A method and terminal for predicting carbon emissions based on dynamic time-lag model

Abstract

The present invention discloses a method and terminal for predicting carbon emissions based on a dynamic time-lag model, comprising the following steps: S1, collecting raw data of factors influencing carbon emissions, and obtaining the main influencing factors of carbon emissions through standardization processing and maximum information coefficient method screening; S2, constructing a first cumulative sequence of the influencing factors and a second cumulative sequence of carbon emissions; S3, using an impulse response function to determine the dynamic response relationship between variables and obtain the optimal lag parameters between the variables; S4, determining whether there is a time-lag relationship between the influencing factors and carbon emissions; if so, setting a time-lag interval and calculating the time-lag weight, and calculating the model parameter value; if not, directly calculating the model parameter value; S5, substituting the model parameter value and the main influencing factors into an enhanced multivariate dynamic time-lag discrete grey prediction model, and calculating the fitted value and predicted value of carbon emissions under the second cumulative sequence. This reflects the lag process of different influencing factors and improves the prediction accuracy of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of carbon emission prediction, and in particular to a method and terminal for predicting carbon emissions based on a dynamic time-lag model. Background Art

[0002] Continued greenhouse gas emissions, primarily carbon dioxide, pose multiple risks to humanity, leading to widespread concern about carbon reduction. Reliable carbon emission forecasts can effectively monitor CO2 emissions, enabling better responses to climate change. This means adjusting emission reduction strategies, developing feasible action plans, and achieving low-carbon, sustainable development.

[0003] Existing research has provided meaningful empirical and theoretical results for carbon emission forecasting. Numerous models have been developed for carbon emission forecasting, including statistical models such as regression techniques and machine learning models such as support vector machines and back-propagation neural networks (BPNNs). However, statistical models and machine learning methods require large amounts of historical data. To address the limited sample size forecasting problem that arises in practical applications, researchers have used the grey prediction model, which performs well for small sample sizes. Consequently, the grey prediction model has been widely used in research across many fields.

[0004] However, the above methods ignore the time lag effects of various factors on carbon emissions. Carbon emissions are constrained by numerous factors, and typically, there are varying time lags between carbon emissions and their related factors. For example, different technologies and policies require varying amounts of time to impact carbon emissions. The effects of technologies or policies that reduce carbon emissions may not manifest until months or years have passed, and the time lag effects of many factors on carbon emissions do not persist over time. The time interval from the onset of an effect to its disappearance is called the effective lag interval. The lag effect cannot be represented as a linear process; it varies nonlinearly over time. For example, the lag effect of technological investment on carbon emissions tends to increase initially and then decrease, while the effectiveness of policy implementation is often greater initially and then gradually decreases, resulting in a gradually decreasing overall lag effect on carbon emissions. Numerous studies have investigated the analysis or determination of time lags in the real world. Numerous models have been proposed, such as the autoregressive distributed lag (ARDL). Analyzing time lag relationships and determining lag periods are of great significance. However, few studies have explored the dynamic lag effects of related factors on carbon emissions, and the dynamic response relationship between the two remains unclear. In summary, the hysteresis relationship between carbon emissions and related factors has not been thoroughly studied. On the other hand, existing static hysteresis models cannot reflect the dynamic hysteresis processes that change over time. Furthermore, in similar studies, the impact of linear relationships is often underestimated, which limits the model's adaptability to a wider range of data types. Although hysteresis effects have an effective hysteresis range in many practical applications, they have received little attention. Therefore, there is still considerable room for improvement in the study of the underlying dynamic hysteresis mechanisms that more closely reflect the dynamic evolution of real-world systems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and terminal for predicting carbon emissions based on a dynamic time-lag model, which reflects the lag process of different influencing factors and improves the prediction accuracy of the model.

[0006] In order to solve the above technical problems, a technical solution adopted by the present invention is:

[0007] A method for predicting carbon emissions based on a dynamic time-lag model comprises the following steps:

[0008] S1. Collecting original data on factors affecting carbon emissions, standardizing the original data to obtain secondary data, and using the maximum information coefficient method to screen the secondary data to obtain the main influencing factors of carbon emissions;

[0009] S2. Constructing a first cumulative sequence of influencing factors and a second cumulative sequence of carbon emissions based on the main influencing factors;

[0010] S3. Use the impulse response function to determine the dynamic response relationship between variables and obtain the optimal lag parameters between variables;

[0011] S4. Based on the first cumulative sequence and the second cumulative sequence, determine whether there is a time lag relationship between the influencing factor and the carbon emissions; if so, set a time lag interval and calculate a time lag weight, and calculate a model parameter value; if not, directly calculate the model parameter value;

[0012] S5. Establish an enhanced multivariable dynamic time-lag discrete grey prediction model, substitute the model parameter values ​​and the main influencing factors into the enhanced multivariable dynamic time-lag discrete grey prediction model, and calculate the fitting value and predicted value of carbon emissions under the second cumulative sequence.

[0013] In order to solve the above technical problems, another technical solution adopted by the present invention is:

[0014] A terminal for predicting carbon emissions based on a dynamic time-lag model comprises a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, each step of the above-mentioned method for predicting carbon emissions based on a dynamic time-lag model is implemented.

[0015] The beneficial effects of the present invention are: for prediction problems with lag factors, the time-lag driving term is used to reflect the lag process of different factors in the carbon emission system, and a linear correction term is introduced to improve the applicability of the model; for whether there is a dynamic lag relationship between carbon emissions and its influencing factors, the dynamic response relationship between variables is reflected by the impulse response function, thereby obtaining the lag parameters, as well as the lag interval and the weights of the impact at different time points, thereby enhancing the high adaptability to the time-lag system and improving the prediction performance; at the same time, a flexible prediction platform is provided for the time-lag system, from which the lag relationship and other relationships between variables can be explored, and the platform can enhance the generalization ability and modeling performance of the time-lag system prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flowchart of the steps of a method for predicting carbon emissions based on a dynamic time-lag model according to an embodiment of the present invention;

[0017] Figure 2 A flowchart of a method for predicting carbon emissions based on a dynamic time-lag model according to an embodiment of the present invention;

[0018] Figure 3 Schematic diagram of impulse response analysis of a method for predicting carbon emissions based on a dynamic time-lag model according to an embodiment of the present invention;

[0019] Figure 4A schematic diagram of a modeling process of a time-delay system prediction platform for a method for predicting carbon emissions based on a dynamic time-delay model according to an embodiment of the present invention;

[0020] Figure 5 This is an architectural diagram of a terminal for predicting carbon emissions based on a dynamic time-lag model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] To illustrate the technical content, achieved objectives and effects of the present invention in detail, the following description is given in conjunction with the embodiments and accompanying drawings.

[0022] An embodiment of the present invention provides a method for predicting carbon emissions based on a dynamic time-lag model, comprising the following steps:

[0023] S1. Collecting original data on factors affecting carbon emissions, standardizing the original data to obtain secondary data, and using the maximum information coefficient method to screen the secondary data to obtain the main influencing factors of carbon emissions;

[0024] S2. Constructing a first cumulative sequence of influencing factors and a second cumulative sequence of carbon emissions based on the main influencing factors;

[0025] S3. Use the impulse response function to determine the dynamic response relationship between variables and obtain the optimal lag parameters between variables;

[0026] S4. Based on the first cumulative sequence and the second cumulative sequence, determine whether there is a time lag relationship between the influencing factor and the carbon emissions; if so, set a time lag interval and calculate a time lag weight, and calculate a model parameter value; if not, directly calculate the model parameter value;

[0027] S5. Establish an enhanced multivariable dynamic time-lag discrete grey prediction model, substitute the model parameter values ​​and the main influencing factors into the enhanced multivariable dynamic time-lag discrete grey prediction model, and calculate the fitting value and predicted value of carbon emissions under the second cumulative sequence.

[0028] From the above description, it can be seen that the beneficial effects of the present invention are: for prediction problems with lag factors, the time-lag driving term is used to reflect the lag process of different factors in the carbon emission system, and a linear correction term is introduced to improve the applicability of the model; for whether there is a dynamic lag relationship between carbon emissions and its influencing factors, the dynamic response relationship between variables is reflected by the impulse response function, thereby obtaining the lag parameters, as well as the lag interval and the weights of the impact at different time points, thereby enhancing the high adaptability to the time-lag system and improving the prediction performance; at the same time, a flexible prediction platform is provided for the time-lag system, from which the lag relationship and other relationships between variables can be explored. The platform can enhance the generalization ability and modeling performance of the time-lag system prediction.

[0029] Furthermore, in step S1, the secondary data obtained by normalizing the original data is specifically:

[0030] The Z-score standardization method was used to normalize the secondary data.

[0031]

[0032] Where μ represents the mean of all original data; σ represents the standard deviation of all original data.

[0033] As can be seen from the above description, normalization facilitates the comparison and weighting of metrics with different units or magnitudes. Normalization transforms dimensioned datasets into scalar quantities. Mapping data to a specified range eliminates order-of-magnitude differences between data of different dimensions, simplifying calculations.

[0034] Furthermore, in step S1, the maximum information coefficient method is used to screen the secondary data to obtain the main influencing factors of carbon emissions, which are specifically:

[0035] S101. Calculate the mutual information between carbon emissions and factors affecting carbon emissions:

[0036]

[0037] In the formula, X represents the factors affecting carbon emissions, and Y represents the amount of carbon emissions, where X={x1,...,x n}、Y={y1,...,y n}, n represents the number of samples of the original data, ρ(x,y) represents the joint density between X and Y, ρ(x) and ρ(y) represent the marginal probability densities of X and Y respectively;

[0038] S102: Set the number of columns i and the number of rows j, grid the scatter plot of carbon emission influencing factors and carbon emissions into i×j grids, and find the maximum mutual information value:

[0039]

[0040] Where a and b represent the number of grids divided in the X and Y directions respectively, and B represents the maximum value of the grid.

[0041] As can be seen from the above description, the Maximum Information Coefficient (MIC) method can be used to measure the degree of correlation between influencing factors and carbon emissions. It can detect not only linear relationships between different influencing factors, but also various nonlinear relationships. As long as two variables are not independent, their MIC coefficients are all 1. Using the Maximum Information Coefficient (MIC) method, by selecting the maximum mutual information value, factors with a low impact on carbon emissions can be eliminated, thus screening for the main influencing factors of carbon emissions.

[0042] Furthermore, the first cumulative sequence of influencing factors and the second cumulative sequence of carbon emissions constructed in step S2 are specifically as follows:

[0043] X (1) =X (0) D=(x (0) (1) d ,x (0) (2) d ,…,x (0) (n) d );

[0044]

[0045]

[0046]

[0047] Where, X (0) =(x (0) (1),x (0) (2),…,x (0) (n)) represents the original data sequence, x (0) (k) represents the non-negative observation value at time k, represents the first cumulative sequence, Represents the second cumulative sequence.

[0048] From the above description, it can be seen that the use of 1-AGO sequence (accumulated sequence) can weaken the randomness of the original data and make it present a more obvious characteristic regularity.

[0049] Furthermore, the use of the impulse response function in step S3 to determine the dynamic response relationship between variables is specifically:

[0050] S301. Express the original data as a k-dimensional endogenous variable vector at time t, and obtain the general mathematical expression of the VAR model as follows:

[0051] X t =A1X t-1 +A2X t-2 +…+A p X t-p +εt ,t=1,2,…,Γ;

[0052] Where A i (i=1,2,…,p) represents the k-order coefficient matrix to be estimated;

[0053] S302. Introduce a k-dimensional matrix L as a lag operator in the general mathematical expression of the VAR model:

[0054] X t =(I-A1L-A2L 2 …-A p L p ) -1 ε t

[0055] =(I+C1L+C2L 2 …+C q L q +…)ε t

[0056] =ε t +C1ε t-1 +C2ε t-2 +…+C q ε t-q +…;

[0057] Where C q Represents the partial derivative of the variable matrix X with respect to the random error vector. The specific expression is as follows:

[0058]

[0059] S303, determine the impulse response function as:

[0060]

[0061] Where, Represents the matrix C q The (j, i)th element of the generation represents the response of the variable to the random shock. q represents a variable, which represents different independent variables X when it changes. t represents time. (j, i) represents the position of the current required quantity in the matrix. ε represents the random error.

[0062] From the above description, it can be seen that the lag weight and lag interval of the lag term can be determined through the VAR impulse response function, so as to facilitate the subsequent further calculation of parameters.

[0063] Furthermore, the calculation model parameter values ​​in step S4 are specifically:

[0064] Use the generalized inverse matrix to solve, the specific steps are as follows:

[0065] S401. Let and represent the independent variable sequence and the non - independent variable sequence in the prediction model respectively. is the parameter vector to be determined. Thus, the coefficient matrix B can be obtained as follows:

[0066]

[0067] S402. According to the relationship between the generalized inverse matrix and the solution of the linear equation system:

[0068] If n = N + 3 and |B|≠0, then

[0069] If n > N + 3 and B is a column - full - rank matrix, then

[0070] If n < N + 3 and B is a row - full - rank matrix, then

[0071] As can be seen from the above description, compared with the general method that cannot invert a singular matrix, even if the matrix is singular, there always exists a corresponding Moore - Penrose generalized inverse matrix. Therefore, using the Moore - Penrose generalized inverse matrix for solution can improve the model adaptability.

[0072] Furthermore, the mathematical expression of the enhanced multi - variable dynamic time - lag discrete grey prediction model described in step S5 is:

[0073]

[0074]

[0075] In the formula, represents the predicted value of represents the predicted value of i τ = [τ i1 , τ i2 represents the available lag interval of each factor. As the weight of the lag effect at different times, β1, β2, …, β N+2 represent the undetermined parameters. represents the time - lag driving term in the model, indicating the total influence of X i on X1 within the lag interval τ i ;

[0076] If and τ i = 0, it indicates X iThere is no time interval for the impact on X1. For the linear correction term, k represents time, kβ N+1 +β N+2 Represents the linear relationship between carbon emissions X1 and time k.

[0077] From the above description, it can be seen that for prediction problems with lag factors, the time-lag driven term is intended to reflect the lag process of different factors in the carbon emission system, which significantly improves the accuracy of the prediction model.

[0078] Furthermore, step S5 further includes:

[0079] A preset proportion of the collected data is used as sample data for calculating model parameters and evaluating fitting performance, and the remaining data is used as test data to verify the predictive ability of the model.

[0080] From the above description, we can see that verifying the predictive ability of the model makes the model more accurate, reliable and data-convincing.

[0081] Furthermore, after step S5, the following steps are further included:

[0082] S6. Based on the fitted value and the predicted value, evaluate the carbon emission reduction potential value and generate corresponding emission reduction recommendations.

[0083] As can be seen from the above description, this application provides a flexible prediction platform for time-delay systems, from which the lag relationship and other relationships between variables can be explored. This platform can enhance the generalization ability and modeling performance of time-delay system prediction.

[0084] Please refer to Figure 5 A terminal for predicting carbon emissions based on a dynamic time-lag model includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, each step of the above-mentioned method for predicting carbon emissions based on a dynamic time-lag model is implemented.

[0085] The above-mentioned method and terminal for predicting carbon emissions based on a dynamic time-lag model of the present invention can reflect the lag process of different influencing factors and improve the prediction accuracy of the model. The following is an explanation through specific implementation methods:

[0086] Glossary:

[0087] DTDGM(1, N, τ) model: a multivariable dynamic time-lag discrete grey prediction model. DTDGM(1, N, τ) is a multidimensional grey prediction model, which is a discrete model with a general structure. The solution of this model can be obtained through a recursive method, avoiding the misalignment errors in parameter solution and parameter application in traditional continuous models, improving the accuracy and applicability of the model, and resolving the problem that the one-dimensional grey prediction model only considers the influence of the independent variable itself during prediction, while ignoring the influence of other external factors on the prediction results. Based on the traditional multidimensional grey prediction model, DTDGM(1, N, τ) introduces linear correction terms and time-lag driving terms into the discrete grey prediction model, making the model widely adaptable to sequences affected by time-lag factors.

[0088] Maximum Information Coefficient: MIC (Maximal Information Coefficient) is a new method to detect nonlinear correlation between variables. Its value range is between 0 and 1. The higher the value, the stronger the correlation.

[0089] VAR model: Vector autoregression model, vector autoregression model.

[0090] Hysteresis: This study uses impulse response functions to examine the dynamic hysteresis effect process, including the hysteresis range, impact level, and direction. Hysteresis cannot be represented as a linear process; it varies nonlinearly over time. Time lags are ubiquitous in carbon emission systems, and the time lag effects of many factors on carbon emissions do not persist over time.

[0091] Example 1

[0092] Please refer to Figure 1 and Figure 2 The present invention relates to a method for predicting carbon emissions based on a dynamic time-lag model. This method addresses factors with a lag effect and proposes an improved dynamic time-lag discrete grey prediction model that includes a time-lag driving term and a linear correction term. This model reflects the lag process of different influencing factors and improves the model's prediction accuracy and stability. To address the problem of predicting with limited samples, the present invention uses a grey prediction model that is effective for small sample data, ensuring that the sample more fully meets modeling requirements.

[0093] The grey time-lag model used in the present invention can reveal the hysteresis relationship between variables by introducing a control driving term of a hysteresis coefficient under finite samples.

[0094] Existing methods have proposed multivariate discrete grey prediction models with time lag effects and have made predictions of carbon emissions based on them. However, the lagged relationship between carbon emissions and related factors has not been thoroughly studied. To this end, the vector autoregression (VAR) model has been introduced to determine the dynamic relationship between variables. The VAR model is a type of multiple simultaneous equations model, each of which is formed by the regression of the lagged values ​​of all endogenous variables. The impulse response function based on the VAR model is a method for determining the dynamic response relationship between variables. It reveals the relationship between variables by exploring the dynamic response of each variable to a single integral shock of one standard deviation. Therefore, the impulse response function can be used to examine the dynamic lagged effect process, including the lag range, impact degree, and direction.

[0095] Based on the above principles, the carbon emission prediction method of the multivariable dynamic time-lag discrete grey prediction model of the present invention specifically includes the following steps:

[0096] Step 1: Standardize the input data. The specific operations are as follows:

[0097] 11) Collect raw data

[0098] By consulting statistical yearbooks and other relevant materials or reviewing literature, we collect original data in recent years such as population size, wealth level, technological level, industrial structure, etc.

[0099] 12) Standardization

[0100] The training samples are normalized to eliminate the order of magnitude differences between data of different dimensions and avoid large output errors caused by order of magnitude differences. The Z-score normalization method is used for the data normalization of each influence. The specific normalization formula is as follows:

[0101]

[0102] Where: μ is the mean of all sample data; σ is the standard deviation of all sample data;

[0103] Step 2: Use the MIC method to screen factors affecting carbon emission prediction. The specific steps are as follows:

[0104] 21) Assume that X is the factor affecting carbon emissions and Y is the amount of carbon emissions, where X = {x1,…,x n}、Y={y1,…,y n}, n is the number of samples, and the mutual information between X and Y is:

[0105]

[0106] Where ρ(x,y) is the joint density between X and Y, and ρ(x) and ρ(y) represent the marginal probability densities of X and Y, respectively.

[0107] 22) Given i and j, grid the scatter plot of XY with i columns and j rows, and find the maximum mutual information value MIC.

[0108]

[0109] Where a and b represent the number of grids divided in the X and Y directions respectively, and B is the maximum value of the grid.

[0110] Step 3: Forming a 1-AGO accumulation sequence. The specific operations are as follows:

[0111] Form a sequence using carbon emission data as an independent variable Taking each influencing factor as a non-independent variable to form a sequence Let X1 (1) , X1 respectively (0) and The 1-AGO sequence, i.e.

[0112]

[0113]

[0114] Step 4: Design the DTDGM (1, N, τ) model by introducing the time-lag driving term and the linear correction term into the traditional multivariate grey prediction model to consider the lag effect and enhance the adaptability of the model. The mathematical expression of the DTDGM (1, N, τ) model is as follows:

[0115]

[0116] Where, τ i =[τ i1 ,τ i2 ] represents the available lag intervals for each factor, As the weight of the lag effect at different times. From this, we can get, is the time-lag driving term in the model, indicating that X i For X1 at the lag interval τ i The total impact within. and τ i =0, indicating X i There is no time interval for the effect on X1. β1,β2,…,β N+2 is the parameter to be determined. For the linear correction term, k represents time, kβ N+1 +β N+2 It reflects the linear relationship between X1 and time k.

[0117] Step 5: Please refer to Figure 3, the lag weight of the time lag term is determined by the VAR impulse response function and lag interval t i , the specific steps for determining the time lag term from the impulse response function are:

[0118] 51) Let X t =(X 1t ,X 2t ,…,X kt ) T represents a vector of k-dimensional endogenous variables at time t. The general mathematical expression of the VAR model can be considered as follows:

[0119] X t =A1X t-1 +A2X t-2 +…+A p X t-p +ε t t=1,2,…,I';

[0120] Where: A i is a k-dimensional coefficient matrix to be determined, I' is the number of samples, p represents the number of intervals in the model, ε t =(ε 1t ,ε 2t ,…,ε kt ) T Is a k-order vector representing random error, where cov(ε j ,ε s )=0,(j≠s), and ε t ∈N(0,δ 2 ), where j and s represent the jth and sth observable variables, respectively.

[0121] 52) Let L be a k-dimensional matrix. If LX t =X t-1 , then L is called the lag operator, and the general mathematical expression of the VAR model is:

[0122]

[0123] Where I is an identity matrix.

[0124] 53) Establish the following equation:

[0125]

[0126] The expression of impulse response function is:

[0127]

[0128] In the formula is located in the matrix Cq The element at position (j,i) of . Its size represents X j,t+q For a random shock ε it If j = 1 and i = 2, 3, ..., N, then the impulse response can be expressed as:

[0129]

[0130] Then in time [1,q], X1 has an effect on X i The impulse response size can be expressed as Assumptions Indicates the size of the kth element. The larger the absolute value of is, the greater the hysteresis effect is. If the value is too small, it is considered that there is no hysteresis effect. Therefore, two positive and negative thresholds are set. and This can distinguish whether the impulse response is valid. The formula for identifying a valid impulse response is as follows:

[0131]

[0132] In addition, it is necessary to find the effective time lag interval in the model. The specific equation is as follows:

[0133] a) For positive threshold

[0134]

[0135] b) For negative threshold

[0136]

[0137] The effective time lag interval is denoted as τ i =[τ i1 ,τ i2 ].

[0138] Step 6: Obtain the DTDGM (1, N, τ) model parameter β and solve it. The specific steps are as follows:

[0139] 61) The dynamic time-lag discrete grey prediction model can be expressed as

[0140]

[0141] Where, is the parameter vector to be determined, From this we can get the coefficient matrix B:

[0142]

[0143] Substituting \(k = 2+\tau,3+\tau,\cdots,n\) into the coefficient matrix \(B\), we get:

[0144]

[0145] The above equation contains \(n - 1\) linear equations, where \(\beta_1,\beta_2,\cdots,\beta\) N+2 are unknown parameters, and \(Y = B\beta\) can be derived by the least squares method.

[0146] a. When \(n = N + 3\) and \(|B|\neq0\), \(B\) is an invertible matrix, and the equation has a unique solution, that is

[0147] b. When \(n > N + 3\) and \(B\) is a column full-rank matrix, the full-rank decomposition of \(B\) is \(B = DC\), then the generalized inverse matrix of \(B\) can be expressed as \(B\) + \(= C\) T (CC T ) -1 (D T D) -1 D T , then Since \(B\) is a full-rank matrix, \(C\) can be an identity matrix, \(B = DI\) N , \(B = D\), then

[0148] c. When \(n < N + 3\) and \(B\) is a row full-rank matrix, then \(D\) can be an identity matrix, \(B = I\) n-1 C, \(B = C\), then

[0149] 62) After substituting the parameters into the prediction model, the predicted values are obtained, and the specific representation of the solution of the prediction model is obtained:

[0150]

[0151] According to the properties of the 1-AGO sequence, the predicted values can be obtained:

[0152]

[0153] The method of the present invention considers a carbon emission prediction model including a time-delay driving term and a linear correction term. First, it is proposed to introduce a time-delay driving term into a multivariate grey prediction model, and a linear correction term reflecting the linear relationship between the response variable and time is added; the dynamic response of each variable to a single shock of one standard deviation is determined through the impulse response function, so as to reflect the dynamic response relationship between variables, and thus the lag parameters are obtained, including the lag interval and the weights of shocks at different time points. This method of identifying complex lag relationships can enhance the high adaptability to time-delay systems and improve the prediction performance. Finally, please refer to Figure 4,The present invention provides a flexible prediction platform for time-delay ,systems, from which the lagged relationships and other relationships between ,variables can be explored, which can enhance the generalization capability and ,modeling performance of prediction for time-delay systems.

[0154] Example 2

[0155] Please refer to Figure 5 A terminal for predicting carbon emissions based on a dynamic time-lag model includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, each step of the method for predicting carbon emissions based on a dynamic time-lag model in the first embodiment is implemented.

[0156] In summary, the present invention provides a method for predicting carbon emissions based on a dynamic time-lag model. By analyzing the time-lag relationship between influencing factors and carbon emissions through impulse response analysis, an improved dynamic time-lag discrete grey prediction model including a time-lag driving term and a linear correction term is constructed, thereby reflecting the lag process of different influencing factors and improving the prediction accuracy of the model.

[0157] It should be noted that for the aforementioned method embodiments, for ease of description, they are all expressed as a series of action combinations. However, those skilled in the art should be aware that the present invention is not limited by the order of the actions described, because according to the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

[0158] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0159] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for predicting carbon emissions based on a dynamic time-lag model, characterized in that: The following steps are involved: S1. Collecting original data on factors affecting carbon emissions, standardizing the original data to obtain secondary data, and using the maximum information coefficient method to screen the secondary data to obtain the main influencing factors of carbon emissions; S2. Constructing a first cumulative sequence of influencing factors and a second cumulative sequence of carbon emissions based on the main influencing factors; S3. Use the impulse response function to determine the dynamic response relationship between variables and obtain the optimal lag parameters between variables; S4. Based on the first cumulative sequence and the second cumulative sequence, determine whether there is a time lag relationship between the influencing factor and the carbon emissions; if so, set a time lag interval and calculate a time lag weight, and calculate a model parameter value; if not, directly calculate the model parameter value; S5. Establish an enhanced multivariable dynamic time-lag discrete grey prediction model, substitute the model parameter values ​​and the main influencing factors into the enhanced multivariable dynamic time-lag discrete grey prediction model, and calculate the fitted value and predicted value of carbon emissions under the second cumulative sequence; In step S1, the maximum information coefficient method is used to screen the secondary data to obtain the main influencing factors of carbon emissions, which are: S101. Calculate the mutual information between carbon emissions and factors affecting carbon emissions: ； In the formula, X represents the factors affecting carbon emissions, and Y represents the amount of carbon emissions. 、 , n represents the number of samples of the original data, represents the joint density between X and Y, and Represent the marginal probability density of X and Y respectively; S102: Set the number of columns i and the number of rows j, grid the scatter plot of carbon emission influencing factors and carbon emissions into i×j grids, and find the maximum mutual information value: ； Where a and b represent the number of grids divided in the X and Y directions respectively, and B represents the maximum value of the grid; The construction of the first cumulative sequence of influencing factors and the second cumulative sequence of carbon emissions in step S2 is specifically as follows: X (1) = X (0) D =( x (0) (1) d , x (0) (2) d ,…, x (0) ( n ) d )； x (0) ( k ) d = ， k =1,2,…, n ； ； ； Where, represents the original data sequence, represents the non-negative observation value at time k, represents the first cumulative sequence, Represents the second cumulative sequence.

2. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 1, characterized in that: In step S1, the secondary data obtained by normalizing the original data is specifically: The Z-score standardization method was used to normalize the secondary data. : ； Where, µ represents the mean of all original data; σ Represents the standard deviation of all raw data.

3. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 1, characterized in that: The method of using the impulse response function to determine the dynamic response relationship between variables in step S3 is as follows: S301. Express the original data as a k-dimensional endogenous variable vector at time t, and obtain the mathematical expression of the VAR model as follows: ； Where, Represents the k-order coefficient matrix to be estimated; S302. Introduce a k-dimensional matrix L as a lag operator in the mathematical expression of the VAR model: ； Where C q Represents the partial derivative of the variable matrix X with respect to the random error vector. The specific expression is as follows: ； S303, determine the impulse response function as: ； Where, Representation matrix The first generation elements, whose values ​​represent the response of the variable to random shocks, q represents a variable, which represents different independent variables X when changing, t represents time, (j, i) represents the position of the current quantity in the matrix, Represents random error.

4. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 1, characterized in that: The calculation model parameter values ​​in step S4 are specifically: Use the generalized inverse matrix to solve, the specific steps are as follows: S401、Set and They represent the independent variable sequence and the non-independent variable sequence in the prediction model respectively. is the parameter vector to be found, , thus the coefficient matrix B is: ； S402. According to the relationship between the generalized inverse matrix and the solution of the linear equation system: If n=N+3 and ,but ; If n>N+3 and B is a full column rank matrix, then ; If n < N + 3 and B is a matrix with full row rank, then .

5. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 1, characterized in that: The mathematical expression of the enhanced multivariable dynamic time-lag discrete grey prediction model in step S5 is: ； ； Where, express The predicted value of express The predicted value of represents the available lag intervals for each factor, As the weight of the lag effect at different times, Indicates pending parameters, represents the time-lag driving term in the model, right In the lag interval Total impact within like and , indicating X i There is no time interval for the impact on X1. For the linear correction term, k represents the time. Indicates carbon emissions Linear relationship with time k.

6. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 5, characterized in that: Step S5 further includes: A preset proportion of the collected data is used as sample data for calculating model parameters and evaluating fitting performance, and the remaining data is used as test data to verify the predictive ability of the model.

7. The method for predicting carbon emissions based on a dynamic time-lag model according to claim 1, characterized in that: After step S5, the following steps are also included: S6. Based on the fitted value and the predicted value, evaluate the carbon emission reduction potential value and generate corresponding emission reduction recommendations.

8. A terminal for predicting carbon emissions based on a dynamic time-lag model, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, the processor implements the steps of the method for predicting carbon emissions based on a dynamic time-lag model as described in any one of claims 1 to 7.

Images