Forecasting Chinese provincial carbon emissions using a novel grey prediction model considering spatial correlation

Highlights

• A two-stage background value calculation method is given.

• The novel grey model considering spatial correlation (SGM(1,1,m)) is proposed.

• The validity of the SGM(1,1,m) model is verified using carbon emission data.

• •The SGM(1,1,m) model is applied to forecast China's provincial carbon emissions.

Abstract

In response to the errors caused by the uniform background value coefficients in the traditional grey model and the lack of analysis ability of panel data, this study proposes a two-stage background value calculation method and introduces a spatial weight matrix to employ the spatial correlation of variables in the grey model, creating a spatial grey model SGM(1,1,m) and realizing the modeling of spatial data by a grey model. The validity of the SGM(1,1,m) model was tested using carbon emission data from 30 provinces in China, and the carbon emissions of these provinces are predicted from 2020 to 2025. Conclusions are drawn as follows. First, the two-stage background value optimization mode and the addition of spatial overflow term in the model are reasonable, and the SGM(1,1,m) model improves the modeling performance in a certain sense compared with the GM(1,1) model while realizing regional association modeling. Second, the SGM(1,1,m) model has some formal similarities with the grey multivariate model, but while both are similar in terms of modeling requirements, the modeling purposes or economic meanings represented are different and should not be confused. Third, the SGM(1,1,m) model can achieve modeling predictions while providing a simple analysis of the spatial correlation of carbon emissions. Fourth, the prediction results present that the rise of carbon emissions in eastern China will level off, but the rise of carbon emissions in the central and western China will accelerate, which is largely because of the faster rise of carbon emissions in key provinces such as Shaanxi, Gansu, Ningxia, and Inner Mongolia.

Introduction

In recent decades, the problem of global warming has become increasingly serious, leading countries to pay close attention to controlling carbon emissions. Carbon emission prediction, which is the core task of emission reduction, has naturally drawn the attention of researchers. Only by making accurate predictions of carbon emissions can specific and targeted emission reduction measures be formulated. At present, there are many methods applied to carbon emission forecasting, which can be classified as follows: The first category is system optimization models, such as the IPAC model and IAMC model (Beek et al., 2020, Jiang et al., 2021). The second category is macroeconomic models. These include input–output models, CGE models, and LEAP models (Sbroiavacca et al., 2016, Shi et al., 2017, Dong et al., 2018). The third category is indicator decomposition models, such as the Kaya constant equation, IPAT, and STIRPAT models (Ma and Cai, 2018, Danish et al., 2021, Huang et al., 2021). The fourth category is artificial intelligence models, such as artificial neural networks, support vector machines, and extreme learning machines (Acheampong and Boateng, 2019, Wen and Cao, 2020, Sun and Huang, 2022). The fifth is grey prediction models. The majority of the abovementioned methods need to incorporate the factors influencing carbon emissions into the model, which requires a large amount of data collection. Grey models, on the other hand, can directly forecast carbon emissions without considering the influence of factors, solving the problem of uncertainty due to a small amount of data or insufficient information. Therefore, grey methods are widely used for carbon emission forecasting due to their advantages of ease of use, simple modeling process, and high accuracy (Yan et al., 2020, Wang et al., 2020, Xie et al., 2021, Ye et al., 2021).

As one of the most active branches of grey theory recently (Deng, 1982), the grey model is a novel direction for prediction theory and has been widely applied in many fields of social and natural sciences. It can be said that grey models have been effective at solving numerous problems in the real world and scientific research due to their small sample size and excellent predictive ability. Over nearly 40 years of development, grey prediction models have become increasingly mature, and there are an increasing number of types of models, which can be classified as two types: univariate models and multivariate models. Univariate models are those that have only one variable, ignore the effects of other variables, and model the explanatory variables alone. Multivariate models, on the other hand, consist of one dependent variable and one or more independent variables, modeling the influence of relevant factors on system changes, and are typical causal prediction models. As shown in Table 1, to improve the predictive performance of models, the structure and parameters of the traditional grey model from different perspectives were optimized, including background value optimization (Ma et al., 2019, Wu et al., 2020, Xu et al., 2021), construction of fractional order cumulative and reverse cumulative operations (Wu et al., 2013, Yan et al., 2020, Xie et al., 2020, Liu et al., 2021), data preprocessing (Wu et al., 2018, Zeng et al., 2018), model parameter optimization (Wei et al., 2018, Ma et al., 2019, Wu et al., 2020, Li and Wu, 2021), model structure extension (Ding, 2019, Zeng et al., 2020, Kang et al., 2021), information prioritization and rolling prediction mechanisms (Xu et al., 2019, Ceylan, 2021, Zhou et al., 2021), and construction of combinatorial models (Chen et al., 2019, Yang et al., 2019). These new grey models not only theoretically broaden the basic form of traditional grey models but also improve the prediction accuracy and adaptation range in a certain sense and are widely used in social and economic fields, such as electric power (Ding et al., 2018, Wu et al., 2021), renewable energy (Wu, Ma, Zeng, Wang, & Cai, 2019), natural gas (Zheng et al., 2021, Liu et al., 2022), tight gas (Zeng et al., 2020), air pollution (Xiong, Huang, Peng, & Wu, 2020), traffic flow (Xiao, Duan, & Wen, 2020), industrial development (Ding, 2019), landslides (Wu et al., 2020), and COVID-19 (Saxena, 2021, Ceylan, 2021).

In summary, scholars have improved grey models from several perspectives and made effective progress, but there are still some shortcomings in model optimization and carbon emission prediction. First, the literature calculates background values using the same background value coefficients, which leads to bias of parameter estimation to some extent. Second, existing grey models are mainly applied to modeling time-series data, with insufficient ability to model panel data or associate spatial data, especially in predicting carbon emissions, which fails to consider the spatial correlation among different regions. As shown by Ojagh, Cauteruccio, Terracina, and Liang (2021), the consideration of spatial correlation can increase the prediction accuracy to some extent. According to the first law of geography, any economic activity is spatially correlated. The spatial correlation of carbon emissions has been confirmed by many scholars; that is, a region's carbon emissions can affect those of its neighbors (Song et al., 2019, Wang and He, 2019). Existing studies can be classified as two main types. The first examines the spatial correlation characteristics of carbon emissions by social network analysis method (Wang et al., 2018, Song et al., 2019, Shen et al., 2021). Based on vector autoregression (VAR), gravity model or Granger causality, this method builds a spatial correlation network of carbon emissions to investigate the spatial characteristics. The second type uses spatial econometric methods, mainly introducing a spatial weight matrix in an econometric model and examines the spatial correlation of carbon emissions through Moran’s I index. Through the above methods, scholars have found that carbon emissions show a significant positive spatial correlation, which is stronger the closer regions are geographically (Fan and Zhou, 2019, Wang et al., 2021, Wang et al., 2022). Spatial correlation is more likely to occur in locations that are geographically adjacent and economically connected. Therefore, in this case, considering spatial correlation in a prediction model is more helpful for the accurate prediction of carbon emissions and geospatial linkage analysis.

Therefore, to address the above deficiencies, this study first analyzes the sources of background value errors in grey models and proposes a two-stage background value calculation method. Second, spatial correlation is introduced into the GM(1,1) model using a spatial weight matrix, thus creating a spatial grey model SGM(1,1,m), and realizing the modeling of spatial panel data by a grey model using spatial correlation. Finally, the SGM(1,1,m) model is validated using carbon emission data of 30 provinces in China and the provincial carbon emissions in the next six years are forecast. Following are the main contributions.

• A two-stage background value calculation is proposed, which further reduces the modeling error and further reflects the prioritization of new information in the modeling process.

• We introduce spatial correlation into a grey model using a spatial weight matrix, change the structure of the model, build a bridge between the spatial data and grey prediction model, and propose a spatial grey prediction model SGM(1,1,m).

• The panel data is applied to further increase the scope of the grey model and increase the analysis method for short panel data.

• The SGM(1,1,m) model is validated by utilizing carbon emission data from 30 provinces in China, proving its superiority in spatially linked modeling and prediction and achieving a simple analysis of spatial correlation within the region.

• The SGM(1,1,m) model is applied to forecast the 30 provincial carbon emissions in China from 2020 to 2025.

Following is the rest of this paper. Section 2 illustrates the traditional GM(1,1) model and proposes a two-stage background value optimization method to construct the SGM(1,1,m) model with a spatial spillover term. In Section 3, the SGM(1,1,m) model is validated by utilizing the carbon emission data of 30 Chinese provinces and the provincial carbon emissions in 2020–2025 are predicted. Section 4 is the conclusion.