Carbon price prediction method and system based on graph G and model prediction algorithm

Abstract

The invention discloses a carbon price prediction method and system based on a graph G and a model prediction algorithm, and the method comprises the steps: firstly building a carbon price network, representing the network in the form of the graph G, then introducing a structural equation model to capture key variables of the network, and enabling the structural equation model to be expressed in the form of a matrix, adding additional items into the structural equation model to dynamically and accurately capture the carbon price fluctuation in the complex environment, and finally, constructing a carbon price prediction model by taking the minimum weighted prediction error and policy deviation cost as objective functions, and solving the model by adopting an artificial hummingbird algorithm and adding a chaotic mapping Bernoulli initialized population method. And obtaining the predicted carbon price. According to the carbon price prediction method, the carbon emission price with obvious fluctuation characteristics can be accurately predicted, and the effectiveness of the carbon emission trading market can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to a carbon price prediction method and system based on a graph G and a model prediction algorithm. Background Art

[0002] With the acceleration of the global carbon neutrality process, the Emissions Trading System (ETS) has become the core mechanism to achieve climate goals. As a key signal, the carbon price promotes the low-carbon transformation of the economy by guiding enterprises to reduce emissions and allocate resources. However, the carbon price formation mechanism is complex: in the short term, it is affected by energy fluctuations, policy adjustments, and market speculation, and in the long term, it is related to slow variables such as the macro economy and technological progress, resulting in non-linear characteristics such as sharp peaks and heavy tails, and sudden jumps. Traditional models (such as ARIMA) are difficult to capture the price fluctuation law because they ignore the coupling of multiple factors and non-stationarity. For example, the EU carbon price has been in a long-term slump due to overabundant quotas and then soared sharply after being impacted by policies and the energy crisis in 2021, highlighting the deficiencies of traditional methods in identifying structural mutations and cross-market risk transmission.

[0003] Especially under the drive of the "dual carbon" goal, the industries covered by the Chinese carbon market have expanded from electricity to steel, building materials, etc., the MRV (Monitoring, Reporting, Verification) system has been dynamically adjusted, and the external impact of international carbon tariffs (such as the EU CBAM) has further amplified the curse of dimensionality problem in price prediction.

[0004] Therefore, there is an urgent need to build a new prediction framework to improve the prediction reliability. Summary of the Invention

[0005] The purpose of the present invention is to provide a carbon price prediction method and system based on a graph G and a model prediction algorithm to solve the problem of low reliability in existing carbon price prediction under obvious fluctuation characteristics.

[0006] The technical solution of the present invention is as follows: A carbon price prediction method based on a graph G and a model prediction algorithm includes the following steps:

[0007] Step 1: Establish a carbon price network represented in the form of a graph G;

[0008] Step 2: Establish a structural equation model of the carbon price network to capture the key variables of the network;

[0009] Step 3: Add additional terms to the structural equation model of the carbon price network;

[0010] Step 4: Construct a carbon price prediction model with the minimization of the weighted prediction error and the policy deviation cost as the objective function; Step 5: Solve the carbon price prediction model to obtain the predicted carbon price with the optimal objective function.

[0011] In step 1, entities related to carbon prices are taken as nodes in graph G; the relevance between nodes is taken as edges in graph G; graph G is represented by (V, E), where V = {v1, v2,..., v k} represents all vertices, and E = {e ij} represents all edges connecting vertices.

[0012] In step 2, establishing a structural equation model includes:

[0013] The state η of carbon price network node i i is expressed as:

[0014]

[0015] In the formula, i and j respectively represent node numbers, where i ≠ j; a i,j , b i are weight coefficients respectively; ξ i represents the variable related to the node state, and z i is the error term;

[0016] Express formula (1) in matrix form:

[0017] η = Aη + Bξ + z (2)

[0018] In the formula, matrices A, B, and z are the matrix expressions corresponding to a i,j , b i , and z i respectively, η is the endogenous latent variable, and ξ is the exogenous latent variable.

[0019] In step 3, introduce the Kalman filter to associate the unobservable latent state with the carbon price, then the additional term added is:

[0020]

[0021] In the formula, θ t is the value of the latent state variable at the current moment, θ t-1 is the value of the latent state variable at the previous moment, η t is the carbon price observed at the current moment, G t , F t are the state transition matrix and the observation matrix, w t , v t are the process noise and the observation noise.

[0022] In step 3, introduce the additional term, specifically:

[0023] Define the external shock e t , then the impulse response of the external shock to the carbon price network is:

[0024]

[0025] In the formula, Δη is the carbon price fluctuation caused by external time shocks, K is the number of time points determined within the time window period, and β k is the marginal effect coefficient of the external shock on the carbon price at the k-th time point when the external shock occurs, and e t+k is the occurrence or intensity of the external shock at the k-th time point, and ò t is the random error term.

[0026] In step 4, the objective function of the carbon price prediction model is:

[0027]

[0028] In the formula, a is the weight coefficient; E 排放 is the actual emission vector; E 配额 is the quota allocation vector; Ψ t is the predicted carbon price sequence in the t-th period; is the actual carbon price sequence in the t-th period; ||·||2 is the L2 norm.

[0029] The constraint conditions of the carbon price prediction model include:

[0030] Structural equation model constraint

[0031] η = Aη + Bξ + z(6)

[0032] Market stability constraint

[0033]

[0034] In the formula, n is the upper limit value of the electricity price fluctuation, and Ψ t-1 is the carbon price sequence in the (t - 1)-th period;

[0035] Technical feasibility constraint

[0036] ΔE i ≤ γ i E i,基准 (8)

[0037] In the formula, ΔE i represents the emission reduction volume of the i-th industry; E i,基准 is the benchmark carbon emission of the i-th industry; γ i represents the upper limit of the emission reduction ratio;

[0038] Economic protection constraint

[0039]

[0040] In the formula, C iIt represents the total carbon emission cost of the i-th industry; δ is the cost ratio threshold; N represents the total number of industries involved in carbon emissions; GDP represents the gross national product.

[0041] In step 5, the artificial hummingbird algorithm with chaotic map Bernoulli initialization of the population is used to solve the carbon price prediction model.

[0042] Among them, the Bernoulli equation is:

[0043]

[0044] In the formula, x(t) is the state variable at time t, and x(t + 1) is the state variable at time t + 1; λ is a constant parameter, where 0 ≤ λ ≤ 1, which is used as the threshold and scale factor of the piecewise function.

[0045] The specific steps of the artificial hummingbird optimization algorithm are as follows:

[0046] 1) Chaotic map Bernoulli initialization of the population

[0047] Randomly generate an initial value x0 ∈ (0, 1), and generate a chaotic sequence through Bernoulli mapping iteration:

[0048]

[0049] In the formula, x n is the chaotic number generated by the n-th iteration; x n+1 is the chaotic number generated by the (n + 1)-th iteration; p is the asymmetric parameter that controls the piecewise slope of the Bernoulli mapping.

[0050] Map the chaotic sequence values linearly to the variable domain, generate the initial population individuals, and apply Bernoulli perturbations to the individuals with a fixed probability.

[0051] 2) Calculate the fitness value of each individual.

[0052] 3) Each hummingbird updates its position according to the current optimal solution. If the fitness of the new position is higher, replace the old position.

[0053] 4) Select high-quality solutions according to the fitness probability and perform local search.

[0054] 5) If the global optimal solution has not been improved for 3 consecutive generations, replace a fixed proportion of the worst individuals in the population and generate new solutions using Bernoulli mapping.

[0055] 6) When the convergence condition is met or the maximum number of iterations is reached, output the result.

[0056] A carbon price prediction system based on graph G and a model prediction algorithm, including:

[0057] A carbon price network model is used to establish a carbon price network represented in the form of a graph G;

[0058] An equation module is used to establish a structural equation model of the carbon price network to capture the key variables of the network; an additional module is used to add additional terms to the structural equation model of the carbon price network;

[0059] A prediction module is used to construct a carbon price prediction model with the objective function of minimizing the weighted prediction error and the policy deviation cost;

[0060] A solution module is used to solve the carbon price prediction model to obtain the predicted carbon price with the optimal objective function.

[0061] In the operation of the present invention, through the deep integration of graph embedding representation learning and multi-step optimization algorithms, the interpretability of non-stationary carbon price sequences is enhanced, the environmental adaptability and reliability of the prediction system are improved, the decision-making uncertainty of carbon market participants is reduced, and innovative methodological support is provided for constructing a digital carbon management system. Brief Description of the Drawings

[0062] Figure 1 It is a schematic diagram of the working process of the proposed carbon price prediction method. Detailed Embodiments

[0063] As Figure 1 shown, the present invention provides a carbon price prediction method based on a graph G and a model prediction algorithm, including the following steps:

[0064] Step 1: Establish a carbon price network represented in the form of a graph G, where the nodes of the graph G are selected as entities related to carbon prices (such as national or regional carbon markets, industries or enterprises, and carbon financial products, etc.), and the edges of the graph G are selected as the correlations between nodes (such as the correlation of price fluctuations, the carbon price transmission mechanism, and the linkage of policies or trades, etc.).

[0065] Step 2: Establish a structural equation model (SEM) of the carbon price network to capture the key variables of the network.

[0066] Step 3: Add additional terms to the structural equation model of the carbon price network to achieve dynamic and accurate capture of carbon price fluctuations in a complex environment.

[0067] Step 4: Construct a carbon price prediction model with the objective function of minimizing the weighted prediction error and the policy deviation cost, while considering market constraints, technical constraints, and economic constraints.

[0068] Step 5: Solve the carbon price prediction model using the artificial hummingbird algorithm, and introduce the chaotic map Bernoulli to initialize the population to achieve diversification and uniform distribution of the population, and obtain the optimal predicted carbon price of the objective function.

[0069] First, take the entities related to the carbon price as the nodes in the graph G; take the relevance between the nodes as the edges in the graph G; the graph G can be represented by (V, E), where V = {v1, v2,..., v i} represents all vertices, and E = {e ij} represents all the edges connecting the vertices; according to the actual situation of the selected carbon price data, set the attributes of the nodes and the weights of the edges.

[0070] Secondly, introduce the structural equation model to express the carbon price, and define the following model variables: Define the endogenous latent variable η as the carbon price fluctuation, and the exogenous latent variables ξ as the policy influence, supply and demand pressure, energy price, etc. Represent the state η i of the carbon price network node i as:

[0071]

[0072] In the formula, i and j respectively represent the node numbers, where i ≠ j; a i,j , b i are the weight coefficients respectively; ξ i represents the state variable related to the node, and z i is the error term;

[0073] Express Equation (1) in matrix form:

[0074] η = Aη + Bξ + z (2)

[0075] In the formula, the matrices A, B, and z are the matrix expressions corresponding to a i,j , b i , and z i respectively.

[0076] Thirdly, to achieve dynamic and accurate capture of carbon price fluctuations, an additional term needs to be introduced based on the structural equation model formula (2) to handle the time-varying problem in the carbon price structural equation model.

[0077] Specifically: Introduce the Kalman Filter in Equation (2) to associate the unobservable latent states (such as the market panic index, policy influence intensity, etc.) with the carbon price, then the additional term added is:

[0078]

[0079] In the formula, θ t is the value of the latent state variable at the current moment (such as the market panic index, etc.), θt-1 is the value of the potential state variable at the previous moment, η t is the carbon price observed at the current moment, G t , F t are the state transition matrix and the observation matrix, w t , v t are the process noise and the observation noise.

[0080] Based on Equation (2), an additional term caused by external shocks is introduced to address the problem of external shocks in the carbon price model.

[0081] Specifically: Define the external shock e t (such as extreme weather, regional conflicts, etc.), then the impulse response of the external shock to the carbon price network is:

[0082]

[0083] In the formula, Δη is the carbon price fluctuation caused by external time shocks, K is the number of time points determined within the time window, β k is the marginal effect coefficient of the external shock on the carbon price at the k-th time point of the external shock occurrence, reflecting the dynamic impact of the shock at different time points within the event window, e t+k is the occurrence or intensity of the external shock at the k-th time point (this variable has two common forms, one is a dummy variable representing whether the shock occurs, that is, when the shock occurs, the variable value is 1, and when the shock does not occur, the variable value is 0; the other is a continuous variable representing the quantified intensity of the shock; the definition of this variable here is the occurrence or intensity of the shock at the k-th time point), ò t is the random error term.

[0084] Based on Equation (2), an additional term is introduced to address the problem of modeling non-linear relationships in the carbon price model.

[0085] Specifically:

[0086] Embed a machine learning module in the SEM, and use neural network algorithms to capture the non-linear interaction relationships between variables and the non-linear residuals existing in the system. The hybrid model architecture is as follows:

[0087]

[0088] Finally, construct the objective function and constraint conditions of the carbon price prediction model. The objective function is to minimize the weighted prediction error and the policy deviation cost:

[0089]

[0090] In the formula, a is the weight coefficient; for E 排放 is the actual emission vector; E 配额 is the quota allocation vector; Ψt is the historical predicted carbon price sequence for the t-th period; is the historical actual carbon price sequence for the t-th period. ||·||2 is the L2 norm, measuring the overall deviation degree between carbon emissions and carbon quotas.

[0091] Among them,

[0092]

[0093] The model constraint conditions include:

[0094] Structural equation model constraint

[0095] η = Aη + Bξ + z(6)

[0096] Market stability constraint

[0097]

[0098] In the formula, n is the upper limit value of electricity price fluctuation, Ψ t-1 is the carbon price sequence for the (t - 1)-th period;

[0099] Technical feasibility constraint

[0100] ΔE i ≤γ i E i,基准 (8)

[0101] In the formula, ΔE i represents the emission reduction amount of the i-th industry; E i,基准 is the benchmark carbon emission of the i-th industry; γ i represents the upper limit of the emission reduction ratio.

[0102] Economic protection constraint

[0103]

[0104] In the formula, C i represents the total carbon emission cost of the i-th industry; is the direct input cost for emission reduction; Ψ is the carbon price; δ is the cost ratio threshold; N represents the total number of industries involved in carbon emissions; GDP represents the gross national product.

[0105] The artificial hummingbird algorithm (Artificial Hummingbird Algorithm, AHA) with the method of adding a chaotic mapping Bernoulli initialization population is used to solve the carbon price prediction model. The chaotic sequence generated by the chaotic mapping can generate a more diverse and uniform population, which can improve the solution ability of complex optimization models.

[0106] The Bernoulli equation is as follows:

[0107]

[0108] Wherein, x(t) is the state variable at time t, and x(t + 1) is the state variable at time t + 1; λ is a constant parameter, where 0 ≤ λ ≤ 1, and is used for the threshold and scale factor of the piecewise function.

[0109] Improve the artificial hummingbird algorithm, and the specific steps for improving the artificial hummingbird optimization algorithm are as follows:

[0110] 1) Initialize the population by chaotic mapping Bernoulli

[0111] Randomly generate an initial value x0 ∈ (0, 1), and generate a chaotic sequence through Bernoulli mapping iteration.

[0112]

[0113] Wherein, x n is the chaotic number generated by the nth iteration; x n+1 is the chaotic number generated by the (n + 1)th iteration; p is an asymmetric parameter, which controls the piecewise slope of the Bernoulli mapping to avoid periodicity.

[0114] Linearly map the chaotic sequence values to the variable domain to generate the initial population individuals.

[0115]

[0116] Wherein, v i,j is the value of the jth dimension of the ith individual variable; are the maximum and minimum values of the jth dimension variable; x (i-1)×d+j is the kth value in the chaotic sequence, where k = (i - 1) × d + j, and is used for linear mapping to the variable range.

[0117] Apply Bernoulli perturbation to the individuals with a fixed probability.

[0118] v i,j ← v i,j + ò·B(η)

[0119] Wherein, ò is the perturbation step size; B(η) is the Bernoulli distribution, which means randomly generating 0 and 1 with a probability of η × 100%.

[0120] 2) Calculate the fitness value of each individual.

[0121]

[0122] Wherein, F i is the fitness value of the ith individual; F(v i ) is the objective function value.

[0123] 3) Each hummingbird updates its position according to the current optimal solution. If the fitness of the new position is higher, the old position is replaced.

[0124]

[0125] Where v new and v old represent the new and old positions of the hummingbird; w is the chaotic weight factor; Δv is the moving step size.

[0126] 4) Select high-quality solutions according to the fitness probability and perform local search.

[0127] 5) If the global optimal solution has not been improved for three consecutive generations, replace 10% of the worst individuals in the population and generate new solutions using the Bernoulli map.

[0128] 6) When the convergence condition is met or the maximum number of iterations is reached, output the result.

[0129] The present invention also provides a carbon price prediction system based on graph G and a model prediction algorithm, including:

[0130] A carbon price network model for establishing a carbon price network represented in the form of graph G;

[0131] An equation module for establishing a structural equation model of the carbon price network to capture the key variables of the network; an additional module for adding additional terms to the structural equation model of the carbon price network;

[0132] A prediction module for constructing a carbon price prediction model with the objective of minimizing the weighted prediction error and the policy deviation cost;

[0133] A solution module for solving the carbon price prediction model to obtain the predicted carbon price with the optimal objective function.

[0134] The present invention has the following advantages:

[0135] 1) By constructing a carbon price prediction model based on the dynamic structure of graph G and combining the rolling optimization characteristics of the model prediction algorithm, it can respond to price fluctuation signals in the carbon market in real time and accurately predict price trends even in a complex and changing macroeconomic environment.

[0136] Furthermore, by setting multi-dimensional influencing factors at the graph nodes and performing joint deduction, it can effectively analyze the non-linear correlations in the carbon emission rights trading, thus significantly improving the spatio-temporal correlation modeling ability of price prediction, enhancing the risk aversion ability of market participants and the scientific nature of hedging decisions;

[0137] 2) The prediction framework proposed by this method can adapt to the topological evolution of graph G, and is compatible with dynamic scenarios such as market expansion and adjustment of industry coverage without reconstructing the model. This endogenous adaptability not only reduces the cost of model iteration and maintenance, but also captures changes in industry correlation through dynamic graph neural networks, ensuring prediction stability in situations such as carbon quota allocation mechanism reform or sudden policy regulation, providing technical support for building a resilient carbon market;

[0138] 3) By integrating graph representation learning and multi-step rolling prediction mechanism, a new path is opened up for the intelligent supervision of the carbon finance market. The probabilistic price corridor output by the prediction model provides a quantitative basis for optimizing trading strategies, assisting regulatory authorities in identifying abnormal trading patterns, and at the same time enabling entities such as power generation groups to conduct multi-period carbon asset portfolio management. The industry correlation knowledge graph constructed by this method provides an extensible analysis framework for macro decisions such as cross-regional carbon market linkage and carbon tax policy simulation.

[0139] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A carbon price prediction method based on graph G and model prediction algorithm, characterized in that: The following steps are involved: Step 1: Establish a carbon price network represented by graph G; Step 2: Establish a structural equation model of the carbon price network to capture the key variables of the network; Step 3: Add additional terms to the structural equation model of the carbon price network; Step 4: Construct a carbon price prediction model with the objective function of minimizing the weighted prediction error and policy deviation cost; Step 5: Solve the carbon price prediction model to obtain the predicted carbon price with the optimal objective function.

2. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized by: In step 1, the entities related to carbon prices are taken as nodes in the graph G; the associations between nodes are taken as edges in the graph G; the graph G is represented by (V, E), where V = {v1, v2, ..., v k } represents all vertices, E={e ij } represents all the edges connecting the vertices.

3. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized in that: In step 2, the structural equation model is established including: State η of node i in the carbon price network i It is expressed as: In the formula, i and j represent the node numbers respectively, where i≠j; a i,j , b i are weight coefficients respectively; i Represents the node state variable, z i is the error term; Express equation (1) in matrix form: η=Aη+Bξ+z (2) In the formula, matrices A, B, and z are respectively i,j , b i 、z i The corresponding matrix expression is, η is the endogenous latent variable, and ξ is the exogenous latent variable.

4. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized in that: In step 3, Kalman filtering is introduced to associate the unobservable potential state with the carbon price, and the additional term is added as: In the formula, θ t is the potential state variable value at the current moment, θ t-1 is the value of the potential state variable at the previous moment, η t is the carbon price observed at the current moment, G t 、F t is the state transfer matrix and observation matrix, w t 、v t are process noise and observation noise.

5. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized in that: In step 3, additional items are introduced, specifically: Definition of external shock t , then the impulse response of the external shock to the carbon price network is: In the formula, Δη is the carbon price fluctuation caused by external time shock, K is the number of time points determined within the time window, and β k is the marginal effect coefficient of the external shock on carbon price at time k, e t+k is the occurrence or intensity of the external shock at time point k, t is a random error term.

6. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized by: In step 4, the objective function of the carbon price prediction model is: Where a is the weight coefficient; E 排放 is the actual emission vector; E 配额 is the quota allocation vector; t Predict the carbon price series for period t; is the actual carbon price sequence in the tth period; ||·||2 is the L2 norm.

7. The carbon price prediction method based on graph G and model prediction algorithm according to claim 6 is characterized by: The constraints of the carbon price prediction model include: Structural Equation Model Constraints η=Aη+Bξ+z(6) Market stability constraints Where n is the upper limit of electricity price fluctuation, Ψ t-1 is the carbon price sequence in period t-1; Technical feasibility constraints ΔE i ≤γ i E i,基准 (8) In the formula, ΔE i represents the emission reduction of the i-th industry; E i,基准 The benchmark carbon emissions of the i-th industry; γ i Indicates the upper limit of emission reduction ratio; Economic protection constraints In the formula, C i represents the total carbon emission cost of the ith industry; δ is the cost ratio threshold; N represents the total number of industries involved in carbon emissions; GDP represents gross national product.

8. The carbon price prediction method based on graph G and model prediction algorithm according to claim 1 is characterized by: In step 5, the artificial hummingbird algorithm is used to add the chaotic mapping Bernoulli initialization population method to solve the carbon price prediction model; The Bernoulli equation is: Where x(t) is the state variable at time t, x(t+1) is the state variable at time t+1; λ is a constant parameter, where 0≤λ≤1, used for the threshold and scaling factor of the piecewise function.

9. A carbon price prediction method based on graph G and model prediction algorithm according to claim 8, characterized in that: Artificial Hummingbird optimization algorithm, the specific steps are as follows: 1) Chaotic Map Bernoulli Initialization Population Randomly generate an initial value x0∈(0,1) and iterate the chaotic sequence through Bernoulli mapping: In the formula, x n The chaotic number generated for the nth iteration; x n+1 is the chaotic number generated in the n+1th iteration; p is the asymmetric parameter, which controls the segmented slope of the Bernoulli mapping; Linearly map the chaotic sequence values ​​to the variable definition domain, generate the initial population individuals, and apply Bernoulli perturbations to the individuals with a fixed probability; 2) Calculate the fitness value of each individual; 3) Each hummingbird updates its position according to the current optimal solution. If the new position has higher fitness, it replaces the old position. 4) Select high-quality solutions based on fitness probability and conduct local search; 5) If the global optimal solution has not been improved for three consecutive generations, replace a fixed proportion of the worst individuals in the population and use Bernoulli mapping to generate a new solution; 6) When the convergence condition is met or the maximum number of iterations is reached, output the result.

10. A carbon price prediction system based on graph G and model prediction algorithm, characterized in that: include: The carbon price network model is used to establish a carbon price network represented by a graph G; The equation module is used to build the structural equation model of the carbon price network to capture the key variables of the network; the additional module is used to add additional terms to the structural equation model of the carbon price network; The prediction module is used to build a carbon price prediction model with the objective function of minimizing the weighted prediction error and the policy deviation cost; The solution module is used to solve the carbon price prediction model and obtain the predicted carbon price with the optimal objective function.

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