In the past few decades, China’s development has heavily relied on coal, and the country has become the world's largest coal producer and consumer (Wang et al. 2022). However, China has recently come to face a dilemma: relying on coal use to ensure energy security or reducing coal to reach carbon peak and neutrality goals (Guo et al. 2016; Wyrwa et al. 2022; Zhang et al. 2021). This brings uncertainties to the coal market and causes the imbalance of coal supply and demand to increase coal price volatility (Knights and Scanlan 2019; Liu et al. 2013; Wang et al. 2020a, b). Considering that coal is upstream of many products in industries such as electricity, steel, chemical, and building materials, coal price volatility may create contagions through industry chains to cause system risk in the macroeconomy (Cui and Wei 2017). Therefore, analyzing coal price volatility is an important issue. Currently, it has more particular significance because the coal market's instability has largely increased because of policy-guided market reconstruction and a series of exogenous shocks, such as geographical conflicts and environmental climate changes (Jones 2022; Song and Wang 2016). To tackle this problem, locating and monitoring the volatility source of coal prices helps alleviate rising market instability and prevent energy-induced system risk (Lin et al. 2022). Based on this background, we aim to find an effective method to identify the potential volatility source of coal prices by quantifying the influence of coal price volatility.

In the previous literature, the influence of coal price volatility is commonly studied from a macroscopic perspective (Guo et al. 2016). Studies found that coal prices can influence other energy commodities’ prices or even influence CPI and PPI through interfuel substitution and intermarket channels (Cao et al. 2022; Li et al. 2019). However, from a microscopic perspective, coal prices determined by coal producers in China’s different regions vary significantly. There is a lack of knowledge regarding which coal-producing areas have influential price volatility. Considering that coal is a scarce energy source, supply-side actors, i.e., coal producers, dominates the coal market (Li et al. 2020); analyzing the influence of coal-producing areas’ price volatility provides a more detailed information target regarding the volatility source of coal prices and improves the precise prevention and management of energy-induced risk. Therefore, this paper is dedicated to exploring the coal price volatility of China’s coal-producing areas. Defining the coal-producing areas whose price volatility has a stronger influence as coal price volatility spreaders (CPVSs), we propose a hybrid method to identify CPVSs by analyzing the inner market price comovement.

Recently, researchers and policymakers have reached a consensus that analyzing price comovement helps quantify the influence of price volatility (Li and Zhao 2016). They consider an entity to have a strong ability to influence other entities if it has many comovement correlations with them (Li and Zhao 2016; Liu and Jin 2020). Furthermore, studies adopt complex network theory to provide more precise and convenient quantifications by abstracting entities and their comovement correlations as nodes and edges (An et al. 2014; Chen et al. 2022; Xu et al. 2019). From the network perspective, the nodes’ influence can be measured by investigating their network topology features in different ways, such as direct, indirect, global, local, and intermediary influences. Related research has achieved significant progress in finding price volatility spreaders in stock, commodity, and future markets (Chien et al. 2022; Wang et al. 2019). However, this issue has not been studied in the context of the coal market. Therefore, we build a coal price comovement network (CPCN) to quantify the influence of coal-producing areas’ price volatility.

To build the CPCN, precisely estimating comovement correlations among coal price time series is vital. Unlike other entities, China’s coal pricing mechanism is not entirely market-oriented (Guo et al. 2016). Specifically, during 1985–2012, China implemented a dual-track pricing policy (Yang et al. 2018). Coal output was divided into unified and nonunified distribution coal, where the market determined the price of the former, and the government guided the price of the latter (Zhang et al. 2019). This policy was abolished and changed to a market-oriented pricing mechanism during 2013–2015. However, since 2016, China has re-executed a new dual-track pricing policy to ensure energy security (Yang et al. 2018). In this case, coal prices may have nonlinear, nonstationary, and nonnormal features, which makes many widely adopted econometric models, such as Pearson, Granger, and GARCH, unsuitable for analysis (Wang et al. 2019). To address this problem, we introduce the transfer entropy method. It is an information theory-based method that measures the asymmetric and nonlinear causalities between time series, such as meteorological, medical, and audio data (Hu et al. 2022). Because it is free of strict assumptions and complex parameter estimations, the transfer entropy method has attracted increasing attention in studying comovement correlations among price time series (Schreiber 2000); therefore, it can also be flexibly used for analyzing coal price comovement.

By investigating the transfer entropy-based CPCN, we can quantify the influence of the coal-producing areas’ price volatility and identify the CPVSs according to the rank of their influence. However, the available network analysis methods have different emphases, such that the same coal-producing area may have partial evaluations and CPVSs may be inaccurately identified. Therefore, we need a more universal and comprehensive evaluation of the influence of coal price volatility. To tackle this problem, we use a rank aggregation method (Dourado et al. 2019). The rank aggregation problem, a hot issue in social choice theory, helps a group of voters who need to rank the available alternatives to obtain a consensus result. In our research (Çakır et al. 2015), the price volatility influences calculated by different network analysis methods can be seen as alternatives to identifying the CPVSs, providing the basis of rank aggregation. This paper introduces a newly proposed method named the competition graph (CG) method to identify CPVSs, as it is regarded as a simple yet accurate method compared to many classic methods, such as the Borda method (Ivanov 2022), the Dowdall method (Reilly 2002), and the minimum violations ranking method.

To summarize, this paper aims to identify the CPVSs to help locate the price volatility source on the supply side of China’s coal market. We collected 938 weekly coal price data of coal-producing areas (involving 22 provinces and 94 cities) between 2006.9.4 and 2021.7.12 from the China Coal Big Data Website. By conjointly using the transfer entropy method (Korbel et al. 2019), complex network theory (Wang et al. 2019), and the rank aggregation method (Xiao et al. 2021), we propose a hybrid method to quantify the influence of coal-producing areas’ price volatility. The validity test demonstrates that the proposed hybrid method efficiently identifies the CPVSs as they correlate to many price determinants, e.g., electricity and coal consumption, generation, and inventory (Yan et al. 2019). The empirical results show that coal price comovement patterns changed dramatically in 2016, 2018, and 2020 under the influence of energy and environmental policies. From the evolution perspective, we found 4 types of coal-producing areas following the downward, rise-fall, fall-rise and waving trends. Before 2018, coal-producing provinces with strong demand for coal and electricity, e.g., Jiangxi, Chongqing, and Sichuan, were CPVSs; after 2019, those that with comparative advantages in coal supply, e.g., Gansu, Ningxia, were CPVSs.

This study contributes to the literature in three main ways. (1) Transfer entropy networks are established to investigate the price comovement of coal-producing areas. To the best of our knowledge, we are the first to unveil the inner interactions of the supply side of China’s coal market. (2) A hybrid method combining complex network theory and the rank aggregation method is introduced to identify CPVSs. Compared to the classic network-based method, it provides a more universal and comprehensive evaluation of the influence of coal price volatility. (3) An empirical analysis is conducted to study the evolution of CPVSs, which deepens our understanding of China’s coal market and helps us prevent the system risk caused by coal price volatility.

The rest of this paper is organized as follows. Section 2 introduces the data and methods in our research. Section 3 presents the validity test of our method and conducts an empirical study. Section 4 summarizes the main conclusions.

2.1 Data source and preprocessing

To study the CPVSs, we access a valuable dataset containing 938 weekly coal price time series of different coal-producing areas from the China Coal Big Data Website. The time span of the dataset is from 2006.9.4 to 2021.7.12, for a total of 776 weeks. The coal-producing areas of the dataset involve 94 cities and 22 provinces in China. Each coal-producing area has up to 5 types of coal varieties determined by heat output, including lignite coal, anthracite coal, coking coal, thermal coal, and coal injection. Considering that a coal-producing area may have a stronger influence if it has more coal varieties, we use the price time series of all the coal varieties for analysis.

Furthermore, each coal variety has up to 3 types of prices determined by trading methods, i.e., pit mouth price, vehicle plate price, and factory price. To eliminate redundant information, we only choose only one type of price for one coal variety. Specifically, we preferentially use the pit mouth price; if a coal variety does not have a pit mouth price, we use the vehicle plate price, then the factory price. Doing so helps provide more data for analysis, as most coal varieties have pit mouth prices, but fewer have vehicle plate and factory prices.

To make a holistic study of CPVSs, we use the sliding window method to analyze the evolution of CPVSs. The sliding window method divides the full data into time-related subsets. In this paper, the length and interval of the window are set to 150 and 1 week, respectively. Therefore, we obtain 626 subsets. For the price time series in each subset, we exclude those with unequal length and those with continuous missing values longer than 10% of the window length (15 weeks). To fill in other missing values, we use linear interpolation. Finally, we obtain 601 nonempty subsets that can be used for analysis.

In addition, we collected 5 types of macroeconomic data that can reflect the coal price volatility influence of the coal-producing areas to help test the validity of our proposed method. Based on supply and demand theory, we collected the coal consumption, raw coal production, and coal inventory of the state-owned coal mine data. Moreover, considering that the electric power sector is China's most important coal consumer, we collected electricity consumption and electricity generation data. All the data are annual data of the relevant coal-producing areas obtained from the Wind Database with the same time span as the coal price data.

2.2 Methods

To identify CPVSs, this paper introduces a hybrid method with three methodological steps. First, we build a complex network to capture the price comovement of the 938 coal price time series by calculating the transfer entropy between each pair of price time series. Second, we quantify the influence of each coal-producing area by using 7 classic network centrality indicators. Third, we aggregate the rank based on the results of the 7 network indicators using the competition graph method to obtain the final result for the CPVSs.

2.2.1 Transfer entropy and the coal price comovement network

The transfer entropy method was proposed based on information theory by Schreiber (Schreiber, 2000). It measures the degree of the reduced uncertainty of a variable’s future state conditional on another variable’s past state. Commonly, transfer entropy is calculated based on Shannon entropy (Korbel et al. 2019). However, the coal price time series used in our research is considered to have multifractal features (Zhao et al. 2016). Therefore, we introduce a more suitable method to calculate transfer entropy, namely, the Rényi entropy (Korbel et al. 2019). Unlike Shannon entropy quantifies the minimal amount of binary information necessary to encode a message, Rényi entropy describes the minimal cost necessary to encode a message when the cost is an exponential function of the message length. For a discrete random variable \(X\), \(p(x)\) is its probability distribution, and \(\rho_{q} (x)\) is the escort distribution (Zhao et al. 2016) of order \(q\) used to measure the Rényi entropy (Jizba and Arimitsu 2004), whose equation is as follows.

For the price time series of two coal varieties, we denoted them as \(X(t)\) and \(Y(t)\). Their transfer entropy depends on history indices \(m\) and \(l\), where we denote \(x_{m + 1} = X(m + 1)\), \({\rm X}_{m} = \left\{ {X(m),X(m - 1), \ldots ,X(1)} \right\}\) and \(\Upsilon_{{\text{m}}}^{l} = \left\{ {Y(m), \ldots ,Y(m - l + 1)} \right\}\). Then, we can measure the Rényi transfer entropy (denoted as RTE) according to the following equation.

In Eq. 2, if \(q < 1\), the Rényi transfer entropy highlights the tail parts of the distribution, if \(q > 1\), it accentuates central parts of the distribution, if \(q = 1\), it equals the transfer entropy calculated using the Shannon entropy. Considering that the coal market is sensitive to exogenous factors, the tail parts of the coal price time series may be informative. Therefore, we adopt an empirical value, \(q = 0.5\), to quantify RTE.

Moreover, the calculation of RTE can get a stable value if \(m \to \infty\). However, this is unrealistic due to the finite size of the sample data. Commonly, \(m\) and \(l\) are set to 1 to capture the Markov feature of price time series. To avoid the finite-size effect and spurious information transfer in-depth, we shuffle the coal price time series to calculate the effective transfer entropy (denoted as RETE) and its p-value, which can be expressed as follows.

For a pair of coal prices time series, we shuffle them 100 times to calculate the mean value of RETE as a result. If RETE > 0 and the p-value of the calculation is less than 0.05, we consider this result to be a credible causality describing the price comovement. For the 938 coal price time series used in our research, we calculate the RETE and p-value of each pair of them. Regarding the coal price time series as nodes (recorded in a set \(V\)) and the transfer entropy causality as edges (recorded in a set \(E\)), we can get a directed weighted network capturing all the comovement correlations among the coal price time series, which could be mathematically represented as a matrix (denoted as CPCN) as follows.

2.2.2 Network indicators for coal price volatility influence

As mentioned above, we use the complex network analysis method to quantify the influence of coal price volatility. From the network perspective, nodes in different structural positions show different topological features with various influences. Therefore, such a method can help analyze the CPCN and identify the CPVSs (Wang et al. 2019). Specifically, we select 7 classic network indicators that measure a node's influence with different emphases to provide a comprehensive quantification (Wang et al. 2020a, b). The network indicators are the out-degree, in-degree, betweenness centrality, closeness centrality, cluster coefficient, eigenvector centrality, and PageRank algorithm, whose equations and mean ideas are described in the following table (Wang et al. 2019; Wang et al. 2020a, b). More detailed explanations can be found in the relevant references (Table 1).

As mentioned in Sects. 2.1 and 2.2.1, a node in the CPCN represents the price of one coal-producing area’s coal variety. To obtain a coal-producing area’s influence, we in-depth calculate the summation of the coal varieties’ influence corresponding to the coal-producing area, as one has up to 5 coal varieties. To eliminate the effect of differences in scale and range of values, we adopt the maximum and minimum standardization method to normalize the results of each of the 7 network indicators. Then, we can obtain the influence of the coal-producing areas measured by the 7 network indicators. However, these coal-producing areas differ geographically; some are cities, and some are counties. To facilitate analysis, this paper studies coal-producing areas at the provincial level. We determine the province for each coal-producing area, and then calculate the average of the influence (counting only the nonzero values) to act as the province's influence.

2.2.3 Rank aggregation based on the competition graph method

Commonly, the CPVSs are identified according to the rank of their influence. Considering that we use 7 network indicators to quantify the influence of the coal price time series, they have 7 different rank results. To achieve a more universal and comprehensive evaluation, this paper introduces the rank aggregation method, i.e., the competition graph (CG) method (Xiao et al. 2021).

For \(M\) coal-producing areas analyzed by \(N\) network indicators, CG statistics indicate the number of times a coal-producing area \(i\) ranks ahead of another area \(j\) according to each network indicator, whose results are recorded in a matrix shown in Eq. 5:

In Eq. 5, \(R_{i}^{n}\) and \(R_{j}^{n}\) are the ranks of the coal-producing area \(i\) and \(j\) according to the quantification of network indicator \(n\), \(q_{ij}^{n}\) quantifies whether area \(i\) ranked ahead of area \(j\) according to network indicator \(n\), and \(aq_{ij}\) measures the total number by which area \(i\) ranks ahead of area \(j\), which are the entries recorded in matrix \(\text{CG}\). Based on this matrix, the CG method calculates the ratio of out- and in-degrees (ROID) to comprehensively measure a coal-producing area’s aggregate performance, whose equation is as follows.

In Eq. 6, matrix \(\text{CG}\) is regarded as a network whose nodes are the coal-producing areas. \(\sum\nolimits_{j = 1}^{M} {aq_{ij} }\) quantifies a node’s out-degree, which represents the number of times it ranks ahead of other areas. \(\sum\nolimits_{i = 1}^{M} {aq}_{ij}\) quantifies a node’s in-degree, which represents the number of times it ranks behind other areas. The idea of ROID is that an influential coal-producing area should rank ahead of many other areas but rank behind few areas.

3.1 Evolution analysis of the coal price comovement network

As mentioned in the Methods section, this paper built 601 coal price comovement networks (CPCNs) to study the coal price volatility spreaders (CPVSs). For the 601 CPCNs, we first study the evolution of their structural characteristics to unveil the comovement patterns of the coal market. Specifically, we choose 4 typical network indicators capturing the global structural characteristics, i.e., node number, edge number, average distance, and the assortativity coefficient. Among them, node and edge numbers help portray the size and density of the network. If their values are large and the ratio of edge and node numbers is large, the coal market is considered tightly connected through comovement correlations. The average distance of the network measures the average shortest path between each pair of nodes. If the average distance is short, the influence of coal price volatility can spread rapidly through the market. The assortativity coefficient quantifies the correlation pattern between the large- and small-degree nodes. The results of the above indicators are shown in Fig. 1.

Evolution of the CPCN’s global structural characteristics. a The total number of edges/nodes of the CPCNs; b The average distance and assortativity coefficient of the CPCNs

From Fig. 1a, we find that the evolution of the node number went through 5 stages corresponding to significant market reforms and exogenous shocks. During 2010–2012, the node number was small. This is because the coal pricing mechanism was not market-oriented (China implemented a dual-track pricing policy), and there were few comovement correlations in the coal market. Then, the node number increased continuously during 2013–2015. This is because the dual-track pricing policy was abolished and changed to a market-oriented pricing mechanism; the coal price comovement efficiently reflected the supply and demand changes in the coal market. However, the node number remained stable during 2016–2018. This is because China re-executed a new dual-track pricing policy to ensure energy security. Then, the node number increased rapidly to a new stable level during 2018–2020. This was influenced by the US-China trade dispute, limiting China’s coal import and improving domestic demand. Last, it declined rapidly during 2020–2021. This is because China put forward the goals of achieving peak carbon emissions and carbon neutrality and suffered the outbreak of COVID-19, which limited both the supply and demand of China’s coal market. The evolution trend of the edge number is similar to that of the node number. However, it was more volatile during the stable periods (2016–2018 and 2018–2020) of the node number. This means that even though the coal price is not entirely market-oriented, it is not a stable system and is influenced by market changes. The edge number is a sensitive indicator to study coal price comovement.

From Fig. 1b, the evolution of the average distance and assortativity coefficient are more volatile than both the node number and edge number. This proves that China’s coal market could be influenced by market changes. Overall, the average distance is less than 2, which means that the distance between the nodes is short, and the influence of coal price volatility can spread through the market rapidly; the assortativity coefficient is less than 0, meaning that the influential nodes prefer to connect the nodes with little influence. Moreover, the evolution of the two indicators has an inverse trend, as the assortativity coefficient is low when the average distance is high. From the network perspective, this may be due to changes in the influential nodes' movement patterns. Considering that the influential nodes prefer to connect with the nodes with little influence, the connections among the influential nodes are fewer, making the network have a high average distance. However, if the connections among the influential nodes increase, the average distance will decrease, and the assortativity coefficient will increase. This indicates that monitoring the comovement behavior of the influential nodes is vital to understanding the coal market's status.

Based on the above analysis, we investigate the nodes’ influence in depth. As mentioned in the Methods section, we introduce 7 network indicators to calculate the nodes’ influence. Among them, out-degree and closeness centrality may obtain similar results, while in-degree, eigenvector centrality, and the PageRank algorithm may obtain similar results. Limited by the length of the paper, we present only the results of the out-degree, betweenness centrality, cluster coefficient, and PageRank algorithm. Moreover, to facilitate understanding, we present the influence of the coal-producing areas at the province level, and the results are shown by a heatmap in Fig. 2.

The evolution of the influence of the coal-producing areas at the province level. a The influence quantified by the out-degree; b The influence quantified by betweenness centrality; c The influence quantified by the clustering coefficient; d The influence quantified by the PageRank algorithm

From Fig. 2a–d, we found that the influence of the coal-producing provinces varies greatly in the four network indicators. The influence of the same coal-producing province also varies in different time periods. Taking Sichuan Province as an example, its clustering coefficient obtained high values during 2015–2016, its PageRank obtained high values in 2020, its out-degree obtained high values during 2014–2015, and its betweenness centrality seldom obtained a high value. The other coal-producing provinces present a similar phenomenon. This indicates that the coal-producing areas’ coal price volatility influences have strong time-varying features. Therefore, it is important to analyze the evolution of their coal price volatility influence and thereby identify the CPVSs. In this paper, we regard the influential nodes of the CPCN as the CPVSs. However, different CPVSs are identified by each network indicator. Overall, the betweenness centrality identifies Liaoning as a CPVS, the clustering coefficient identifies Zhejiang as a CPVS, the PageRank algorithm identifies Hunan and Jilin as CPVSs, and the out-degree identifies Zhejiang and Jilin as CPVSs. From the evolution perspective, the CPVSs identified by different network indicators have even larger differences. This confirms our concern that it is difficult to achieve a consensus on CPVSs. Therefore, we use the rank aggregation method to provide a more universal and comprehensive analysis of the CPVSs.

3.2 Evolution analysis of the coal price volatility spreaders

Based on the competition graph method mentioned in Sect. 2.2.3, we calculate the ratio of out- and in-degrees (ROID) to comprehensively measure a coal-producing area’s aggregate performance. Then we rank the coal-producing areas and identify the top-ranked ones as CPVSs. Considering that there are 601 CPCNs in our paper, the results of CPVSs are hard to display. Therefore, we calculate the annual average ROID (using the normalized results based on the maximum and minimum standardization method) of each coal-producing area to conduct an analysis. To clearly show the evolution trend of the coal-producing areas, we use a slope diagram to visualize the results.

In Fig. 3, only the coal-producing provinces that obtained nonzero values are counted. There were only 6 coal-producing provinces in 2010, and then it increased to 20 coal-producing provinces in 2021. This reflects that the coal market has become more interconnected in the recent decades, which corresponds to the results of Fig. 1. Therefore, coal price volatility may more easily spread through the coal market to cause system risk; identifying the CPVSs helps locate the volatility source to mitigate the risk. Overall, during 2010–2012, Hunan Province was the CPVS; during 2013–2015, Jiangxi and Chongqing Provinces were the CPVSs; during 2016–2018, Sichuan Province was the CPVS; during 2019–2021, Gansu Province was the CPVS. No coal-producing province always acts as a CPVS. This indicates that the evolution trend of the coal-producing provinces is unstable and has a significant time-varying feature. More specifically, their evolution trend can be divided into 4 types. It should be noted that Shaanxi and Guizhou Provinces seldom obtain a rank; therefore, we will not analyze them in the following text.

1. (1)

   Downward trend. In Fig. 3, Inner Mongolia, Hebei, Henan, Shandong, and Jiangsu Provinces have low or constantly declining ranks. This result is in line with reality because these provinces shifted their development focus from relying on traditional energy sources to a green economy. Furthermore, these provinces are located near the North China Plain, which plays an important role in supporting the air quality of northern China. They have enacted strict coal decapacity policies, such that their coal price volatility is low and they have less influence. In addition, Chongqing, Sichuan, and Heilongjiang Provinces originally obtained high ranks, but their influence has fallen rapidly since 2018. This result is also reasonable. Originally, Chongqing and Sichuan Provinces' coal capacity could not meet their coal consumption, causing a strong demand for coal and driving up their price volatility influence. Moreover, Heilongjiang Province produces high-quality coal products with a strong price volatility influence. However, these provinces enacted coal decapacity policies around 2018. Furthermore, they also have the advantage of resource endowment to replace coal with other clean energies, such as hydroelectric and wind power. Therefore, their ranks dropped dramatically after 2018.

2. (2)

   Rise-fall trend. Figure 3 shows that Yunnan Province’s rank constantly increased from 2012 to 2019 but declined during 2020–2021. This is because Yunnan Province has a strong demand for coal. On the one hand, Yunnan's economy used to be relatively backward; to achieve rapid development, it invested heavily in infrastructure, increasing coal consumption dramatically. On the other hand, Yunnan’s electricity supply relies on hydroelectricity, causing it to be sensitive to climate changes; i.e., it provides more electricity in the water-abundant season and less electricity in the dry season. This has led to serious electricity consumption problems while increasing the demand for coal to stabilize the electricity supply. Moreover, Yunnan is in the far south of China. Therefore, its coal price is high and has a strong price volatility influence. However, the outbreak of COVID-19 limited its demand and caused its rank to decline after 2020. Xinjiang Province’s rank also follows a rising-decreasing trend. Considering that it is rich in high-quality coal resources and has low mining costs, it has become increasingly important in keeping the coal supply secure in recent years. Therefore, the influence of its coal price volatility has increased since 2015. However, it has also been shocked by COVID-19 since 2019 and has fallen in the rankings.

3. (3)

   Fall-rise trend. Gansu, Ningxia, and Anhui Provinces’ ranks follow a fall-rise trend. Specifically, Gansu and Anhui Provinces’ ranks have increased since 2018, and Ningxia Province’s rank has increased since 2015. This is because they are important provinces supporting China's coal supply security. Among them, Gansu and Ningxia are similar to Xinjiang, which has high-quality coal resources and low mining costs; moreover, they are located closer to the provinces with strong coal demand. During the coal decapacity period since 2015, they have shown advantages in coal production. Therefore, their influence on coal price volatility has increased since 2015. Anhui is the most abundant province in terms of coal resources in East China. It needs to support the coal consumption in the Yangtze River Delta region, which is the most economically developed region in China. Especially since the US-China trade dispute, the Yangtze River Delta region experienced a has decline in overseas coal imports. Therefore, the rank of Anhui Province has increased since 2018. In addition, Zhejiang, Jiangxi, and Jilin follow a fall-rise trend. This is because they use more electricity but produce less coal, making them have strong coal demand to ensure electricity supply. Especially in the context of coal decapacity and carbon neutrality, their coal prices become more sensitive to changes in the coal market as the coal supply is tightened. Therefore, their coal price volatility influence has increased dramatically since 2018.

4. (4)

   Fluctuating trend. The evolution trend of some provinces is relatively complex and may be rise-fall-rise or fall-rise-fall. For simplicity, we categorize them as following a fluctuating trend. Their complex evolution trend is due to many endogenous and exogenous factors. Specifically, Shanxi and Liaoning are traditionally large coal-producing provinces that depend on coal for economic development, so they originally held high ranks. However, after many years of poorly planned mining, they faced unsustainable development problems, such as resource depletion, heavy pollution, and distortion of industrial structure. To solve these problems, they worked hard to reform the coal industry. In particular, China launched policies supporting coal capacity reduction and carbon neutrality. Therefore, their ranks declined. However, in recent years, COVID-19 and extreme climate changes have brought imbalances to the supply and demand in the coal market. To stabilize the coal market, the demand for coal has increased, driving an increase in the ranks of Shanxi and Liaoning. In addition, Hunan and Qinghai Provinces follow a fall-rise-fall trend. They are also influenced by exogenous factors such as energy policy, extreme socioeconomic and climate events, and endogenous factors such as unsustainable development and coal supply and demand imbalances. However, they are not large coal-producing provinces and have comparative disadvantages. Therefore, their ranks show a complex evolutionary trend.

Slope diagram of the rank aggregation’s evolution trend. The vertical lines represent the years. The coal-producing provinces are ranked according to their annual average ROID, where the top-ranked provinces are listed on the top of the vertical lines. A specific color links the ranks of a coal-producing province to visualize its evolution trend

3.3 Validation test of the proposed hybrid method

To prove the credibility of the above results, we conduct a method validity test in this section. Specifically, we conduct a comparative analysis of the proposed rank aggregation method with the 7 network-based indicators used for the rank aggregation method, where the rank aggregation method should be superior to the other 7 network-based indicators. The 7 network-based indicators are the out-degree, in-degree, eigenvector centrality, clustering coefficient, closeness centrality, betweenness centrality, and PageRank algorithm, whose abbreviations are OD, ID, EV, CC, CLN, BC, and PR. For the rank aggregation method, the abbreviation is RA.

Considering that no universal indicator measures the influence of coal price volatility, we collected 5 macroeconomic indicators that can reflect the influence of coal price volatility mentioned in Sect. 2.1. The 5 macroeconomic indicators are electricity consumption, electricity generation, coal consumption, coal generation, and coal inventory of the state-owned coal mine, whose abbreviations are EC, EG, CCS, CG, and CI. We perform a correlation analysis between each influence quantification measurement and each macroeconomic indicator. If the rank aggregation method performs better, it should have more and higher correlations to all 5 macroeconomic indicators than the other 7 network-based indicators.

More specifically, we calculate the annual average of the rank aggregation method and the 7 network-based indicators for analysis as the 5 macroeconomic indicators are annual data. The time span of the data is from 2010 to 2021, for a total of 12 years. Because this paper aims to identify the CPVSs according to the rank of the coal-producing provinces’ influence, we conduct cross-sectional regressions to calculate Kendall correlation coefficients. Considering that there are 12 years, we conduct 5*(7 + 1)*12 = 480 cross-sectional regressions. For each pair of influence quantification measurements and macroeconomic indicators, we can obtain 12 Kendall correlation coefficients. To facilitate analysis, we calculate the absolute average of Kendall correlation coefficients as a result. If an influence quantification measurement is highly correlated to a macroeconomic indicator, their absolute average Kendall correlation coefficient is high. The results are shown in Table 2.

In Table 2, we mainly analyze the Kendall correlation coefficients calculated based on the significant values (\(\left|{\tau }_{1}\right|\) and \(\left|{\tau }_{2}\right|\)) and use the Kendall correlation coefficients calculated based on the nonzero values (\(\left|{\tau }_{0}\right|\)) as assistance because they may contain biased information. It can be found that no influence quantification measurements have high correlations with all of the macroeconomic indicators. Therefore, we need to evaluate their compositive performances. Overall, the proposed AR method has better performance. On the one hand, AR has higher correlations with CG and CI. Considering that coal is scarce, the supply side dominates the coal market; thus, CG and CI can reflect the influence of the coal market’s supply side. As shown in \(\left|{\tau }_{2}\right|\), AR has the highest correlation with CG and CI. On the other hand, it has higher correlations with EC and EG. Considering that China’s coal is mostly used to generate electricity, the coal-producing provinces with more electricity consumption and generation may have stronger coal demand, which drives their coal price volatility influence. Among the influence quantification measurements, CC has the highest correlations according to \(\left|{\tau }_{0}\right|\). However, according to \(\left|{\tau }_{1}\right|\) and \(\left|{\tau }_{2}\right|\), OD has the highest correlations, and our proposed method AR performs similarly to OD. Comprehensively, AR has higher correlations with CG, CI, EC, and EG. However, it does not have a higher correlation with CCS. Among the influence quantification measurements, CC has the highest correlation with CCS, and the correlation coefficient is approximately 0.49. In comparison, the correlation coefficient of AR is approximately 0.44, which does not have a large gap of 0.49 and presents an acceptable performance. In summary, the proposed method AR achieves a better performance comprehensively, with more and higher correlations to all 5 macroeconomic indicators, which proves the credibility of our research.

This research investigates the coal price comovement of China's coal market’s supply side to identify the coal price volatility spreaders (CPVSs), which helps determine the price volatility source to prevent energy-induced system risks. We access a valuable dataset containing 938 weekly coal price time series of different coal-producing areas from 2006.9.4 to 2021.7.12 to study the evolution of CPVSs at the provincial level. We propose a hybrid method to quantify the influence of coal price volatility and rank its influence to identify CPVSs by conjointly using the transfer entropy method, complex network theory, and the rank aggregation method. The proposed method aims to achieve a more universal and comprehensive evaluation of the CPVSs. Through an empirical analysis, we obtain the following four main findings.

1. (1)

   By analyzing the coal price comovement based on network theory, the correlation pattern of China's coal market’s supply side is found to change dramatically in 2016, 2018, and 2020. On the one hand, this is caused by the reforms of China’s coal pricing mechanism. On the other hand, this is influenced by coal decapacity policies, carbon neutrality policies, and the shocks of COVID-19 and extreme climate changes. This indicates that China’s coal market is unstable and sensitive to energy policy and external shocks.

2. (2)

   By ranking the coal-producing provinces according to their coal price volatility influence, we find that the evolution trend of their ranks follows 4 types, i.e., downward, rise-fall, fall-rise, and fluctuating trends. This indicates that the evolution trend of the coal-producing provinces has uncertainties and presents a significant time-varying feature.

3. (3)

   We identify the CPVSs according to the rank of their price volatility influence. Before 2018, coal-producing provinces with strong demand for coal and electricity, e.g., Jiangxi, Chongqing, and Sichuan, were CPVSs. However, after 2019, those that have comparative advantages in coal supply, e.g., Gansu and Ningxia, were CPVSs.

4. (4)

   By conducting cross-sectional regressions between the adopted methods and 5 macroeconomic indicators that can reflect the influence of coal price volatility, we find that the proposed hybrid method has a better comprehensive performance than 7 other network indicators. This proves the validity of the method and the credibility of our research.

According to the above findings, we obtain the following policy implications. First, considering that China’s coal market is sensitive to exogenous factors, regulators should be cautious in proposing energy policies. Moreover, they should prevent the combined action of several policies (for example, a combination of energy- and environmental-induced policies) from causing overshoot effects on the coal market, especially in a context full of exogenous uncertainties. Second, policymakers and market participants are suggested to monitor and manage CPVSs to improve energy security, avoid policy-induced instability and prevent risks caused by coal price fluctuations. Specifically, we suggest paying more attention to the coal-producing provinces with strong demand for coal and electricity and the coal-producing provinces with comparative advantages in coal supply.