Quantifying Tail Risk Spillovers in Chinese Petroleum Supply Chain Enterprises: A Neural-Network-Inspired Multi-Layer Machine Learning Framework

Abstract

This study constructs a neural-network-inspired multi-layer machine learning model ($RQLNet$) to measure and analyze the effects of tail risk spillover and its associated sensitivities to macroeconomic factors among petroleum supply chain enterprises. On this basis, the study constructs a tail risk spillover network and analyzes its network-level structural features. The results show the following: (1) The proposed model improves the accuracy of tail risk measurement while addressing the issue of excessive penalization in spillover weights, offering enhanced interpretability and structural stability and making it particularly suitable for high-dimensional tail risk estimation. (2) Tail risk spillovers propagate from up- and midstream to downstream and ultimately to end enterprises. Structurally, the up- and midstream are the main sources, whereas the downstream and end enterprises are the primary recipients. (3) The tail risk sensitivities of Chinese petroleum supply chain enterprises exhibit significant differences across macroeconomic factors and across types of enterprises. Overall, the sensitivities to CIMV and LS are higher. (4) The network evolves in stages: during trade frictions, spillovers accelerate and core nodes strengthen; during public-health events, intra-community cohesion increases and cross-community spillovers decline; in the recovery phase, cross-community links resume and concentrate on core nodes; and during geopolitical conflicts, spillovers are core-dominated and cross-community transmission accelerates.

1. Introduction

As a key pillar of the global energy system, oil exerts substantial influence over macroeconomic performance and geopolitical developments [1]. As one of the most important global energy commodities, oil price volatility affects energy costs and inflation. It also generates systemic shocks across economies through trade, investment, and financial channels [2,3,4,5]. With the acceleration of the global push toward carbon neutrality and the ongoing energy transition, oil’s carbon risk profile has become more salient. Its prices and demand exhibit heightened sensitivity to green policies, climate-related shocks, and geopolitical conflicts [6,7]. Oil enterprises span exploration, production, transportation, refining, and marketing. They perform key resource-allocation functions in international energy markets and serve as a critical hub for risk transmission between the industrial supply chain and the financial system [8]. As traditional energy enterprises, these enterprises face price-volatility pressures from deepening energy financialization. Under emission constraints and the green transition, they also face uncertainty in operations and asset values [9,10]. Petroleum supply chain enterprises are vulnerable to external shocks and can significantly affect other industries under extreme scenarios [11]. Therefore, accurately measuring tail risk spillovers among petroleum supply chain enterprises is crucial. It helps elucidate risk transmission in energy markets, assess carbon-risk exposure, and safeguard industrial stability as well as financial-system security.

The current measurement approaches to tail risk spillovers can be broadly classified into three categories. First, VAR, GARCH, and their extensions are employed to characterize tail risk spillovers [12,13,14]. For instance, Bei et al. [15] employ a GARCH-Copula-CoVaR framework to examine extreme spillovers between the shipping and commodity markets. Second, traditional $CoVaR$ models based on $lasso$ regression, as well as quantile-regression approaches, are widely adopted; however, in high-dimensional settings, they are prone to estimation bias and overfitting [16,17,18]. While Chen et al. [19] incorporate machine learning methods to improve estimation accuracy, the approach may still induce excessive penalization of inter-node spillover weights. Third, deep-learning neural networks and related architectures are increasingly being used to measure tail risk spillovers; however, such approaches generally exhibit limited economic interpretability [20,21,22,23]. For example, Lu et al. [24] employ a quantile LSTM-GNN to quantify tail risk spillovers between energy and agricultural commodity markets. To address these limitations, this paper proposes a neural-network-inspired multi-layer machine learning model ($RQLNet$). The model is designed for high-dimensional tail risk measurement, preserves estimation accuracy and economic interpretability, and effectively mitigates excessive penalization. This constitutes the paper’s first contribution.

Extant research on tail risk spillovers among petroleum supply chain enterprises largely focuses on energy enterprises in the aggregate, with limited systematic exploration of the internal structure of the oil supply chain [25,26,27,28,29,30]. These studies also predominantly rely on enterprise-level log returns to measure spillover effects, while devoting limited attention to the systematic influences of both macroeconomic and micro-level factors. Although Chen et al. [19] introduced certain macro- and micro-level variables, they did not cover key factors such as geopolitical risk and crude-oil prices, which are highly salient for the oil market. There remains a lack of systematic assessment of aggregate tail risk sensitivities to macro-factors for petroleum supply chain enterprises, as well as evidence on heterogeneity across supply chain segments. Building on these gaps, this study incorporates a more comprehensive set of macro-variables to improve the precision of spillover measurement for Chinese petroleum supply chain enterprises. On this basis, this study constructs a tail risk spillover network and conducts a systematic sensitivity analysis by supply chain segment, thereby uncovering the heterogeneous responses of segment-level tail risks to macro-factors. These elements constitute this paper’s second contribution.

In summary, this study integrates the hierarchical structure of neural networks with the regularization-driven feature selection mechanism of machine learning. To address the limited economic interpretability of neural networks and the accuracy and over-penalization issues in traditional $lasso$ and machine learning approaches, this study develops $RQLNet$ to measure tail risk spillovers among petroleum supply chain enterprises and their sensitivities to macroeconomic factors. On this basis, this study constructs a tail risk spillover network and analyzes its network-level structural features. The contributions of this paper include the following: (1) The proposal of a neural-network-inspired multi-layer machine learning model, which further enhances estimation accuracy and economic interpretability in high-dimensional tail risk measurement, effectively mitigating excessive penalization and enabling more precise identification of tail risks. (2) The incorporation of macro-factors highly relevant to the oil sector—such as geopolitical risk and crude-oil prices—to improve the precision of tail risk measurement for petroleum supply chain enterprises, and, on that basis, the construction of the tail risk spillover network. (3) This study yields the following meaningful conclusions: the up- and midstream are the primary sources of risk spillovers, while the downstream and end enterprises are the main recipients within the network. Tail risk sensitivities to macro-factors exhibit significant heterogeneity across both factor dimensions and enterprise-type dimensions, and the network evolves in stages—spillovers accelerate and core nodes strengthen during trade frictions; they concentrate within communities with constrained cross-community links in the early public-health phase, followed by recovery and greater concentration toward core nodes; and they become core-dominated with faster cross-community transmission during geopolitical conflicts.

2. Model Construction

Figure 1 illustrates the overall research framework and process adopted in this study.

2.1. $CoVaR$ Estimation via a Neural-Network-Inspired Multi-Layer Machine Learning Model

The Value-at-Risk ($VaR$) model is defined as follows:

$$P(X_{i,t}\le Va{R}_{i,t,\tau }^{Tail})=\tau$$

(1)

Using quantile regression, we estimate each node’s $VaR$ from macroeconomic factors and log weekly returns. The specification is given by

$$X_{i,t}={\alpha }_i^{Tail}+{\gamma }_i^{Tail}+{\epsilon }_{i,t},\widehat{Va{R}_{i,t,\tau }^{Tail}}={\widehat{\alpha }}_i^{Tail}+{\widehat{\gamma }}_i^{Tail}{M}_{t-1}$$

(2)

where $X_{i,t}$ denotes the log weekly return of node $i$ at time $t$. Log return is calculated as $X_{i,t}=\ln p_t-\ln p_{t-1}$. $p_t$ represents the price of node $i$ at time $t$. $M_{t-1}$ denotes the macroeconomic factor observed at time $t-1$. ${\alpha }_i^{Tail}$ and ${\gamma }_i^{Tail}$ are parameters to be estimated.

The Conditional Value-at-Risk ($CoVaR$) model is defined as follows:

$$P\{X_{j,t}\le CoVa{R}_{j,t,\tau }^{Tail}|R_{j,t}\}=\tau$$

(3)

Extending the frameworks introduced in Härdle et al. [31] and Chen et al. [19], this study constructs a neural-network-based multi-layer machine learning algorithm. This algorithm estimates the $CoVaR$ and associated link functions for nodes within Chinese petroleum supply chain enterprises. The estimation equations are given by

$$X_{j,t}=g({\beta }_{j|R_j}^{{\rm T}}{R}_{j,t})+{\epsilon }_{j,t}$$

(4)

$$\widehat{{CoVaR}_{j|{\tilde{R}}_j,t,\tau }^{Tail}}=\widehat{g}({\widehat{\beta }}_{j|{\widehat{R}}_j}^{{\rm T}}{\tilde{R}}_{j,t})$$

(5)

where $R_{j,t}=\{X_{-j,t},M_{t-1},B_{j,t-1}\}$ represents the set of multivariate variables associated with the node. $X_{-j,t}=\{X_{1,t},X_{2,t},\cdots ,X_{k-1,t}\}$ denotes log returns of all other nodes except for the given node, and k − 1 is the number of these other nodes. $B_{j,t-1}$ denotes enterprise-specific characteristics of the individual node and ${\beta }_{j|R_j}={\{{\beta }_{j|-j},{\beta }_{j|M},{\beta }_{j|B_j}\}}^{{\rm T}}$ denotes the parameter set associated with the explanatory variable $R_{j,t}$. Equation (5) indicates that $CoVaR$ is influenced not only by other nodes but also by the smooth link function $g(.)$. Moreover, ${\tilde{R}}_{j,t}=\{\widehat{Va{R}_{-j,t,\tau }^{Tail}},M_{t-1},B_{j,t-1}\}$. Additionally, Figure 2 illustrates the $CoVaR$ estimation procedure built on the $RQLNet$ model proposed in this paper.

The $RQLNet$ model is designed to handle high-dimensional financial time-series data efficiently and adopts a multi-layer architecture to mitigate the excessive penalization often encountered in conventional machine learning frameworks. In contrast to traditional neural networks that focus on accurate point forecasting, the present framework centers on quantile estimation, making it especially suitable for $CoVaR$ analysis. Recent studies have demonstrated the effectiveness of these approaches in handling high-dimensional data redundancy and optimizing the structural stability of models [32,33,34]. The underlying algorithm adapts the Lasso regression of Belloni and Chernozhukov [35] and Chernozhukov et al. [36], and integrates quantile and path-tracking techniques tailored to tail risk features. The specific details are as follows:

Layer 1 combines quantile regression and path-following Lasso regularization to perform initial quantile estimation and variable selection, providing the foundation for subsequent nonlinear processing and kernel estimation in the weighting layer. In this layer, the number of paths is set to 150, and generalized cross-validation is used to ensure the optimal regularization parameter. Quantile regression utilizes the quantile loss function to accurately estimate tail risk and optimizes path selection through the path-following algorithm. Through the initial Lasso regularization, the regression coefficients for each node are assigned different weights, which provide foundational support for subsequent steps. These coefficients serve as initial weights for the kernel regression in the following weighting layer, ensuring reasonable weight distribution for each variable in the subsequent regression process, avoiding excessive penalization, and improving the model’s stability and accuracy.

Layer 2 transforms the linear quantile regression results from Layer 1 into nonlinear quantile regression to better capture the nonlinear characteristics of financial markets, especially during extreme periods such as financial crises [27].

Layer 3 performs kernel regression using the initial variable selection coefficients from Layer 1 and the nonlinear functions, assigning appropriate weights to each variable and thus providing reasonable kernel weights for the variables in the subsequent Layer 4.

Layer 4 further optimizes the model by using a path-following Lasso regularization regression with kernel weights. In this layer, the number of paths is set to 500, and the optimal path is selected using the AIC criterion. Tail risk is accurately estimated through nonlinear quantile regression and the quantile loss function. Based on this, Lasso regularization is performed using the kernel-weighted path regression coefficients, reducing over-penalization and improving the model’s accuracy and stability, thereby providing more reasonable support for the final regression results. The iteration process stops when the change in coefficients between iterations is smaller than a predefined threshold or when the maximum number of iterations is reached.

2.2. Measuring Tail Risk Spillover Effects and Constructing the Tail Risk Spillover Network

Based on Equation (5), the tail risk spillover effect is defined as follows:

$${\widehat{D}}_{j|{\tilde{R}}_j}={\displaystyle \frac{\partial \widehat{g}({\widehat{\beta }}_{j|R_j}^{{\rm T}}{R}_{j,t})}{\partial R_{j,t}}}{|}_{R_{j,t}={\tilde{R}}_{j,t}}={\widehat{g}}^{\prime }({\widehat{\beta }}_{j|{\tilde{R}}_j}^{{\rm T}}{\tilde{R}}_{j,t}){\widehat{\beta }}_{j|{\tilde{R}}_j}$$

(6)

where ${\widehat{D}}_{j|{\tilde{R}}_j}$ denotes the gradient that measures the marginal effect of covariates. ${\widehat{D}}_{j|{\tilde{R}}_j}={\{{\widehat{D}}_{j|-j},{\widehat{D}}_{j|M},{\widehat{D}}_{j|B_j}\}}^{{\rm T}}$, where ${\widehat{D}}_{j|-j}=\left\{{\widehat{D}}_{j|i}\right|1\le i\le k,i\ne j\}$ captures the risk spillover effects among nodes.

The directed weighted tail risk spillover network is constructed, with its adjacency matrix given as follows [31]:

$$A_s=\left(\begin{array}{ccccc}0& \left|{\widehat{D}}_{1|2}^s\right|& \left|{\widehat{D}}_{1|3}^s\right|& \dots & \left|{\widehat{D}}_{1|k}^s\right|\\ \left|{\widehat{D}}_{2|1}^s\right|& 0& \left|{\widehat{D}}_{2|3}^s\right|& \dots & \left|{\widehat{D}}_{2|k}^s\right|\\ \left|{\widehat{D}}_{3|1}^s\right|& \left|{\widehat{D}}_{3|2}^s\right|& 0& \dots & \left|{\widehat{D}}_{3|k}^s\right|\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ \left|{\widehat{D}}_{k|1}^s\right|& \left|{\widehat{D}}_{k|2}^s\right|& \left|{\widehat{D}}_{k|3}^s\right|& \dots & 0\end{array}\right)$$

(7)

where the $k$-order adjacency matrix $A_s$ represents the risk spillover effects among nodes in petroleum supply chain enterprises. Here, $\left|{\widehat{D}}_{1|2}^s\right|$ is the absolute value of ${\widehat{D}}_{1|2}^s$, representing the tail risk spillover weight from nodes 2 to 1. $\left|{\widehat{D}}_{2|1}^s\right|$ represents the tail risk spillover weight from nodes 1 to 2.

2.3. Network-Level Structural Metrics

At the network level, the average path length, average clustering coefficient, network density, modularity, assortativity, and degree centralization constitute key metrics for assessing overall connectedness among nodes. This study uses these metrics to characterize the tail risk spillover network among petroleum supply chain enterprises, as follows:

(1)

The average clustering coefficient captures the tendency of nodes to form cohesive local groups. Higher values reflect stronger local substructures, potentially accelerating the accumulation and spillover of tail risk.

(2)

The average path length represents the mean of the shortest paths between any two nodes. Smaller values reflect the faster propagation of tail risk spillovers across the network.

(3)

Network density measures the ratio of observed to potential links. Larger values indicate denser spillover relations.

(4)

Modularity evaluates the extent of community partitioning. Higher modularity indicates more distinct subgroups and, to some extent, constrains cross-community tail risk spillovers.

(5)

Assortativity captures the degree correlation between connected nodes. With positive assortativity, high-degree nodes tend to connect with high-degree nodes (and low with low), whereas negative assortativity implies that high-degree nodes are more likely to connect with low-degree nodes, and vice versa.

(6)

Degree centralization gauges the extent to which degrees concentrate in a few core nodes. Networks with high degree centralization are more likely to be dominated by core nodes in tail risk spillovers, whereas those with low degree centralization favor risk dispersion and structural stability.

3. Empirical Analysis

3.1. Data

The sample includes Chinese petroleum supply chain enterprises publicly traded in China’s A-share market. In selecting and classifying the enterprises, this study employs the following three criteria: (1) the GICS classification and relevant literature [19,27], which provide a framework for categorizing enterprises along the upstream, midstream, downstream, and end segments of the petroleum supply chain; (2) authoritative financial databases, including WIND, RESSET, and iFinD, which offer comprehensive and reliable information for verifying the business scope and operations of potential candidates; (3) a thorough examination of each enterprise’s core business operations, its strategic direction for future development, and its position within the supply chain. For state-owned enterprises, special attention is given to their national strategic roles and their specific mandates, which often reflect their importance in national energy security and market stability. This approach ensures that the selected enterprises are representative of the petroleum supply chain. The enterprises are categorized into four groups: oil exploration and production enterprises (upstream enterprises), oil transportation and storage enterprises (midstream enterprises), oil refining and sales enterprises (downstream enterprises), and petrochemical product enterprises (end enterprises).

The sample period spans 3 July 2015 to 31 March 2023. This horizon covers major events, including large swings in China’s financial markets starting in 2016, which significantly impacted the oil market [19]; intensified trade frictions between China and the United States beginning in 2018, which disrupted global energy markets [37]; the global public-health event (COVID-19) starting in late 2019, which led to substantial volatility in oil prices [38]; and regional geopolitical conflicts, particularly the Russia–Ukraine war beginning in 2022, which further heightened energy price instability [39]. Prior research shows that knowledge and information agglomeration within supply chain networks amplifies the propagation of external shocks across enterprises [40]. Enterprise-level data are drawn from the RESSET database; detailed enterprise information and classifications are reported in

Table 1. Enterprise (node) information and classification.

Exploration	Transportation	Refining	Petrochemical
(1) CPCC (600028)	(9) OOE(600583)	(17) RP (002493)	(25) JES(000301)
(2) CNPC (601857)	(10) CPE(600339)	(18) YYXCP (000819)	(26) SET(601208)
(3) COSL (601808)	(11) ZJJLHM(002318)	(19) NHCI (000059)	(27) GHRAP(300320)
(4) HBP (002554)	(12) GE (600256)	(20) SSP (600688)	(28) AAMT(300218)
(5) QHEC (300191)	(13) HYEG (600387)	(21) HYP(000703)	(29) STINM(300321)
(6) TPC (300164)	(14) SIC (600500)	(22) MPS(000637)	(30) JYFT(300305)
(7) XJZDPTC (002207)	(15) SSCG (002469)	(23) DQHK(000985)	(31) JSSFPM(600370)
(8) ZJRZ (002629)	(16) HZOPG (002430)	(24) SSTP (000554)	(32) HFC(002064)

Note(s): The format is enterprise number, English abbreviation, stock code.

.

The selection of internal characteristic variables for petroleum supply chain enterprises follows Naeem et al. [41]. This study includes total assets (SIZE) to reflect enterprise size, the market-to-book ratio (MTB) to capture growth potential, the leverage ratio (LEV) to represent capital structure, and maturity mismatch (MM) to proxy liquidity risk. Variable definitions and descriptions are provided in

Table 2. Microeconomic factors.

Intra-Enterprise Characteristic Variables	A Concrete Explanation
Total assets (SIZE)	Total assets on firm financial statements
Market-to-book ratio (MTB)	Market price of shares/net assets value per share
Maturity mismatch (MM)	(Current liabilities—current assets)/total liabilities
Leverage (LEV)	Total assets/total equity

; data are sourced from the RESSET database.

Following Gong et al. [42], this study selects macro-variables spanning financial markets, energy markets, and geopolitics. In addition, this study incorporates indicators that reflect changes in government economic, financial, and monetary policies to more comprehensively characterize the external environment shaping tail risk spillovers among petroleum supply chain enterprises. Definitions and sources are summarized in

Table 3. Macroeconomic factors.

Macro-State Variables (M)	A Concrete Explanation
China implied volatility index (CIMV)	Calculated from the VIX algorithm
Chinese crude-oil futures return (OIL)	Weekly log return of crude-oil futures traded on the Shanghai Futures Exchange
China geopolitical risk index (GPR)	Constructed following Caldara et al. [43]
Oil market macro-yield (WI)	Weekly returns for oil, gas, and fuels for consumption (Full Return Index)
Term spread (YS)	Yield to maturity on 10-year Treasury bonds minus yield to maturity on 6-month Treasury bonds
Liquidity spread (LS)	March interbank offered rate minus March Treasury yield to maturity rate
Chemical firm index return (CR)	SSE chemical firm weekly returns
Credit spread (CS)	Difference between the yield to maturity on 10-year Treasury bonds and the yield to maturity on 10-year AAA corporate bonds
China economic policy uncertainty index (EPU)	Constructed following Baker, Bloom, and Davis [44] and extended by Huang and Luk [45]

. Specifically, CIMV comes from the PBC School of Finance, Tsinghua University, and is drawn from the RESSET database; WI is taken from the Wind database; YS and LS are provided by the Ministry of Finance of the People’s Republic of China together with the China Foreign Exchange Trade System; OIL is from the Shanghai International Energy Exchange; and EPU index is obtained from the Federal Reserve Bank of St. Louis (FRED) database.

3.2. Comparative Analysis of Competing Models

Figure 3 compares measurements of five models of tail risk ($CoVaR$). A large body of research [46,47,48] uses Quantile Vector Autoregression (QVAR) to identify tail risk spillovers; however, QVAR is mainly suited to low-dimensional settings, and its estimation stability and coverage decline markedly in high-dimensional environments, as also seen in Figure 3. To alleviate high dimensionality, many studies [49,50,51] introduce Lasso with quantile regression to induce sparsity and enhance interpretability, yet Figure 3 shows that its calibration for tail risk measurement in high dimensions remains insufficient. By contrast, the Gradient Boosting Machine combined with quantile regression achieves higher point accuracy than the preceding two, but when tail sparsity, conditional heteroskedasticity, and temporal dependence coexist, the tree model’s high variance and piecewise, discontinuous approximation more readily lead to an overshoot of conditional quantiles, so the estimated tail risk exceeds the realized level and $CoVaR$ violations occur [52]. In comparison, the machine learning model integrating quantile regression proposed by Chen et al. [19] ($ML$) markedly improves accuracy in high-dimensional samples and reduces overfitting, albeit with some shrinkage in spillover weights. Building on these developments, the $RQLNet$ proposed in this paper further raises overall measurement accuracy—especially achieving a closer fit to realized returns in non-tail periods—while effectively avoiding excessive penalization of spillover weights, thereby attaining a better trade-off between accuracy and structural robustness.

Table 4. Statistical assessment of $CoVaR$ estimates based on five models.

Model	Mean Pinball Loss	Mean Pinball Loss 95% CI (Low–High)	Christoffersen Stat	Christoffersen p-Value
RQLNet	0.00103	(0.00091–0.00114)	0.05233	0.81906
lasso	0.01416	(0.01161–0.01670)	21.41423	0
ML	0.00162	(0.00140–0.00183)	0.45638	0.49932
GBM	0.00305	(0.00219–0.00392)	0.47848	0.48911
QVAR	0.07144	(0.05730–0.08558)	3.53833	0.05997

reports the statistical evaluation of $CoVaR$ estimates across the five models. Following the visual comparison in Figure 3, the $ML$ model and our $RQLNet$ rank highest in measurement accuracy; moreover, Table 4 shows that $RQLNet$ attains the lowest mean pinball loss and passes the Christoffersen conditional-coverage test [53].

Table 5. Statistical evaluation of $CoVaR$ measures across quantile levels for the $RQLNet$ model.

Quantile-Level Pair	Pearson Correlation Coefficient	Two-Sided p-Value	Significance
0.05–0.03	0.94716	6.24952 × 10−173	***
0.05–0.01	0.9278	3.21060 × 10−150	***
0.03–0.01	0.97535	3.81145 ×10−229	***

Node(s): p < 0.01, significance = ‘***’; p < 0.05, significance = ‘**’; p < 0.1, significance = ‘*’.

examines robustness under small changes in the quantile level, and the results indicate that $RQLNet$ delivers high Pearson correlations with extremely small two-sided p-values, demonstrating strong stability against quantile perturbations.

Figure 4a,b compare the spillover weights between nodes for the $ML$ model and the proposed $RQLNet$ model at a selected point in time. Compared to traditional $ML$ models, the proposed $RQLNet$ model achieves accurate $CoVaR$ estimation without sacrificing tail risk spillover weights. Moreover, it significantly reduces excessive penalization, yielding a more reasonable and structurally robust spillover network.

Figure 5 illustrates the aggregated spillover weights during the sample period. The $ML$ model exhibits noticeable excessive penalization, with some nodes showing zero spillover weights throughout the period. By contrast, the $RQLNet$ model significantly mitigates this issue by effectively preserving spillover weights between nodes and more comprehensively capturing the structural characteristics of the tail risk spillover network.

3.3. Analysis of Tail Risk Spillover Effects and Their Sensitivities to Macroeconomic Factors

Table 6. Ranking of tail risk spillover targets by intensity for all enterprises.

Node	Top 3 Spillover Targets	Node	Top 3 Spillover Targets
CPCC	CNPC > SSP > STINM	RP	HZOPG > HYP > JES
CNPC	GHRAP > CPCC > STINM	YYXCP	DQHK > ZJRZ > HZOPG
COSL	OOE > QHEC > HYEG	NHCI	ZJRZ > MPS > RP
HBP	TPC > DQHK > QHEC	SSP	NHCI > COSL > CPCC
QHEC	SSCG > SSTP > TPC	HYP	RP > JES > JYFT
TPC	XJZDPTC > HBP > ZJRZ	MPS	ZJRZ > JYFT > YYXCP
XJZDPTC	TPC > ZJRZ > MPS	DQHK	YYXCP > ZJRZ > SSTP
ZJRZ	YYXCP > SSTP > HFC	SSTP	ZJRZ > QHEC > DQHK
OOE	COSL > ZJJLHM > ZJRZ	JES	XJZDPTC > RP > DQHK
CPE	AAMT > MPS > SET	SET	GHRAP > AAMT > MPS
ZJJLHM	JES > MPS > ZJRZ	GHRAP	SSCG > YYXCP > SET
GE	MPS > JES > SSCG	AAMT	JYFT > STINM > GHRAP
HYEG	ZJRZ > MPS > HYP	STINM	AAMT > JYFT > JSSFPM
SIC	YYXCP > MPS > JES	JYFT	STINM > ZJJLHM > AAMT
SSCG	ZJRZ > STINM > JYFT	JSSFPM	JES > AAMT > DQHK
HZOPG	MPS > RP > XJZDPTC	HFC	ZJRZ > RP > JSSFPM

reports, for each enterprise, the top three spillover targets ranked by tail risk spillover intensity during the sample period. The ranking reveals the principal directions and structural characteristics of tail risk spillovers across enterprise categories within the network. The main findings are as follows:

First, upstream enterprises: The main directions of tail risk spillover intensity remain concentrated on downstream and end enterprises, while intra-upstream spillovers persist at the selected nodes. Overall, upstream spillovers are dominated by vertical diffusion toward downstream and end enterprises, accompanied by a small degree of spillovers to midstream enterprises. A typical case is the bidirectional spillover relation between CPCC and CNPC.

Second, midstream enterprises: Tail risk spillover intensity is predominantly cross-category, pointing mainly to downstream and end enterprises, while retaining bidirectional spillover paths with upstream enterprises. Overall, midstream enterprises continue to serve as a bridge in the supply chain, transmitting risks from the resource end to the processing and terminal stages.

Third, downstream enterprises: Tail risk spillover intensity is strong within downstream enterprises themselves and extends visibly to end enterprises, accompanied by selective reverse spillovers toward upstream enterprises in the updated ranking. Overall, downstream enterprises form within-category cyclic spillovers while extending to end enterprises, whereas spillover paths to upstream enterprises appear at a limited set of nodes.

Finally, end enterprises: Tail risk spillover intensity first concentrates within same-category end enterprises, extends to downstream enterprises, and, to some extent, traces back to up- and midstream enterprises. Overall, the main spillover directions are toward same-category end enterprises and downstream enterprises, accompanied by a small number of spillover paths to up- and midstream enterprises.

Table 7. Ranking of tail risk acceptance sources by intensity for all enterprises.

Node	Top 3 Acceptance Source	Node	Top 3 Acceptance Source
CPCC	CPE > COSL > HZOPG	RP	HZOPG > HYP > JES
CNPC	CPCC > SSTP > COSL	YYXCP	SIC > DQHK > ZJRZ
COSL	OOE > QHEC > HBP	NHCI	SSP > YYXCP > HBP
HBP	TPC > QHEC > ZJRZ	SSP	SSTP > CPCC > COSL
QHEC	HBP > COSL > TPC	HYP	RP > HYEG > QHEC
TPC	HBP > XJZDPTC > QHEC	MPS	HZOPG > XJZDPTC > CPE
XJZDPTC	TPC > HBP > JES	DQHK	YYXCP > HBP > ZJRZ
ZJRZ	TPC > SSTP > XJZDPTC	SSTP	QHEC > ZJRZ > DQHK
OOE	COSL > TPC > CPE	JES	HBP > JSSFPM > RP
CPE	HBP > TPC > JES	SET	CPE > GHRAP > STINM
ZJJLHM	STINM > JYFT > ZJRZ	GHRAP	STINM > AAMT > SET
GE	SET > HBP > JES	AAMT	STINM > CPE > JSSFPM
HYEG	ZJRZ > SSTP > COSL	STINM	JYFT > AAMT > TPC
SIC	YYXCP > AAMT > SSCG	JYFT	STINM > AAMT > HYP
SSCG	QHEC > ZJRZ > STINM	JSSFPM	STINM > DQHK > HYP
HZOPG	RP > YYXCP > STINM	HFC	ZJRZ > JSSFPM > RP

reports, for each enterprise, the top three sources by tail risk acceptance intensity during the sample period. This ranking highlights the principal directions and structural characteristics of risk acceptance across different categories of enterprises within the tail risk spillover network. The main findings are as follows:

First, upstream enterprises: Sources of tail risk acceptance intensity concentrate within same-category upstream enterprises, followed by mid- and downstream enterprises. Overall, the resource stage forms a strong internal chain of risk acceptance, while some nodes accept tail risk spillovers from mid- and downstream enterprises. A representative case is TPC, whose primary sources are HBP, XJZDPTC, and QHEC, indicating dense intra-upstream acceptance among core upstream nodes.

Second, midstream enterprises: Sources are predominantly cross-category, coming mainly from up- and downstream enterprises, and retaining reverse spillovers from end enterprises. Overall, the midstream serves as a bridge within the supply chain, accepting tail risk spillovers from upstream and reverse spillovers from downstream. A representative case is CPE, whose sources are dominated by upstream nodes such as HBP and TPC, reflecting close risk linkages with the resource stage at the transportation segment.

Third, downstream enterprises: Sources of tail risk acceptance intensity are strong within same-category downstream enterprises, and also come from up- and midstream enterprises; some nodes accept spillovers from end enterprises. Overall, the downstream forms a within-category network of risk acceptance in the processing stage and concentrates acceptance from upstream segments. A representative case is RP, whose primary sources are HZOPG and HYP, indicating sustained linkages to the midstream while preserving strong within-downstream connections.

Finally, end enterprises: Sources of tail risk acceptance intensity first concentrate within same-category end enterprises, come from downstream enterprises, and, finally, come from up- and midstream enterprises at some nodes. Overall, end enterprises form a strong internal network of risk acceptance in the terminal stage and accept spillover inputs from earlier segments of the supply chain. A representative case is STINM, whose primary sources are JYFT and AAMT, evidencing dense risk acceptance relationships among end enterprises.

For each enterprise acting as an intermediate node along tail risk spillover paths,

Table 8. Ranking of top three intermediary spillover targets by number for intermediate nodes in tail risk spillover paths.

Node	Top Three Spillover Targets	Node	Top Three Spillover Targets
CPCC	CNPC > SSP > RP	RP	JES > HZOPG > HYP
CNPC	CPCC > SSTP > STINM	YYXCP	DQHK > QHEC > JYFT
COSL	OOE > QHEC > SSP	NHCI	HZOPG > SSP > XJZDPTC
HBP	TPC > JES > QHEC	SSP	CPCC > JYFT > COSL
QHEC	TPC > ZJJLHM > SSTP	HYP	RP > JES > TPC
TPC	HBP > XJZDPTC > QHEC	MPS	HYEG > XJZDPTC > CPCC
XJZDPTC	TPC > SSCG > HBP	DQHK	YYXCP > SSTP > HBP
ZJRZ	YYXCP > ZJJLHM > SSCG	SSTP	ZJRZ > QHEC > TPC
OOE	COSL > ZJJLHM > TPC	JES	RP > XJZDPTC > GE
CPE	HZOPG > HYEG > OOE	SET	GHRAP > JES > GE
ZJJLHM	JSSFPM > JES > HZOPG	GHRAP	ZJRZ > JYFT > SET
GE	SSTP > HZOPG > JES	AAMT	SET > SSCG > DQHK
HYEG	HBP > ZJRZ > MPS	STINM	TPC > QHEC > ZJRZ
SIC	SSTP > NHCI > JES	JYFT	STINM > HFC > DQHK
SSCG	ZJRZ > QHEC > STINM	JSSFPM	AAMT > DQHK > ZJJLHM
HZOPG	ZJRZ > RP > XJZDPTC	HFC	AAMT > ZJRZ > RP

and

Table 9. Ranking of top three intermediary acceptance sources by number for intermediate nodes in tail risk spillover paths.

Node	Top Three Acceptance Sources	Node	Top Three Acceptance Sources
CPCC	QHEC > DQHK > XJZDPTC	RP	HYP > HZOPG > HFC
CNPC	GHRAP > ZJJLHM > STINM	YYXCP	ZJRZ > GHRAP > SIC
COSL	OOE > CPE > SSP	NHCI	HYEG > SSP > SET
HBP	TPC > CPE > COSL	SSP	SSTP > JSSFPM > HYEG
QHEC	HBP > TPC > COSL	HYP	HYEG > RP > QHEC
TPC	HBP > STINM > XJZDPTC	MPS	HZOPG > CPE > HYEG
XJZDPTC	TPC > MPS > JES	DQHK	YYXCP > JES > HBP
ZJRZ	HYEG > DQHK > HZOPG	SSTP	DQHK > SIC > HBP
OOE	COSL > CPE > GE	JES	RP > GE > HYP
CPE	HBP > TPC > GHRAP	SET	AAMT > GHRAP > JSSFPM
ZJJLHM	ZJRZ > QHEC > HZOPG	GHRAP	JES > HYEG > NHCI
GE	CPE > JSSFPM > SET	AAMT	CPE > JSSFPM > STINM
HYEG	MPS > HYP > COSL	STINM	SSCG > JYFT > HYEG
SIC	SSP > JES > NHCI	JYFT	JES > ZJJLHM > GHRAP
SSCG	ZJJLHM > JYFT > AAMT	JSSFPM	ZJJLHM > DQHK > HYEG
HZOPG	NHCI > RP > CPE	HFC	NHCI > JSSFPM > ZJJLHM

summarize the top three spillover targets by count and the top three acceptance sources by count. Taken together, these rankings indicate where intermediary nodes predominantly absorb tail risk inputs and where they subsequently route them within the supply chain network.

First, upstream enterprises: As intermediary nodes, upstream firms primarily accept inputs from upstream peers, supplemented by mid- and downstream sources; they route spillovers chiefly toward the mid- and downstream while retaining intra-upstream channels. A representative case is QHEC, which accepts from HBP, TPC, and COSL and routes to TPC, ZJJLHM, and SSTP.

Second, midstream enterprises: Midstream intermediaries absorb spillovers cross-category, mainly from up- and downstream, with selected end inputs, and relay them both upward and downward, consistent with a bridge role. For example, HZOPG accepts from NHCI, RP, and CPE and routes to ZJRZ, XJZDPTC, and RP.

Third, downstream enterprises: Downstream intermediaries receive substantial inputs within the downstream segment, alongside material inflows from midstream, and transmit onward to the end and midstream while maintaining within-downstream circulation. A representative case is RP, which accepts from HYP, HZOPG, and HFC and routes to JES, HZOPG, and HYP.

Finally, end enterprises: End-segment intermediaries first accept from same-category end firms, followed by mid- and downstream sources, and route primarily within the end segment and toward the downstream, with limited paths back to the upstream. For instance, JYFT accepts from JES, ZJJLHM, and GHRAP and routes to STINM, HFC, and DQHK.

Figure 6 and

Table 10. T-test results for network-level tail risk sensitivities to macroeconomic factors.

Comparison	Statistic	p-Value	Significance	Comparison	Statistic	p-Value	Significance
CIMV vs. LS	4.39484	1.29375 × 10−5	***	LS vs. GPRD	−0.19113	0.848485
CIMV vs. OIL	8.94413	3.40046 × 10−18	***	LS vs. EPU	1.10074	0.27141
CIMV vs. GPRD	3.45090	5.93302 × 10−4	***	OIL vs. GPRD	−4.67188	3.61378 × 10−6	***
CIMV vs. EPU	4.85238	1.50780 × 10−6	***	OIL vs. EPU	−3.79086	1.63308 × 10−4	***
LS vs. OIL	5.51952	4.86362 × 10−8	***	GPRD vs. EPU	1.08519	0.27821

Node(s): p < 0.01, significance = ‘***’; p < 0.05, significance = ‘**’; p < 0.1, significance = ‘*’.

document significant cross-factor differences in the network-level tail risk sensitivities of Chinese petroleum supply chain enterprises. Pairwise tests show that sensitivities to CIMV are statistically higher than those to LS, OIL, GPR, and EPU; LS exceeds OIL but is not statistically different from GPR or EPU; OIL is significantly lower than GPR and EPU; and GPR and EPU do not differ significantly. CIMV dominates, LS is second-order but persistent, while OIL is weaker and more state-contingent; and GPR and EPU are material and often co-move. This result contrasts with existing studies emphasizing crude oil price fluctuations and geopolitical disturbances as key drivers of tail risks in oil enterprises [54,55].

First, 2018: Trade frictions accompanied by pronounced volatility in China’s financial markets. Tail risk sensitivities to CIMV and LS rise the most, consistent with elevated option-implied volatility and tighter domestic funding conditions. GPR and EPU also strengthen as uncertainty surrounding external relations and policy calibration increases, whereas the OIL channel remains comparatively contained, reflecting China’s importer position and partial policy buffers that dampen the price pass-through to listed firms.

Second, early 2020: Public-health shock. Sensitivities tilt toward CIMV—reflecting a volatility surge—while LS remains elevated amid precautionary liquidity demand; cross-community diffusion weakens and local clustering rises. OIL becomes comparatively muted as demand compression and inventory/administrative adjustments dominate the commodity channel. GPR and EPU are present but do not exceed the volatility–liquidity channels during the initial shock phase.

Third, 2021: Post-pandemic recovery. With demand normalization, the OIL factor strengthens and narrows its gap with LS, though CIMV remains the leading driver. Episodic increases in EPU accompany regulatory recalibrations, while GPR contributes intermittently. Shorter average spillover paths and higher clustering are consistent with a re-connected network in which commodity and volatility channels jointly transmit tail risks.

Fourth, 2022: Regional geopolitical conflict. Sensitivities to GPR and EPU rise markedly, and CIMV remains high; the OIL channel also intensifies with supply risk and price spikes, yet on average remains below GPR with EPU. Elevated degree centralization and low modularity indicate accelerated cross-community spillovers under core-node dominance, with geopolitical/policy uncertainty and market-volatility channels jointly amplifying tail risk transmission.

Figure 7 and

Table 11. T-test results for tail risk sensitivities to macroeconomic factors across four types of enterprises.

Comparison	Statistic	p-Value	Significance	Comparison	Statistic	p-Value	Significance
Exploration–Transportation (CIMV)	−1.95757	0.05068	*	Transportation–Refining (CIMV)	0.25384	0.79969
Exploration–Refining (CIMV)	−1.82282	0.06876	*	Transportation–Petrochemical (CIMV)	−2.20149	0.02803	**
Exploration–Petrochemical (CIMV)	−4.17484	3.37337 × 10−5	***	Refining–Petrochemical (CIMV)	−2.56816	0.01044	**
Exploration–Transportation (LS)	1.26905	0.20487		Transportation–Refining (LS)	1.69495	0.09053	*
Exploration–Refining (LS)	2.72236	0.00665	***	Transportation–Petrochemical (LS)	4.31011	1.88308 × 10−5	***
Exploration–Petrochemical (LS)	4.94328	1.01539 × 10−6	***	Refining–Petrochemical (LS)	2.44645	0.01468	**
Exploration–Transportation (OIL)	−1.99939	0.04595	**	Transportation–Refining (OIL)	−3.85917	1.25163 × 10−4	***
Exploration–Refining (OIL)	−5.54355	4.30165 × 10−8	***	Transportation–Petrochemical (OIL)	−3.52300	4.56410 × 10−4	***
Exploration–Petrochemical (OIL)	−5.23148	2.26088 × 10−7	***	Refining–Petrochemical (OIL)	0.34247	0.73209
Exploration–Transportation (GPR)	−0.72417	0.46920		Transportation–Refining (GPR)	−4.96557	8.76225 × 10−7	***
Exploration–Refining (GPR)	−5.55705	3.99297 × 10−8	***	Transportation–Petrochemical (GPR)	−3.58337	3.66999 × 10−4	***
Exploration–Petrochemical (GPR)	−4.12261	4.27329 × 10−5	***	Refining–Petrochemical (GPR)	0.77228	0.44021
Exploration–Transportation (EPU)	−4.95614	9.36660 × 10−7	***	Transportation–Refining (EPU)	−5.08178	4.91907 × 10−7	***
Exploration–Refining (EPU)	−9.60548	3.63996 × 10−20	***	Transportation–Petrochemical (EPU)	−3.04850	0.00239	***
Exploration–Petrochemical (EPU)	−7.21224	2.08910 × 10−12	***	Refining–Petrochemical (EPU)	1.69773	0.09000	*

Node(s): p < 0.01, significance = ‘***’; p < 0.05, significance = ‘**’; p < 0.1, significance = ‘*’.

indicate significant differences in tail risk sensitivities to macroeconomic factors among different types of petroleum supply chain enterprises.

First, 2018: Trade frictions accompanied by pronounced volatility in China’s financial markets. Tail risk sensitivities to CIMV and LS rise across the network. This increase is most visible for end and downstream enterprises in the CIMV and GPR/EPU dimensions—consistent with headline-risk exposure and demand-side uncertainty—whereas the up- and midstream exhibit stronger sensitivity to LS, reflecting tighter funding conditions in China. The OIL channel remains comparatively contained for all four categories.

Second, early 2020: Public-health shock. Sensitivities tilt toward CIMV, and LS remains elevated. The up- and midstream maintain higher sensitivity to LS than the downstream and end, while OIL weakens for all categories as demand compression and inventory adjustments dampen the commodity channel. GPR and EPU are present but remain below the volatility–liquidity channels during the initial shock.

Third, 2021: Post-pandemic recovery. With demand normalization, sensitivity to OIL strengthens especially in downstream and end enterprises, narrowing its gap with LS, while CIMV continues to lead. Episodic increases in EPU are concentrated in the downstream and end segments. Table 11 is consistent with these patterns: OIL sensitivities are significantly higher in the downstream and end than in the up- and midstream.

Fourth, 2022: Regional geopolitical conflict. Sensitivities to GPR and EPU rise markedly, with the downstream and end registering the largest responses. CIMV remains high for all categories, and OIL intensifies, again mostly in the downstream and end. By contrast, LS remains stronger in the up- and midstream, in line with the pairwise results showing higher LS sensitivities for those categories. These patterns indicate that, under core-node dominance, geopolitical and policy-uncertainty channels together with market-volatility transmit tail risks broadly across the supply chain tiers in China.

3.4. Network-Level Structural Analysis of Tail Risk Spillovers

Figure 8 reports the network-level metrics of the tail risk spillover network among Chinese petroleum supply chain enterprises over the sample period. The detailed evidence is as follows:

First, 2018: Trade frictions accompanied by pronounced volatility in China’s financial markets. Network density and the average clustering coefficient rose jointly, while the average path length remained relatively short. These patterns indicate more spillover paths, tighter local ties, and shorter spillover routes. Assortativity remained negative, implying frequent spillovers from core nodes to peripheral nodes. Modularity was moderate to episodically elevated, and degree centralization increased without sustained concentration. Overall, spillover paths multiplied and tail risk spillovers accelerated, forming a core-to-periphery structure. Cross-community paths remained open, and under core-node dominance, the network retained some capacity for diversified risk absorption.

Second, early 2020: Public-health shock. Network density declined and the average path length increased, whereas the average clustering coefficient and modularity remained elevated. This configuration indicates stronger intra-community cohesion and weaker cross-community spillovers. Assortativity moved from near-zero back to negative with small magnitude; degree centralization showed episodic upticks but no persistent escalation. Overall, tail risk spillovers concentrated within local communities, cross-community spillovers were constrained, and the overall connectivity of spillovers declined.

Third, 2021: Post-pandemic recovery. Network density and the average clustering coefficient rebounded and remained relatively high, while the average path length shortened markedly. Modularity declined, assortativity remained negative, and degree centralization reached temporary highs. Overall, cross-community spillover paths reconnected and spillover efficiency recovered. The core–periphery structure remained stable, with spillovers further concentrated in a few core nodes.

Fourth, 2022: Regional geopolitical conflict. Network density remained high; the average path length was on average shorter, albeit volatile; and modularity was low. Assortativity was negative and stable, while degree centralization rose significantly. Overall, spillover paths became more core-dominated, and cross-community spillovers accelerated and broadened in scope. Core nodes centrally bore and transmitted tail risks from many nodes, producing a concentrated exposure pattern with high dependence.

Figure 9 indicates the tail risk spillover network structure derived from the $RQLNet$ model. The results indicate that this model identifies spillover directions and intensities, whose distribution across distinct categories of petroleum supply chain enterprises closely corresponds to the empirical patterns documented in Chen et al. [19]. This demonstrates that the model effectively resolves the excessive penalization problem associated with traditional $CoVaR$ estimation methods. While maintaining estimation accuracy, the model also captures a more realistic spillover mechanism of tail risk among nodes, highlighting its robustness and methodological rigor.

3.5. Data Validation

Table 12. Robustness tests of log returns for all enterprises (nodes).

Node	ADF Statistic	p-Value	Conclusion	Node	ADF Statistic	p-Value	Conclusion
CPCC	−8.78779	0.01	Stationary	RP	−8.00738	0.01	Stationary
CNPC	−9.41773	0.01	Stationary	YYXCP	−8.68618	0.01	Stationary
COSL	−8.44555	0.01	Stationary	NHCI	−8.30375	0.01	Stationary
HBP	−8.81947	0.01	Stationary	SSP	−9.30011	0.01	Stationary
QHEC	−7.52207	0.01	Stationary	HYP	−8.66639	0.01	Stationary
TPC	−8.21989	0.01	Stationary	MPS	−8.68147	0.01	Stationary
XJZDPTC	−7.26603	0.01	Stationary	DQHK	−9.95472	0.01	Stationary
ZJRZ	−8.69848	0.01	Stationary	SSTP	−8.71814	0.01	Stationary
OOE	−7.94459	0.01	Stationary	JES	−7.51487	0.01	Stationary
CPE	−8.01611	0.01	Stationary	SET	−7.84043	0.01	Stationary
ZJJLHM	−8.38214	0.01	Stationary	GHRAP	−8.05384	0.01	Stationary
GE	−7.89440	0.01	Stationary	AAMT	−7.73304	0.01	Stationary
HYEG	−8.64128	0.01	Stationary	STINM	−8.03354	0.01	Stationary
SIC	−8.87732	0.01	Stationary	JYFT	−8.19052	0.01	Stationary
SSCG	−8.62344	0.01	Stationary	JSSFPM	−7.47226	0.01	Stationary
HZOPG	−7.78242	0.01	Stationary	HFC	−8.63309	0.01	Stationary

Node(s): p < 0.05 = Stationary.

reports the ADF unit-root test results for the log-return series of each node (enterprise) in the Chinese petroleum supply chain. All series refute the unit-root null at the 1% significance level; the ADF statistics range from −9.95 to −7.27, indicating stationarity. This stationarity provides the necessary precondition for subsequent tail risk spillover measurement and network construction. Methodologically, the ADF test is a classical tool for assessing stationarity in financial time-series and is widely used in empirical energy-finance research [56].

Table 13. Distributional characteristics of log returns for all nodes.

Node	Skewness	Kurtosis	Node	Skewness	Kurtosis
CPCC	0.04369	4.14728	RP	0.37958	4.27340
CNPC	0.41836	5.03359	YYXCP	0.19951	4.17136
COSL	0.15752	4.45500	NHCI	−0.27604	3.86351
HBP	0.21164	4.49154	SSP	0.53951	5.52913
QHEC	1.27034	8.27444	HYP	−0.14542	3.29013
TPC	−0.18948	3.94094	MPS	0.36872	3.8083
XJZDPTC	0.27202	4.77516	DQHK	0.33623	4.66559
ZJRZ	0.45627	5.62533	SSTP	−0.21684	4.30000
OOE	−0.35904	4.79589	JES	0.43088	5.64143
CPE	0.40018	4.71072	SET	−0.01044	3.81477
ZJJLHM	−0.1418	4.14639	GHRAP	−0.06489	4.58036
GE	0.31493	4.55317	AAMT	0.00255	4.07500
HYEG	−0.34601	4.02324	STINM	−0.46136	4.64365
SIC	−0.49671	5.17934	JYFT	0.13895	4.84106
SSCG	−0.07371	4.37548	JSSFPM	0.19930	5.55749
HZOPG	0.15100	3.43068	HFC	−0.16906	3.91033

reports the skewness and kurtosis of node-level returns for Chinese petroleum supply chain enterprises, which capture the asymmetry and tail heaviness of the log-return distribution. All nodes exhibit kurtosis above 3, indicating pronounced leptokurtosis and heavy tails. Skewness is two-sided across nodes—some are right-skewed and others are left-skewed—with a few nodes approximately symmetric. These characteristics indicate clear departures from normality and an elevated probability of tail events. Accordingly, tail-oriented risk measures provide a solid statistical foundation for this study. Identifying tail risk spillovers within a quantile framework enables a more accurate characterization of risk intensity and direction under extreme states, thereby providing a robust foundation for constructing the tail risk spillover network.

Figure 10 presents Q–Q plots of log returns for CPCC, CNPC, COSL, and QHEC to assess deviations from the theoretical normal distribution. The mid-quantiles broadly align with the reference line, while both tails bend away: the lower tail deviates downward and the upper tail upward, revealing pronounced asymmetry and heavy tails. This visual evidence corroborates the statistical findings in Table 9 and further indicates that the standard normal assumption is inadequate for capturing extreme risks in the oil market.

4. Conclusions

This study uses A-share listed Chinese petroleum supply chain enterprises from 2015 to 2023 as the sample. Incorporating micro- and macro-factors, we build the $RQLNet$ model to measure tail risk spillovers at the enterprise level and their sensitivities to macroeconomic factors. On this basis, we construct the tail risk spillover network and analyze its network-level structural features. The conclusions are as follows:

(1)

The proposed $RQLNet$ model improves tail risk estimation accuracy and enhances risk identification during non-tail states. Compared with traditional methods, this model alleviates excessive penalization of spillover weights. It also provides stronger economic interpretability and structural stability, particularly suitable for high-dimensional tail risk measurement.

(2)

Tail risk spillovers generally propagate from up- and midstream to downstream and ultimately to end enterprises. Reverse spillovers are limited in scope. Upstream enterprises direct outgoing spillovers mainly to down- and midstream enterprises, with occasional links to end enterprises, while risk acceptance is predominantly intra-category. Midstream enterprises direct outgoing spillovers chiefly to downstream enterprises, while also routing to the upstream and, at a limited set of nodes, to end enterprises; risk acceptance comes mainly from up- and downstream enterprises. Downstream enterprises exhibit strong within-category spillovers that extend to the end and midstream enterprises; their risk acceptance is primarily within the category and from up- and midstream enterprises. End enterprises direct outgoing spillovers mainly within the category and to downstream enterprises; their risk acceptance is primarily within the category, with a non-trivial share originating from mid- and downstream enterprises. Structurally, the up- and midstream are the principal sources, whereas the downstream and end enterprises are the principal recipients.

(3)

Tail risk sensitivities of Chinese petroleum supply chain enterprises differ significantly across macroeconomic factors, generally showing higher sensitivity toward China’s financial market fluctuations and liquidity tightening. Meanwhile, tail risk sensitivities also vary distinctly across enterprise types. Downstream and end enterprises display elevated sensitivities to financial-policy conditions and market signals, and they respond materially to GPR and EPU in major shock episodes. Upstream enterprises are more sensitive to LS than to OIL, and oil-price shocks raise their tail risk in an episodic rather than persistent manner. Midstream enterprises remain relatively less sensitive in most periods, with a stronger response to LS and material increases only when logistics are severely disrupted.

(4)

The tail risk spillover network of Chinese petroleum supply chain enterprises exhibits stage-wise dynamics over the sample period. During trade frictions, spillover paths increase and propagation accelerates, core-to-periphery spillovers strengthen, while cross-community spillovers remain accessible. In the early phase of public-health events, spillovers concentrate within local communities, cross-community spillovers are constrained, and overall reachability declines. In the subsequent phase, cross-community links recover, spillover efficiency improves, and tail risk spillovers become further concentrated in a few core nodes. During geopolitical conflicts, spillovers are core-dominated, cross-community spillovers accelerate and broaden in coverage, and the network exhibits heightened dependence on core nodes.

This study constructs the $RQLNet$ model to improve the accuracy of tail risk estimation and optimize the excessive penalization issue in spillover weights. However, this study faces limitations due to the reliance on cross-sectional data, which is commonly used in most econometric analyses of financial data, such as log-returns at specific time points. While some research has adopted interval econometrics to enhance the representativeness of the data over time, these approaches still exhibit limitations. Future research can expand upon this work by incorporating the latest artificial intelligence algorithms to capture more comprehensive interval data, which will provide better time representativeness for risk measurement and contribute to a more robust tail risk analysis.