test samples; The normalized average width of the prediction interval, PINAW, is expressed as: In the formula, , These represent the maximum and minimum values ​​of the actual observed values ​​in the test set, respectively. The PINAW is the ratio of the average width of the prediction interval to the data range. The smaller the PINAW, the more compact the interval and the more accurate the prediction. Normalization makes the PINAW values ​​comparable across different datasets.

[0036] The cumulative width deviation (AWD) is expressed as: It reflects the degree to which the interval boundary deviates from the actual value. The closer the AWD is to 0, the more symmetrical and reliable the prediction interval is, indicating that the actual value is located near the center of the interval.

[0037] In this embodiment, the dataset is divided into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. To verify the effectiveness of the integrated model, Support Vector Machine (SVM), XGBoost, MLP, and BiLSTM models are selected as comparison objects, as these models are representative in time series prediction. The results after experimental operation are shown in Table 1. Table 1. Comparison of results between this embodiment and existing models. Table 1 shows the experimental conclusions: the MFE-BiGRU model proposed in this embodiment achieved the best results in this study, with a MAE of 1.6905, MSE of 4.065, RMSE of 2.0162, and MAPE of 2.44%. Compared with MFE-BiLSTM, MFE-BiGRU reduced MAE by 10.9%, MSE by 28.5%, RMSE by 15.4%, and MAPE by 9.3%. These results indicate that, compared with other models, BiGRU has a stronger ability to capture long-term dependencies and nonlinear features in time series data.

[0038] Figure 2 This paper compares the predicted curves of five models—MFE-SVM, MFE-XGBoost, MFE-MLP, MFE-BiLSTM, and MFE-BiGRU—with the actual carbon price curves. The horizontal axis represents the test set time index, and the vertical axis represents the carbon price. The solid black line represents the actual price, and the five dashed lines of different colors represent the prediction results of the five models. The graph clearly shows that the predicted curves of MFE-BiGRU (red dashed line) and MFE-BiLSTM (blue dashed line) are closest to the actual values, while MFE-SVM (green dashed line) and MFE-XGBoost (yellow dashed line) show significant deviations. The graph also includes magnified views of key fluctuation areas to further highlight the advantages of MFE-BiGRU.

[0039] As shown in Table 2, MFE-BiGRU outperforms other models in terms of coverage reliability, interval width control, and overall prediction capability. By accurately modeling time-series dependencies, MFE-BiGRU can dynamically balance coverage probability and interval sharpness, providing more accurate and information-rich interval predictions and offering key support for decision-making processes in risk management.

[0040] Table 2. Interval Prediction Performance Evaluation Results Figure 3 The MFE-BiGRU model demonstrates its powerful predictive capabilities. The actual price curve fits the predicted price curve closely, and the confidence intervals at the 85%, 90%, and 95% confidence levels effectively capture the fluctuations in EU Emissions Allowance (EUA) prices. This indicates that the model can balance the trade-off between interval width and coverage, providing a reliable prediction interval that is both accurate and applicable to practical situations.

[0041] Example 2 This embodiment provides a carbon futures price prediction system based on multi-level feature engineering and two-way gating, including: The data acquisition and preprocessing module is used to acquire the raw carbon price time series and preprocess it. The multi-level feature engineering module extracts original features, statistical features, difference features, and similarity features based on the preprocessed carbon price time series, and concatenates the multiple features to form an enhanced feature matrix; The prediction model building module is used to build a two-layer bidirectional gated recurrent unit network prediction model BiGRU and train it. The futures price prediction module uses a trained bi-dimensional gated recurrent unit network (BiGRU) prediction model to predict carbon futures prices and outputs the price prediction results. Futures price range prediction is based on point prediction results. A Gaussian process is used to construct prediction ranges with multiple confidence levels to quantify the uncertainty of price fluctuations.

[0042] The embodiments and descriptions above are merely illustrative of the principles and preferred embodiments of the present invention. Various changes and modifications may be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A carbon futures price prediction method based on multi-level feature engineering and bidirectional gating, characterized in that, Includes the following steps: S1) Preprocess the original carbon price time series; S2) Based on the preprocessed carbon price time series, extract the original features, statistical features, difference features and similarity features, and concatenate the multiple features to form an enhanced feature matrix; S3) Construct a two-layer bidirectional gated recurrent unit network prediction model BiGRU and train it. S4) Use the trained bi-layer bidirectional gated recurrent unit network (BiGRU) prediction model to predict carbon futures price points and output the price point prediction results. S5) Based on the point prediction results, a Gaussian process is used to construct a prediction interval with multiple confidence levels to quantify the uncertainty of price fluctuations.

2. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 1, characterized in that: In step S2), the extraction of statistical features is as follows: calculate the mean, standard deviation, range, skewness and kurtosis of each window, and concatenate the five statistical features into a statistical feature.

3. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 2, characterized in that: In step S2), the difference features include first-order difference, second-order difference and fourth-order difference, which respectively capture short-term, medium-term and long-term dynamic changes.

4. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 3, characterized in that: In step S2), similarity features are generated using a probability density network (PDN) and a random walk similarity propagation (SRW) method; specifically, the following steps are included: S241) Construct a probability density network and calculate a normalized similarity score. The probability density network is a weighted network constructed by quantifying the distribution similarity between time windows to capture the implicit patterns of carbon price series. Each time window is regarded as a node in the network. S242) Enhance the global consistency of the initial similarity matrix by random walk similarity propagation, capture the indirect relationships between nodes, accumulate the transition results through multi-step iteration, normalize the weights by combining the weighted out-degree of nodes and the total weight of the network, and eliminate directional bias through symmetry processing to obtain the global similarity matrix; S243) Calculate similarity features for each window based on the generated global similarity matrix.

5. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 4, characterized in that: In step S241), a probability density network is constructed and a normalized similarity score is calculated; specifically as follows: S2411) Calculate the cumulative distribution function (CDF) for each time window. and The probability density function is estimated using kernel density estimation. Then, the cumulative distribution function is obtained by integrating the estimated density function. ;Right now: ； In the formula, For bandwidth parameters; For kernel functions; Indicates the index of the sliding window; This represents the number of sliding windows; S2412), in the interval , N equally spaced sampling points For each sampling point Calculate the CDF difference between the left and right offsets, i.e.: ； ； In the formula, The neighborhood radius parameter; , These represent the differences in CDF values ​​for left and right offsets, respectively. , Time windows , The cumulative distribution function; By comparing the offset differences of CDF at multiple sampling points, the similarity between two window distributions can be finely characterized. S2413) Generate similarity scores and identify windows. CDF relative to window Maximum excess of offset CDF and minimum deficiency And adjust it to the effective range: In the formula, , These are the maximum insufficiency on the left side of the normalized data and the maximum insufficiency on the right side of the normalized data, respectively. , These represent the minimum values ​​of the left-offset CDF difference and the right-offset CDF difference, respectively. , These are the maximum left-side overflow and the maximum right-side overflow under normalization, respectively. , These represent the maximum values ​​of the left-offset CDF difference and the right-offset CDF difference, respectively. Then calculate the proportion of the overlapping area: In the formula, , These are the left overlap ratio and the right overlap ratio, respectively. Finally, the normalized similarity score is obtained. : in, , The larger the value, the higher the similarity of the distributions between the two windows.

6. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 5, characterized in that: In step S242), the global consistency of the initial similarity matrix is ​​enhanced through random walk similarity propagation, capturing indirect relationships between nodes, as follows: S2421), based on the initial similarity score matrix Construct a weighted transition matrix ,Right now: In the formula, A Boolean parameter indicating whether to use weighted normalization; Indicates the index of the time window; By using a weighted transfer method, nodes are allocated transfer probabilities proportionally, thus preserving the original similarity weight information; (S2422) Accumulates transition results through multi-step walk iterations. In each iteration, the transition matrix of the random walk is updated, and the result is added to the final similarity matrix. In; that is: ； In the formula, express Step transition matrix; (S2423) Combining the weighted out-degree of nodes and the total network weight, weight normalization is performed, and directional bias is eliminated through symmetry processing to obtain the global similarity matrix. ; In the formula, Represents the normalized similarity matrix ; express The transpose of the matrix; in, Represents a node Weighted out-degree; This represents the total weight of the network.

7. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 6, characterized in that: In step S243), similarity features are calculated for each window based on the generated global similarity matrix. ; For each window, select the top three most similar windows and calculate their mean characteristics, i.e.: ； In the formula, Indicates the first The top 3 most similar windows of the sliding window; This represents the feature value of the k-th window.

8. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 7, characterized in that: In step S3), the BiGRU prediction model consists of two GRU networks with opposite propagation directions, which simultaneously learn the forward and backward dependencies of the sequence. The BiGRU prediction model consists of the following layers from bottom to top: input layer, first bidirectional GRU layer, Dropout layer, second bidirectional GRU layer, and fully connected output layer. The first bidirectional GRU layer and the second bidirectional GRU layer both include a forward GRU sublayer and a backward GRU sublayer.

9. The carbon futures price prediction method based on multi-level feature engineering and bidirectional gating according to claim 8, characterized in that: In step S5), based on the point prediction results, a Gaussian process is used to construct a prediction interval with multiple confidence levels to quantify the uncertainty of price fluctuations, as detailed below: S51) Assuming prediction error Follows a mean of 0 and a standard deviation of Gaussian distribution ; S52) For a given confidence level The upper and lower bounds of the prediction interval, i.e.: In the formula, The lower bound; The upper boundary; The quantiles of the standard normal distribution; The significance level parameter; S53) The predicted interval coverage probability (PICP), the predicted interval normalized average width (PINAW), and the cumulative width deviation (AWD) are used to evaluate the interval prediction performance.

10. A carbon futures price forecasting system based on multi-level feature engineering and bidirectional gating, characterized in that, include: The data acquisition and preprocessing module is used to acquire the raw carbon price time series and preprocess it. The multi-level feature engineering module extracts original features, statistical features, difference features, and similarity features based on the preprocessed carbon price time series, and concatenates the multiple features to form an enhanced feature matrix; The prediction model building module is used to build a two-layer bidirectional gated recurrent unit network prediction model BiGRU and train it. The futures price prediction module uses a trained bi-dimensional gated recurrent unit network (BiGRU) prediction model to predict carbon futures prices and outputs the price prediction results. Futures price range prediction is based on point prediction results. A Gaussian process is used to construct prediction ranges with multiple confidence levels to quantify the uncertainty of price fluctuations.

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