Research on statistical measure under double carbon target - Self-moving regression model of grey prediction based on entropy weight method

1.1 Research background

With the rapid progress of industrialization and urbanization, global carbon emissions continue to increase, which leads to the increasingly serious problem of climate change. The report issued by the United Nations Intergovernmental Panel on Climate Change (IPCC) points out that since the industrial revolution, the global temperature has risen significantly, and extreme weather events have occurred frequently, posing a serious threat to human society and natural ecosystems. In this context, achieving peak carbon dioxide emissions and carbon neutrality has become the common goal of all countries in the world.

As the largest energy consumer and carbon emitter in the world, China’s energy consumption structure, carbon emission characteristics and economic growth model have an important impact on global climate change. Therefore, China’s goal of double carbon is not only a requirement for its own development, but also a contribution to the global response to climate change.

Although China has shown firm determination and strong action to achieve the goal of double carbon, it still faces many challenges and difficulties in the actual process. First of all, the transformation of energy structure is the key link to achieve the goal of double carbon, but at present, China’s energy consumption is still dominated by coal, and the proportion of clean energy is relatively low, so the transformation of energy structure is under great pressure. Secondly, technological innovation and popularization are the important support to achieve the goal of double carbon, but there is still a certain gap in clean energy technology, carbon capture and storage technology in China. In addition, policies and governance, social and economic transformation and other aspects also need to make great efforts.

Importance of Statistical Measure Research

Under the guidance of the dual-carbon target, how to scientifically and accurately evaluate carbon emissions, analyze the relationship between carbon emissions and economy, population and energy consumption, and predict the future carbon emission trend has become an urgent problem. As an important analytical tool and method, statistical measurement research can provide scientific basis and decision support for formulating targeted policies and measures. Through in-depth analysis of the relationship between carbon emissions and economy, population and energy consumption, as well as the challenges faced by peak carbon dioxide emissions to achieve carbon neutrality, more scientific and reasonable policies and measures can be formulated to promote regional sustainable development and achieve carbon emission reduction targets.

In this study, the grey prediction self-moving regression model based on entropy weight method is used to predict and analyze the carbon emissions in a certain area. As an objective weighting method, entropy weight method can determine the weight of indicators according to the degree of correlation between indicators and the size of information entropy; The grey forecasting model is suitable for forecasting problems with less data and incomplete information. The self-moving regression model can capture the trend and periodicity of time series through the analysis of historical data. By combining these three methods, we can evaluate and analyze the carbon emission situation in this region more comprehensively and accurately, and predict the future carbon emission trend, which provides an important basis for formulating the dual-carbon path planning.

1.2 Research significance

With the increasingly serious problem of global climate change, our government has actively responded to the voice of the international community and put forward the goal of double carbon, namely, peak carbon dioxide emissions and carbon neutrality. This goal means that China should achieve the peak of carbon emissions within the specified time, and gradually reduce carbon emissions in the subsequent time to finally achieve carbon neutrality. In order to achieve this goal better, this study aims to analyze the relationship between carbon emissions and economy, population and energy consumption through in-depth statistical measurement research, so as to provide scientific basis for formulating targeted policies and measures.

This study adopts a grey prediction autoregressive model based on entropy weight method to accurately predict and analyze carbon emissions in a certain region, providing an important foundation for dual carbon path planning. By predicting carbon emissions, we gain a clearer understanding of future trends and formulate targeted policies to promote the achievement of carbon peak and carbon neutrality goals.

In the process of research, we first theoretically analyzed the relationship between carbon emissions and economic, population and energy consumption, and made clear the contribution degree of each factor to carbon emissions. Then, we use the self-moving regression model of grey prediction based on entropy weight method to make an empirical analysis and calculation of carbon emissions in Jiangsu Province. By setting and optimizing the model parameters, we get more accurate carbon emission prediction results.

According to our research, we find that there are many challenges to achieve peak carbon dioxide emissions and carbon neutrality. First of all, the rapid development of China’s economy has brought about the rapid growth of carbon emissions, and it takes great efforts to achieve the peak of carbon emissions in a short time. Secondly, China’s energy consumption structure is dominated by fossil energy, which aggravates the carbon emission problem to some extent. Therefore, in the process of achieving the goal of double carbon, we need to actively promote the optimization of energy consumption structure and increase the proportion of clean energy.

According to our forecast and analysis, we provide targeted policy suggestions for government departments. On the one hand, we should strengthen the control of carbon emissions, promote the adjustment of industrial structure, improve energy efficiency and reduce the intensity of carbon emissions per unit GDP. On the other hand, it is necessary to increase R&D and investment in clean energy and promote the transformation of energy consumption structure. In addition, international cooperation should be strengthened to jointly address global climate change.

Based on the research on the relationship between carbon emissions and economic, population and energy consumption, this study provides beneficial enlightenment for China to achieve the goal of peak carbon dioxide emissions and carbon neutrality. We firmly believe that with the active promotion of government departments, China will be able to successfully achieve the goal of double carbon and make positive contributions to the response to global climate change.

1.3 Literature review

In recent years, the research on double carbon targets in China has been deepened, involving a wide range of fields and diverse research methods. In the research of statistical measurement of carbon emissions, domestic scholars have deeply discussed the changing trend, influencing factors and the relationship with economy, population and energy consumption based on different theoretical frameworks and model methods.

On the one hand, scholars have comprehensively analyzed the influencing factors of carbon emissions by establishing a comprehensive index system including economic indicators, population indicators, energy consumption indicators and carbon emissions indicators. Use a variety of statistical methods and models, such as multiple linear regression, grey prediction, entropy weight method, etc.^1–6 Combined with Kaya model⁷ The changing trend of carbon emissions is predicted and analyzed, which provides an important basis for formulating the dual-carbon path planning.

On the other hand, scholars are also concerned about the challenges and difficulties in realizing peak carbon dioxide emissions and carbon neutrality, especially the transformation of energy structure, technological innovation and promotion, policy and governance, and socio-economic transformation. Through in-depth study of the status quo and problems in these fields, the corresponding policies and suggestions are put forward to promote the realization of China’s double-carbon goal.

In addition, there are some studies that focus on the carbon emissions of specific industries or regions. For example, the carbon emissions of large carbon emitters such as power industry and transportation industry are deeply studied, and their emission characteristics and influencing factors are analyzed, and corresponding emission reduction measures and suggestions are put forward.^8,9 At the same time, some regions have also carried out the exploration and practice of carbon market mechanisms such as carbon emission trading and carbon sink, which provides useful experience and reference for the realization of China’s dual-carbon goal.¹⁰

Internationally, the goal of double carbon has also become the focus of global attention. Governments and scholars all over the world have carried out relevant research to promote the process of global response to climate change.

In the research of statistical measurement of carbon emissions, foreign scholars have also adopted a variety of methods and models to study. They not only pay attention to the changing trend and influencing factors of carbon emissions, but also pay attention to the relationship between carbon emissions and economic development and social well-being. By establishing a global or regional carbon emission database, the global or regional carbon emission situation is comprehensively analyzed and compared, which provides data support for the international community’s emission reduction actions.^11–18

At the same time, foreign scholars are also concerned about the technological and institutional innovations needed to achieve carbon neutrality. They have provided technical support and institutional guarantee for global emission reduction actions through in-depth study of cutting-edge technologies such as renewable energy technology, carbon capture and storage technology, smart grid, and market mechanisms such as carbon emission trading and carbon tax.

In addition, some international organizations and non-governmental organizations also actively carry out research and advocacy work under the goal of double carbon. For example, the International Energy Agency (IEA) regularly issues global carbon emissions reports to analyze the current situation and trends of global carbon emissions; The United Nations Environment Programme (UNEP) actively promotes global cooperation and actions to address climate change.^19–24

To sum up, the research under the dual-carbon target at home and abroad has been deepened and expanded, which has provided strong support and promotion for the global action to deal with climate change.

2.1 Index and model construction

2.2 Indicators and indicator system

In this paper, according to the four indicators of economy, population, energy consumption and carbon emissions, the index system of influencing factors of double carbon target is constructed, and the specific indicators are as follows.

2.3 Status of Regional Carbon Emissions

Requirement 1: The indicators can describe the economy, population, energy consumption and carbon emissions of a certain region;

Requirement 2: Analyze the factors that affect the carbon emissions in this region and their contributions;

Requirement 3: Judge the main challenges that the region needs to face to achieve peak carbon dioxide emissions and carbon neutrality, and provide the basis for the differentiated path selection in the regional dual-carbon (peak carbon dioxide emissions and carbon neutrality) path planning.

During the period of 2010-2015, the carbon emission fluctuated relatively with time, and the overall trend was that it first increased and then decreased. During this period, it can be well fitted by quadratic function. During the period of 2015-2020, the fluctuation of carbon emissions with time is relatively small, and the overall trend is increasing. In 2020, carbon emissions will decrease. During this period, a straight line can be used for fitting (during the whole period (2010-2020), a straight line can be used for fitting: $R^2=0.7605)$

The descriptive statistical analysis of carbon emission data by SPSSPRO shows that the data variance is large, so the carbon emission fluctuates greatly from 2010 to 2020.

To analyze the factors that have an impact on carbon emissions in this region, such as economic growth, population growth, changes in energy consumption structure, etc., and evaluate the contribution to carbon emissions. We use Pearson correlation test, which can effectively test and analyze the influencing factors of carbon emissions.

Using SPSSPRO to test the normality, the following Table 3 and Tables 1-5 is obtained:

The results of normality test based on S-W test or K-S test are as follows:

For the samples of residents’ living consumption, construction consumption sector, transportation consumption sector, total carbon emission and agriculture and forestry consumption sector, the sample number n is less than 5000, so S-W test is adopted.

The results show that the significance p values of these samples are 0.374, 0.571, 0.633, 0.320 and 0.246, respectively, which are not significant, so the original hypothesis can not be rejected, that is, the data of these samples meet normal distribution.

However, for the sample of industrial consumption department, its significance P value is 0.001, which shows the significance level, so the original hypothesis is rejected and the data of this sample does not meet the normal distribution.

It can be seen that Pearson correlation test analysis can be carried out in the next step.

The table shows the parameter result table of model test, including correlation coefficient and significance P value.

From the thermodynamic coefficient diagram formed by the matrix of influencing factors, it can be seen that the main factors affecting carbon emissions are agriculture and forestry consumption departments (0.906), construction consumption departments (0.916), residents’ living consumption (0.895), followed by transportation consumption departments (0.869) and industrial consumption departments (0.857).

2.4 Regional carbon emission indicators and their related models

(1) Standardize and calculate the specific gravity of index value

Firstly, the index is dimensionless.

Positive indicators:

Negative indicator:

Then, calculate the index value proportion:

(2)-(4) Where: is the numerical value of the j-th index in the ith year, is the standardized value, is the minimum value of the j-th index, is the maximum value of the j-th index, and is the index proportion $x_{\mathit{ij}}{x}_{\mathit{ij}}^{\prime }\mathit{min}\left(x_{\mathit{ij}}\right)\mathit{max}\left(x_{\mathit{ij}}\right)y_{\mathit{ij}}$

(2) Entropy weight method to find the weight.

Calculation of information entropy value and information utility value; $e_j{d}_j$

In the above formula, it is the information entropy of the j-th index; M is the number of observed values; K=, which is a constant; Is the information utility value $e_j\frac{1}{\mathit{lnm}}{d}_j$

Finally, calculate the weight of each index.

The above formula: is the weight of j indicators, and n is the number of indicators $W_j$

The weight analysis and calculation results of entropy weight method are shown in Table 6 below.

The chart shows that the weight of GDP is 12.979%, the weight of GDP growth rate is 8.292%, the weight of tertiary industry is 11.887%, the weight of resident population is 9.448%, the weight of industrial added value is 5.961%, the weight of population growth rate is 7.148%, the weight of energy consumption coal is 12.988%, and the weight of total carbon emissions is 11.11. The weight of carbon emission intensity is 10.013%, and the weight of per capita carbon emission is 10.087%, in which the maximum index weight is the proportion of energy consumption coal (12.988%) and the minimum index industrial added value (5.961%).

(3) The grey correlation method is used to calculate the correlation degree.

First, a reference sequence and a comparison sequence are determined. The reference sequence is:

The comparison sequence consists of the optimal values of each index, because the dimensionless indexes belong to the interval [0,1]. Therefore, the maximum value of each index is selected as the comparison sequence =(1,1, …, 1). $x_0$

Secondly, calculate the correlation coefficient:

In the above formula, ρ is the resolution coefficient, and 0≤ρ≤1. Generally, when ρ=0.5, it has higher resolution. (Resolution coefficient ρ∈(0, ∞), the smaller the ρ, the greater the resolution. Generally, the value range of ρ is (0,1), and the specific value can be determined according to the situation. When ρ≤0.5463, the resolution is the best, usually ρ=0.5).

(4) Weighted correlation degree between reference sequence and comparison sequence

Where: is the entropy weight. The correlation degree reflects the closeness between the evaluation object and the optimal state, and the greater the value, the higher the closeness between the I-th evaluation object and the optimal state. Therefore, the evaluation objects can be sorted and classified according to their relevance $w_j{r}_i{r}_i$

The calculation results are shown in Table 7 and Tables 8-15 below:

Analysis: weighting the results of the above correlation coefficient, and finally obtaining the correlation value, and using the correlation value to evaluate and sort the nine evaluation objects; The value of correlation degree is between 0 and 1. The greater the value, the stronger the correlation between it and the parent sequence, which means the higher its evaluation. As can be seen from the above table, for the nine evaluation items, the per capita carbon emission is the highest (correlation degree: 0.997), followed by the resident population (correlation degree: 0.994).

(A) Based on population and economic changes in energy consumption forecasting model

Because GDP and population-related time t show a linear trend, it is preliminarily considered to establish a multiple linear regression model for prediction and analysis. The model formula is

In the previous analysis, both GDP and population have passed the normality test, so linear regression can be carried out. We use the least square method to determine the coefficient.

The result analysis of F-test shows that the P value of significance is 0.000***, which is significant horizontally, and the original hypothesis that the regression coefficient is 0 is rejected, so the model basically meets the requirements. For variable collinearity, variable GDP and VIF value of resident population are more than 10, and there is collinear relationship. The formula of the model is as follows: y (total energy consumption) =-0.001+1.0*GDP+0.001* resident population. Because the collinearity between variables is obvious, and r is 1, which shows that it is a functional relationship rather than a correlation relationship, the linear regression method should be abandoned, and the ridge regression method should be used to predict, and K=0.03 is determined according to the variance expansion factor method.

Analysis: The results of ridge regression show that the P value based on F test is 0.000***, which is significant at the horizontal level, rejecting the original hypothesis, indicating that there is a regression relationship between independent variables and dependent variables. At the same time, the goodness of fit r of the model is 0.996, and the model is excellent. The formula of the model: total energy consumption =-121268.079+16.388× resident population+0.782× GDP.

The prediction results of the model are as follows:

(B) Regional carbon emission prediction model

A multivariate linear regression model can be established to predict carbon emissions and population, GDP and energy consumption. The result analysis of F-test shows that the P value of significance is 0.002***, which is significant horizontally, and the original hypothesis that the regression coefficient is 0 is rejected, so the model basically meets the requirements. The formula of the model is as follows: y=-71496.169+0.034*GDP+16.282* resident population+0.034* total energy consumption.

4.1 Scenario design

According to the requirements of carbon emission policy, the following three scenarios are designed:

4.2 Multi-scenario carbon emission accounting method

Based on the basic assumptions, carbon emissions accounting:

Hypothesis 1: The GDP in 2035 will be doubled compared with the base period, and it will be quadrupled compared with the base period in 2060.

Hypothesis 2: The carbon consumption of ecological carbon sinks in 2060 is 10% of the carbon emissions in the base period. That is to say, the carbon emission intensity is reduced by 10%.

Hypothesis 3: In 2060, the carbon consumption of engineering carbon sinks or carbon transactions is 10% of the carbon emissions in the base period.

4.3 Determine the Double Carbon Target and Path

Note: The change rate of influencing factors in the above table refers to the research results of Rui Qi (2023).

According to the report of World Economic Outlook 2019, the International Monetary Fund (IMF) confirmed by Kaya decomposition method that the decrease of global energy intensity and carbon emission intensity slowed down the growth of total carbon emissions from 2013 to 2017. However, the decrease in energy intensity in 2018 was small, which could not offset the increase in carbon emissions caused by population growth and per capita income growth, resulting in a 1% increase in global carbon emissions in 2017 and a 2% increase in 2018.

Since the 21st century, China’s influence on the growth of global carbon emissions has changed significantly. In 2015, coal consumption in China decreased by 3.7%. In the same year, China’s energy consumption reached 4.3 billion tons of standard coal, and the goal in 2020 is to limit it to 5 billion tons. The government of China has set mandatory targets, including air pollution control and strengthening the development of renewable energy such as wind, solar and nuclear energy.

According to the preliminary accounting of the National Bureau of Statistics, the total energy consumption in China in 2020 is 4.98 billion tons of standard coal, accounting for 56.8% of the total energy consumption, down 0.9 percentage points from the previous year. According to Tollefson, China may reach the peak of total carbon emissions earlier than expected. However, the power demand in China will continue to grow at a high speed, so it is necessary to promote the decarbonization process of the power industry to speed up the reduction of carbon emission intensity.

Three situations in peak carbon dioxide emissions:

Figure 1. Total carbon emissions in baseline scenario.

Figure 2. Total carbon emissions in natural scenarios.

Figure 3. Total carbon emissions in ambitious scenarios.

6.1 Data limitations

The data for this study mainly comes from public channels such as the International Energy Agency (IEA). Although these data are authoritative, their timeliness and completeness may be limited to some extent. Especially for carbon emission data specific to certain regions or sub sectors, there may be missing or inaccurate data, which to some extent affects the accuracy of the analysis. In addition, the collection and organization of carbon emission data involves multiple departments and fields, and the consistency and comparability of the data may also be affected, which may lead to potential biases in the research results.

6.2 Limitations of the method

This study used various methods such as entropy weight method, grey prediction, and autoregressive model. Although these methods have certain advantages in dealing with complex systems, they also have limitations. For example, grey prediction models are more suitable for situations with limited data and incomplete information, while their prediction accuracy may not be as good as other more complex models when there is sufficient data. In addition, although the entropy weight method can objectively determine the weights of indicators, it has certain requirements for the quality and distribution of data. Abnormal or missing data may lead to unreasonable weight allocation, which in turn affects the stability and reliability of the model.

6.3 Assumptions and model limitations

When constructing the model, this study made some assumptions, such as simplifying the impact of economic growth, population growth, and changes in energy consumption structure on carbon emissions as a linear relationship, and ignoring the interactions between various factors. However, the actual situation may be more complex, and nonlinear relationships and interactions between factors may have significant impacts on carbon emissions. In addition, the selection and setting of model parameters may also be influenced by subjective factors, which to some extent increases the uncertainty of prediction results.

6.4 External validity

This study mainly analyzes specific regions, and its research results may not be applicable to other regions or larger areas. There are differences in economic development level, energy consumption structure, policy environment and other factors in different regions, which may significantly affect the trend and influencing factors of carbon emissions. Therefore, when extending the results of this study to other regions, it is necessary to carefully consider these differences and make corresponding adjustments and validations.

6.5 Limitations of practical application

Although this study proposes a series of policy recommendations, these recommendations may face many challenges in practical application. For example, policy implementation requires cooperation and support from multiple parties such as the government, enterprises, and the public, and the demands and interests of different stakeholders may conflict, which may increase the difficulty of policy implementation. In addition, the effectiveness and sustainability of policies also need to be verified through long-term practice, which to some extent limits the immediate impact and application scope of policies.