1.1 Background
With the rapid development of economy, it is bound to be accompanied by energy consumption. Excessive energy consumption has caused damage to the atmospheric environment (Alvarez-Herranz et al. 2017). Over the past 20 years, China has accomplished two important tasks in the air pollution control. One is the peak sulfur dioxide emission from 2001 to 2010 (Zhong et al. 2021). The other is the comprehensive control of haze weather from 2011 to 2020, which is called “the battle of the blue sky” (Jiang et al. 2021). The above two tasks have been basically completed, but the pace of atmospheric governance cannot be slowed down. In 2021, the great blueprint of the carbon peak and the carbon neutrality are formally put forward at the National People's Congress of the People's Republic of China and the Chinese People's Political Consultative Conference (Fang et al. 2019). This also sets a new target for atmospheric governance of 2021 to 2030: “Carbon Peak”. Carbon emission is greenhouse gas emission, including CO2, CH4, N2O and so on. Before the industrial era, carbon emissions mainly came from incineration and natural emissions. After the industrial era, carbon emissions increased exponentially. Carbon emission will cause the temperature rise of the surface and atmosphere (S.Shaikh et al. 2018). Then, the rise of temperature will cause a series of environmental hazards (Zheng et al. 2021). Under the global sustainable development strategy, carbon emission has become an important obstacle to the world's economic development (Fan and Lei 2016). Moreover, excessive carbon emissions have a lot to do with unbalanced economic development (Ali Bekhet et al. 2017). Research shows that more than 58% of carbon emissions come from 40% of high-income people (Liu et al. 2019). Due to the imbalance of the regional economic development in China, there is a significant income gap between urban and rural residents (Huang et al. 2020). The income gap between the east and the west is also getting more attention (Liu et al. 2021). In view of these imbalances caused by economic development, exploring the relationship between income gap and CO2 emission is of great significance to alleviate the wealth gap and reduce the CO2 emissions at the same time.
1.2 Related work
In the 21st century, the sustainable development of environment has become an international hot topic. Moreover, the discussion of environmental protection must include the influence of economic factors. In recent years, Chinese scholars have made many valuable achievements in the interdisciplinary of environment and economy. The first is air pollution. Wang et al. (2017) studied the emission source and proportion of SO2, NOx, shoot and dust in China. The results showed that Hebei and Shanxi were the main emission provinces of air pollutants. Coal energy and heavy industry were the main reasons of air pollution. The second is water pollution. Shi et al. (2021) studied the relationship between economic production development and sewage treatment capacity in 30 provinces of China. The results showed that the efficiency of sewage treatment needed to be improved. The third is soil pollution. Wu et al. (2021) studied the distribution and source of the industrial heavy metals in soil. The results showed that the content of heavy metals in industrial land was much higher than that in agricultural land.
Compared with above environmental pollution, carbon emission is even more frightening. Fortunately, human beings have not neglected the dangers of carbon emission. The coordinated development of carbon emission and economy has been an important study all over the world. Among them, the relationship between fossil energy consumption and carbon emission is the most concerned. The research on carbon emission of coal, oil and natural gas is helpful to put forward the policy of energy structure optimization (Wang and Yan 2022). In addition, the research on the relationship between the three major industries and carbon emission can accurately locate the source of carbon emission. It plays a guiding role in the adjustment of industrial structure (Zheng et al. 2020). The development of urbanization is also an important reason for carbon emission. Reasonable planning of urban energy supply is an important means to reduce carbon emissions (Lai et al. 2022). There are many studies on carbon emission and economic factors. However, these studies are aimed at the behavior of the government, enterprises and the market. Environmental protection is the responsibility for all mankind. So, it is also an important task for the government and researchers to raise people's awareness of carbon reduction. Based on the predicted results of grey prediction model, this paper explores the relationship between the income gap and the CO2 emission in East China and Northwest China. The people's livelihood indicators are introduced into the study of carbon emission. This combination can not only improve the awareness of carbon reduction, but also strengthen people's awareness of supervision over the government and enterprises. There is no doubt that the participation of all people in carbon emission management will contribute to the rapid realization of the carbon peak.
To manage carbon emission reasonably, scientific data prediction is essential. Scientists have studied carbon dioxide since the 18th century. Since the beginning of the 21st century, the excessive emission of carbon dioxide has attracted the attention all over the world (Mostafaeipour et al. 2022). In order to explore the development trend of CO2 emissions, a series of forecasting methods such as the Linear Regression Model (Zhao et al. 2018), the Neural Network Prediction Model (Lagesse et al. 2020), the Markov Chain Prediction Model (Zhou et al. 2011) and the Grey Prediction Model (GM(1,1)) are proposed. Among them, the GM(1,1) has been widely used in energy consumption (Xu et al. 2015), (Wu et al. 2018) and air quality (Wu and Zhao 2018), (Chen and Yi 2015), (Comert et al. 2020). These researches have made outstanding contributions to the environmental science. With the continuous research, the GM(1,1) has been improved on many aspects, and it has been applied to a wide range of fields.
The improvements of the GM(1,1) are mainly reflected on the following two aspects. The first is the improvement of the accumulation mode. The original data is preprocessed by the accumulation operator to make it meet the data requirements of the GM(1,1). The accumulation operator is an important symbol that distinguishes the GM(1,1) from other models. The accumulation mode of the traditional GM(1,1) is 1-order accumulation. This accumulation mode leads to higher requirements and lower applicability for data. Wu et al. (2013) put forward the fractional order accumulation operator, which makes the accumulation order more flexible and improves the smoothness of the original sequence. Liu et al. (2021) proposed the reverse accumulation operator, which is suitable for decreasing sequences. The damping trend factor was introduced as a new parameter of grey generating operator to adjust the trend of the predicted results (Liu and Chen 2021). Tu and Chen (2021) proposed unequal accumulation, the loss of difference information can be effectively reduced. On the other hand, the second improvement is the expansion of the formula of the GM(1,1). Because the GM(1,1) has better compatibility, the improved model can be applied to many different researches. Xie and Liu (2009) proposed a discrete grey model which contributes significantly to the improvement of the GM(1,1). Taking the minimum absolute error as the objective function, Lee and Tong (2010) used the genetic algorithm to optimize the model parameters. Li et al. (2007) used the GM(1,1) Markov chain combination model to predict the number of Air China airlines. According to the modeling method of the GMC(1,1) model, a recursive discrete multivariate grey prediction model was proposed (Ma and Liu 2016). Wang et al. (2018) proposed the seasonal grey prediction model to buffer the influence of seasonal variation on the predicted results. In view of the influence of seasonal variation on prediction, Liu and Wu (2020) also introduced the grey generation operator into the Holt-winters seasonal data model.
The purpose of grey model innovation is to better solve practical problems. In the study of environmental pollution prediction, different grey models have been widely used. Wang and Lin (2019) used non-equilibrium grey verhulst model to study the relationship between CO2 emission and economic growth. Li et al. (2020) studied the non-equilibrium grey Bernoulli model to analyze the relationship between economic growth and pollutants. At the same time, Zhou et al. (2020) also used the Bernoulli seasonal grey model to predict the air quality index of the Yangtze River Delta. The fractional hausdorff grey multivariable model is used to analyze the relationship between population density and air quality (Shi and Wu 2021). Xiong et al. (2020) applied the multivariable grey model to predict the measurable indexes of haze weather in Nanjing. Although the grey models mentioned above have their own advantages, there are also disadvantages. The input variable of some models cannot be non-equidistant sequence, and some models have limitations in the accumulation mode. The CFNGM(1,1) model solves these problems. In this paper, as a non-equidistant input variable, the income gap is used to predict CO2 emissions. This method can not only predict data accurately, but also show the development relationship between the two variables. Meanwhile, in order to eliminate the influence of regional characteristic on the research conclusions, the predicted results in East China and Northwest China are compared. Comparative study makes the research results more scientific for the actual situation of China.
This paper is divided into five parts. The second part introduces the research areas, data sources and the CFNGM(1,1) model. The third part verifies the validity and applicability of the model. In the fourth part, the predicted results are analyzed. The fifth part gives the conclusion of the study.