Analyzing Systemic Risk Spillover Networks Through a Time-Frequency Approach

Abstract

This paper investigates the spillover effects and transmission networks of systemic risk within China’s national economic sectors under extreme conditions from both time and frequency domain perspectives, building upon the spillover index methodology and calculating the ∆CoVaR index for Chinese industries. The findings indicate the following: (1) Extreme-risk spillovers synchronize across industries but exhibit pronounced time-varying peaks during the 2008 Global Financial Crisis, the 2015 crash, and the COVID-19 pandemic. (2) Long-term spillovers dominate overall connectedness, highlighting the lasting impact of fundamentals and structural linkages. (3) In terms of risk volatility, Energy, Materials, Consumer Discretionary, and Financials are most sensitive to systemic market shocks. (4) On the risk spillover effect, Consumer Discretionary, Industrials, Healthcare, and Information Technology consistently act as net transmitters of extreme risk, while Energy, Materials, Consumer Staples, Financials, Telecom Services, Utilities, and Real Estate primarily serve as net receivers. Based on these findings, the paper suggests deepening the regulatory mechanisms for systemic risk, strengthening the synergistic effect of systemic risk measurement and early warning indicators, and coordinating risk monitoring, early warning, and risk prevention and mitigation. It further emphasizes the importance of avoiding fragmented regulation by establishing a joint risk prevention mechanism across sectors and departments, strengthening the supervision of inter-industry capital flows. Finally, it highlights the need to closely monitor the formation mechanisms and transmission paths of new financial risks under the influence of the pandemic to prevent the accumulation and eruption of risks in the post-pandemic era. Authorities must conduct annual “Industry Transmission Reviews” to map emerging risk nodes and supply-chain vulnerabilities, refine policy tools, and stabilize market expectations so as to forestall the build-up and sudden release of new systemic shocks.

1. Introduction

As global economic integration and financial market interconnectedness have intensified, the transmission mechanisms of systemic risk have become increasingly complex. The interdependence between industries has made risk spillover effects a key factor influencing financial stability [1]. In recent years, the rapid development of China’s financial markets and adjustments to its economic structure have further exacerbated the complexity of risk transmission across industries. Systemic risk can not only spread among financial institutions but also diffuse through inter-industry networks to the entire economic system, exerting profound impacts on financial market stability and macroeconomic operations [2]. Therefore, conducting in-depth research on systemic risk spillover effects across industries in China is of great significance for identifying potential financial risks, optimizing resource allocation, and formulating effective macroprudential policies.

Traditional risk analysis methods largely rely on low-frequency data, making it difficult to capture short-term dynamic changes in risk and easy to underestimate risk spillover effects [3]. Time-frequency analysis methods, however, decompose time series into different frequency components, enabling them to simultaneously capture short-term high-frequency fluctuations and long-term low-frequency trends, thereby providing a more comprehensive reflection of the dynamic characteristics of risk [4]. In recent years, this method has been widely applied in financial risk research, revealing differences in risk transmission pathways across different frequencies [1].

In China, the complex network of inter-industry linkages makes it difficult to identify the transmission channels of systemic risk. The financial sector and the real economy are becoming increasingly interconnected, and risks can spread rapidly across different industries through channels such as the credit market and stock market. However, existing research has mostly focused on risk transmission between financial institutions, with relatively little research on systemic risk spillover effects between industries. Furthermore, most studies have used single-frequency analysis methods, which are unable to fully reveal the complex risk transmission mechanisms between industries.

In summary, analyzing the systemic risk spillover effects between industries in China from a time-frequency perspective not only enables more accurate identification of the dynamic transmission paths of risk but also provides more scientific tools for macroprudential regulation. Against this backdrop, accurately identifying and measuring the systemic risk levels of various sectors, including China’s real economy and financial industry, and monitoring the spillover effects and nonlinear characteristics of systemic risks among these sectors are of paramount importance.

Therefore, this paper aims to explore the identification, spillover, and contagion of extreme risks among industries from the aforementioned perspectives. This study intends to employ the Conditional Value-at-Risk (CoVaR) method to characterize extreme risks within Chinese industries and, building upon this, utilize the “spillover index” methodology developed by Baruník and Křehlík (BK) [5] to investigate the spillover effects and network structure characteristics of extreme financial risks across industries. Empirically, we find that (1) extreme-risk spillovers synchronize across industries but exhibit pronounced time-varying peaks during the 2008 Global Financial Crisis, the 2015 crash, and the COVID-19 pandemic; (2) net spillover roles shift over time, with post-pandemic intensification in sectors such as Energy, Materials, Healthcare, and Finance; and (3) long-term spillovers dominate overall connectedness, highlighting the lasting impact of fundamentals and structural linkages.

The potential marginal contributions of this paper are as follows: In terms of research content, after comprehensively characterizing the systemic financial risk levels and evolutionary characteristics of various sectors of the national economy, it further examines the correlation characteristics of financial risks among these sectors and explores the magnitude and direction of systemic risk spillover effects. Methodologically, it introduces the BK spillover index and constructs a correlation network to investigate the differential characteristics of industry risks across various time horizons. Integrating the BK frequency-domain spillover methodology, we decompose contagion into short- (1–5 days), medium- (5–22 days), and long-term (22–250 days) horizons, uncovering distinct transmission mechanisms.

The remainder of this paper is structured as follows: Section 2 provides a literature review, introducing the primary domestic and international methods for measuring systemic financial risk and the current state of research, along with a review of the development of spillover index models. Section 3 outlines the research methodology and data, introducing the DCC-GJR-GARCH-CoVaR model and the BK model [5], and primarily explains the data processing and descriptive statistical analysis. Section 4 presents the empirical research, including the measurement and analysis of systemic risk, Granger causality test in the direction of risk spillover, spillover effects from a static perspective, total and net spillover effects from a dynamic perspective, the empirical results and analysis of the spillover effect correlation network and the robustness test for replacement risk measurement. Finally, Section 5 summarizes the key findings of the paper, proposes policy recommendations, and summarizes the limitations of the paper.

2. Literature Review

In the current open economic environment, financial risks are spreading more and more widely, and financial risk issues are receiving attention. The global financial crisis, ignited by the US subprime mortgage crisis, had a profound negative impact on real economies worldwide, prompting significant attention to the cross-border transmission of financial risks [6]. Consequently, theoretical and empirical research on financial risk has become a focal point for academics [7,8]. Post-crisis research grounded in the realities of financial systems has explored the factors influencing financial risk, including studies examining the impact of economic fluctuations on financial risk in small economies [9]. In recent years, increasing attention has been directed towards financial risks within specific financial subsystems, such as shadow banking [10] and local government debt [11]. Furthermore, influences external to the financial system have also become research hotspots, including the impact of distress in non-financial sectors, the real estate market [12], and specific events like the COVID-19 pandemic [13]. Gkillas et al. study the non-linear causal relation between uncertainty-due-to-infectious-diseases and stock–bond correlation [14]. In addition to the factors influencing financial risk, the increasingly complex nature of financial risk has made it imperative to accurately measure systemic financial risk and characterize risk spillover networks.

Regarding methods for measuring financial risk, through a systematic review of existing research, mainstream financial risk measurement methods can be summarized into three major categories: First, the Early Warning Indicator System (EWIS) approach, which involves studying historical data from countries that have experienced financial crises to identify common signal indicators and their thresholds that reflect the occurrence of crises, thereby developing a monitoring system for predicting systemic financial risks in a given country. However, this method may not be applicable to countries that have never experienced a financial crisis. Second, the econometric modeling methods. Classic risk measurement tools such as Value at Risk (VaR) and Expected Shortfall (ES) are widely used in the industry [15] and have been further developed into composite models such as Marginal Expected Shortfall (MES), Conditional Value at Risk (CoVaR), Systemic Expected Shortfall (SES), and Systemic Risk Index (SRISK), which enable risk comparison across asset classes and portfolios. Third, stress index approaches, which primarily analyze the relative level of risk by measuring financial stress within a given period. However, this method mostly uses subjective weighting, which cannot fully reflect the objective situation of systemic risk. The aforementioned methods have been widely applied in research on financial risk measurement [16].

Among the above methods, the CoVaR method has attracted much attention due to its unique advantages in measuring systemic risk. CoVaR measures the risk faced by the entire financial market when a specific financial institution or sector is in distress; the difference between the Conditional Value-at-Risk (ΔCoVaR) when a financial institution or sector is in distress and under normal conditions represents the contribution of that entity or sector to systemic risk. CoVaR addresses the inadequacy of VaR in measuring tail losses by quantifying losses in the tail of the distribution [17]. While CoVaR assesses the spillover of systemic risk from an individual institution or market to the overall system based on their correlation, it overlooks the institution’s own volatility. For institutions with identical correlations to the broader market but differing volatilities, CoVaR would produce identical results. Moreover, CoVaR neglects factors such as institutional size and leverage, potentially leading to biases in identifying risk contributions. The literature suggests that ΔCoVaR, by focusing on the marginal contribution of individual institutions to systemic risk during periods of distress, effectively identifies and captures extreme tail risks [18]. Therefore, this paper utilizes stock market trading data and employs the ΔCoVaR indicator to measure systemic financial risk within Chinese industries.

On the other hand, with the introduction of spillover index methodologies, a growing body of research has focused on dynamic spillover effects in financial markets. Among these, the connectivity approach pioneered by Diebold & Yilmaz [19] and Diebold & Yılmaz [20] has seen the widest application. This method, based on VAR model forecast errors and variance decomposition, employs a rolling window approach to calculate spillover indices and measure dynamic connectedness, leading to its widespread adoption [21,22]. However, this method is limited to time-domain analysis. Building upon this, Baruník & Křehlík [5] proposed a framework considering both time and frequency dynamics. This approach, a time-frequency adaptation of the Diebold and Yilmaz [20] spillover index, decomposes time-domain spillovers into different frequency bands, enabling the simultaneous assessment of both the magnitude and direction of spillovers across time and frequency. Because risk spillovers at different frequencies play distinct roles in driving overall spillover effects, decomposing extreme risk spillovers between financial markets into the frequency domain allows for the identification of specific frequencies contributing most significantly to market spillovers, thereby facilitating the analysis of long-term, medium-term, and short-term extreme risk spillover effects. Market interconnectedness varies across different time-frequency scales due to the differing investment horizons of agents with varying preferences. Consequently, this method has also been widely applied [16,23,24]. Umar et al. [25] analyzed the time-frequency spillover relationship between clean energy stocks and fossil fuel markets against the backdrop of financial crises, oil crises, and the pandemic. The BK spillover index is utilized in studying the connectedness between uncertainty and exchange rates of oil import countries [26]. Li and Meng [27] used the time-frequency spillover index method to analyze the spillover relationship between cryptocurrencies and renewable energy stocks, finding that renewable energy stocks were the primary spillover contributors in this interconnected system and that short-term spillover effects dominated long-term ones. Mensi and Kang [28] used the time-frequency domain spillover index to examine the time-frequency connectedness between major precious metals markets and the stock indices of their importing and exporting countries, finding higher short-term spillover effects than long-term spillover effects for major precious metal exporting countries. Tiwari et al. [18] applied this method to study the time-frequency causality and connectedness among international energy, food, industrial, agricultural, and metal prices. Compared with the contagion effect, which reflects the abnormal strengthening of market linkages during crises [29], spillover effects reflect the fundamental linkages between markets that exist during normal times, which are relatively stable in nature. The stability of spillover effects not only makes them easier to identify and quantify but also provides a basis for constructing effective risk management models. Therefore, this paper focuses on spillover effects as its core research content.

In summary, while existing research on systemic risk and spillover effects is extensive, studies combining the ΔCoVaR measure of systemic financial risk with spillover indices from a time-frequency perspective are relatively scarce. This paper employs the ΔCoVaR indicator to measure systemic financial risk within various sectors of the Chinese stock market, exploring the evolution of systemic risk levels under extreme conditions. Building upon this, the study integrates spillover indices to analyze the spillover effects and network connectivity characteristics of extreme financial risks across industries from both time and frequency domain perspectives.

3. Methodology and Data

3.1. Systemic Financial Risk Model

The DCC-GJR-GARCH model is a financial time series model that combines Dynamic Conditional Correlation (DCC) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. It is primarily used to analyze and model the dynamic correlations between the returns of multiple financial assets and their respective volatilities. The GJR-GARCH model is an extension of the GARCH model, designed to capture the leverage effect in financial time series. The GJR-GARCH component captures the “leverage effect”, while the DCC component tracks dynamic correlations, enabling the DCC-GJR-GARCH model to excel in describing market volatility clustering, excess kurtosis, and heavy tails. Compared to traditional symmetric GARCH models or fixed correlation coefficient models, it more accurately reflects the complex dynamics of financial markets. Additionally, unlike the Copula-CoVaR model, which is limited in its ability to capture the dynamic characteristics of volatility within a single market, the DCC-GJR-GARCH model approaches the issue from two dimensions: volatility equations and dynamic adjustments to correlation coefficients. This enables it to comprehensively and meticulously describe the evolution of market volatility, providing a more robust and precise foundation for risk assessment and asset pricing in the Chinese market.

To better characterize the features of industry index return series, this paper employs the GJR-GARCH model to estimate the marginal distribution of individual industry series, obtaining standardized residuals for each. These residuals are then used in conjunction with the DCC model to measure the ΔCoVaR risk level for each industry. The ΔCoVaR index measures the systemic financial risk of each industry. Given the return series $R_t^i$ for a specific industry and a confidence level $\tau$, the VaR value for that industry or market can be obtained as follows:

$$\mathit{Pr}\left(R_t^i{\le VaR}_{\tau }^i\right)=\tau$$

(1)

Solving for ${VaR}_{\tau }^i$ yields the following:

$${VaR}_{\tau }^i=F_t^{-1}\left(\tau \right)$$

(2)

Given a specific industry or financial market i, where $R_t^i$ represents the return, ${VaR}_{\tau }^i$ represents the potential loss at confidence level τ, and $F_t(·)$ denotes the cumulative distribution function of $R_t$ at time t. While the VaR index only characterizes the risk level of a specific market or industry, ${CoVaR}_{\tau }^{j|i}$ can be defined as the maximum potential loss faced by industry j at confidence level τ, conditional on industry i experiencing a loss equal to its VaR. Formally, it is as follows:

$$\mathrm{Pr}\left(R_t^j\le {CoVaR}_{\tau }^{j|i}|R_t^i\le {VaR}_{\tau }^i\right)=\tau$$

(3)

Based on the DCC-GJR-GARCH model, the joint probability density function of the return series ${{(R}_t^j,R_t^i)}^{’}$ can be obtained as ${pdf}_t$($R_t^j,R_t^i$). Therefore, the conditional probability distribution formula (3) can be re-expressed as follows:

$$\mathit{Pr}\left(R_t^j\le {CoVaR}_{\tau }^{j|i}|R_t^i\le {VaR}_{\tau }^i\right)={\displaystyle \frac{Pr(R_t^j\le {CoVaR}_{\tau }^{j|i},R_t^i\le {VaR}_{\tau }^i)}{Pr(R_t^i\le {VaR}_{\tau }^i)}}=\tau$$

(4)

Then, we get the following:

$${\int }_{-\infty }^{{CoVaR}_{\tau }^{j|i}}{\int }_{-\infty }^{{VaR}_{\tau }^i}{pdf}_t\left(x,y\right)dydx=\mathit{Pr}(R_t^j\le {CoVaR}_{\tau }^{j|i},R_t^i\le {VaR}_{\tau }^i)={\tau }^2$$

(5)

Furthermore, the marginal spillover or spillover degree from one market participant to an industry is measured by $∆{CoVaR}_{\tau }^{j|i}$, which is defined as follows:

$$∆{CoVaR}_{\tau }^{j|i}={CoVaR}_{\tau }^{j|i}-{CoVaR}_{\tau }^{j|n}$$

(6)

$∆{CoVaR}_{\tau }^{j|i}$ represents the difference in potential losses faced by industry j when industry i is operating under distressed conditions versus normal (n) conditions. Normal conditions for stock market returns are assumed to be within one standard deviation above or below the mean.

3.2. Time-Frequency Spillover Index Model (BK Model)

Inspired by Diebold and Yilmaz’s [20] work on generalized variance decomposition, Baruník and Křehlík [5] extended this framework to the frequency domain, using the spectral representation of the generalized variance decomposition to study connectivity relationships within the frequency domain. Specifically, the spectral behavior of ${∆CoVaR}_t$ can be described by its frequency response function:

$$S_y\left(\omega \right)={\sum }_{h=-\mathrm{\infty }}^{\mathrm{\infty }} E\left({∆CoVaR}_t{∆CoVaR}_{t-h}\right)e^{-i\omega h}=\Psi \left(e^{-i\omega }\right)\Sigma {\Psi }^{\prime }\left(e^{+i\omega }\right)$$

(7)

where $\Psi \left(e^{-i\omega }\right)={\sum }_h{e}^{-i\omega h}{\Psi }_h,h=1,2,\dots ,H$, yielding the Fourier transform coefficients ${\Psi }_h,\sqrt{-1}=i$. The power spectrum $S_{VaR}\left(\omega \right)$ is crucial for understanding frequency dynamics, as it describes how the variance of $y_t$ is distributed across frequency components $\omega$.

The generalized causality spectrum at frequency ω can be expressed as follows:

$$(f(\omega ){)}_{k,j}={\displaystyle \frac{{\Sigma }_{j,j}^{-1}{\left|{\left(\Psi \left(e^{-i\omega }\right)\Sigma \right)}_{k,j}\right|}^2}{{\left(\Psi \left(e^{-i\omega }\right)\Sigma {\Psi }^{\prime }\left(e^{+i\omega }\right)\right)}_{k,k}}}$$

(8)

$\left(f\right(\omega ){)}_{k,j}$ represents the contribution of shocks from variable k to the spectral component of variable j at a given frequency $\omega$, representing causality within the frequency domain. Building upon this, we introduce a weighting function:

$${\Gamma }_j(\omega )={\displaystyle \frac{{\left(\Psi \left(e^{-i\omega }\right)\Sigma {\Psi }^{\prime }\left(e^{+i\omega }\right)\right)}_{k,k}}{\frac{1}{2\pi }{\int }_{-\pi }^{\pi } {\left(\Psi \left(e^{-i\lambda }\right)\Sigma {\Psi }^{\prime }\left(e^{+i\lambda }\right)\right)}_{k,k}d\lambda }}$$

(9)

where ${\Gamma }_j\left(\omega \right)$ represents the power of variable j at a given frequency. Then, given an arbitrary frequency band $d=\left(a,b\right)$, with $a,b\in \left(-\pi ,\pi \right)$, the generalized variance decomposition over frequency band d is defined as follows:

$${\left({\Theta }_d\right)}_{k,j}={\displaystyle \frac{1}{2\pi }}{\int }_d {\Gamma }_k{(\omega )(\Theta (\omega ))}_{k,j}d\omega$$

(10)

This can be further normalized to the following:

$${\left({\tilde{\Theta }}_d\right)}_{k,j}={\displaystyle \frac{{\left({\Theta }_d\right)}_{k,j}}{\sum _j {\left({\Theta }_{\mathrm{\infty }}\right)}_{k,j}}}$$

(11)

where ${\left({\Theta }_{\mathrm{\infty }}\right)}_{k,j}={\displaystyle \frac{1}{2\pi }}{\int }_{-\pi }^{\pi } {\Gamma }_k{\left(\omega \right)\left(\Theta \right(\omega \left)\right)}_{k,j}d\omega$. ${\left({\tilde{\Theta }}_d\right)}_{k,j}$ represents the spillover level from variable k to variable j over the frequency band d.

Furthermore, the total spillover level over frequency band d can be calculated as follows:

$$S_d^W=100\cdot \left(1-{\displaystyle \frac{Tr\left\{{\tilde{\Theta }}_d\right\}}{\sum {\tilde{\Theta }}_d}}\right)$$

(12)

where $Tr\left\{\cdot \right\}$ denotes the trace operator, and $\sum {\tilde{\Theta }}_d$ is the sum of all elements in the matrix ${\tilde{\Theta }}_d$. Given that within-system spillovers disregard the aggregate nature of the series, the contribution of a given frequency band d to the total may be more meaningful. This can be achieved by weighting the within-system measure. Then, the total measure over frequency band d is defined as follows:

$$S_d^F=S_d^W\cdot {\displaystyle \frac{\sum {\tilde{\mathsf{\Theta }}}_d}{\sum {\tilde{\mathsf{\Theta }}}_{\mathrm{\infty }}}}$$

(13)

$S_d^F$ represents the frequency spillover over frequency band d. It should be noted that frequency spillover decomposes the original spillover into different components, i.e., $\sum _{d_s} S_s^F=S$, where S is the total spillover as defined by Diebold and Yilmaz [20].

This method can measure the magnitude of the spillover effect from market j to all other markets over frequency band d, referred to as the “spillover to other markets” (TO):

$$S_{j\to k,t}^d={\sum }_{k=1,j\ne k}^n{\left({\tilde{\mathsf{\Theta }}}_d\right)}_{k,j}$$

(14)

It can also measure the magnitude of the spillover effect received by market j from all other markets over frequency band d, referred to as the “spillover from other markets” (FROM):

$$S_{j\leftarrow k,t}^d={\sum }_{k=1,j\ne k}^n{\left({\tilde{\mathsf{\Theta }}}_d\right)}_{j,k}$$

(15)

Subtracting the “spillover from other markets” from the “spillover to other markets” yields the “net spillover effect” (NET) over frequency band d:

$$S_{j,t}^d=S_{j\to k,t}^d-S_{j\leftarrow k,t}^d$$

(16)

3.3. Data

This paper utilizes stock market trading data, aligned with China’s National Economic Industry Classification system, to analyze systemic financial risk and spillover effects within Chinese stock market sectors. The Shanghai Composite Index (SSCI) is employed as the systemic index, and the first-level industry indices from the Wind database are used as industry indices for this study. These encompass all 11 first-level industry indices: Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, Information Technology, Telecommunication Services, Utilities, and Real Estate. Considering data availability, the sample period spans from 4 January 2005 to 30 April 2025, using daily data to examine spillover effects between stock market sectors. Daily closing prices of each industry index are used to calculate returns, employing the logarithmic difference method to obtain the return series for each industry market index, as follows:

$$R_t=\left[ln\left(P_t\right)-ln\left(P_{t-1}\right)\right]\times 100$$

(17)

where $R_t$ is the logarithmic return, $P_t$ is the daily closing price at time t, and $P_{t-1}$ is the daily closing price at time t − 1.

Prior to empirical analysis, descriptive statistics of the processed return data are presented.

Table 1. Descriptive statistics.

	Mean	Max	Min	S. D.	Skew	Kur	J-B	ADF
SSCI	0.0085	3.9236	−4.0199	0.6518	−0.5709	8.4333	6338.28 ***	−68.74 ***
Energy	0.0097	4.0705	−4.5361	0.8191	−0.3911	6.7956	3088.13 ***	−68.57 ***
Materials	0.0140	4.0586	−4.4421	0.8399	−0.6963	6.8665	3472.90 ***	−64.55 ***
Industrials	0.0145	4.0993	−4.8906	0.7994	−0.7327	7.9137	5406.21 ***	−65.25 ***
Consumer Discretionary	0.0194	4.0975	−4.5204	0.7912	−0.7437	7.5256	4666.40 ***	−64.94 ***
Consumer Staples	0.0255	4.0518	−4.4338	0.7606	−0.4461	6.7225	3013.04 ***	−65.30 ***
Health Care	0.0219	4.6082	−4.4873	0.7995	−0.4952	6.8415	3236.16 ***	−64.37 ***
Financials	0.0204	4.1359	−4.3163	0.7614	−0.1867	7.2848	3803.93 ***	−69.49 ***
Information Technology	0.0177	5.3716	−5.5612	0.9338	−0.5244	6.1702	2292.68 ***	−64.57 ***
Telecommunication Services	0.0103	4.1839	−4.5959	0.9362	−0.1052	7.2301	3688.52 ***	−70.75 ***
Utilities	0.0127	4.1046	−4.5502	0.7241	−0.7301	9.1921	8322.50 ***	−66.95 ***
Real Estate	0.0115	4.1096	−4.3228	0.9174	−0.3695	5.9638	1918.55 ***	−67.03 ***

Notes: The J-B statistic is used to test whether the yield series follows a normal distribution; the ADF is used to test whether the yield series is stationary.* p < 0.1, ** p < 0.05, *** p < 0.01.

summarizes the descriptive statistics for the return variables of each industry market index. In terms of mean daily returns, the Consumer Staples sector exhibits the highest average at 0.0255, followed by Health Care and Financials. Examining the range between maximum and minimum values, the Telecommunication Services sector displays the most extreme values, while the Financials sector shows the least deviation in extreme values. Regarding standard deviation, the Telecommunication Services sector has the highest value (0.9362), significantly higher than other sectors, suggesting greater susceptibility to external shocks. Information Technology (0.9338) and Real Estate (0.9174) also exhibit standard deviations exceeding 0.9. The Utilities sector demonstrates the lowest standard deviation (0.7241), indicating greater stability. Skewness analysis reveals negative values for all 11 markets, indicating left-skewness. Kurtosis analysis shows that the daily return kurtosis for all 11 markets exceeds that of a normal distribution, indicating leptokurtosis (peakedness and fat tails). The Utilities sector exhibits the highest kurtosis, suggesting the most pronounced leptokurtic behavior. The Jarque–Bera test (J-B) for normality rejects the null hypothesis for all variables, with J-B statistics indicating non-normality at a 1% significance level. The ADF is used to test whether the yield series is stationary. ADF tests confirm stationarity for all daily return series at a 1% significance level.

4. Empirical Analysis

4.1. Systemic Risk Measurement

This study first measures the systemic financial risk index, ∆CoVaR, for each industry based on the DCC-GJR-GARCH model. Figure 1a,b illustrate the risk fluctuations of the 11 sampled industries during the observation period. As illustrated in Figure 1, the horizontal axis represents time, while the vertical axis plots the ∆CoVaR values for each industry. The gray-shaded areas highlight three major crises in the Chinese stock market: the 2008 Global Financial Crisis, the 2015 Chinese stock market crash, and the COVID-19 pandemic. As clearly shown in Figure 1, extreme risks demonstrate distinct volatility clustering, with systemic risk peaking during both the 2008 financial crisis and the 2015 market crash, marking the two highest risk levels in the sample period. These crises inflicted severe shocks on the stock market, triggering massive capital erosion and exerting substantial adverse effects on the economy.

A closer examination reveals that all industries exhibit dynamic, time-varying risk patterns. Cross-industry comparisons indicate that systemic financial risks surged around both the 2008 and 2015 crises, though the magnitude of impact varied across sectors. The 2008 crisis, sparked by the U.S. subprime mortgage collapse and subsequent investor panic, escalated into a global liquidity crunch. Given the deep interlinkages among industries and financial markets, the crisis rippled through all sectors, driving risk levels to unprecedented highs. Notably, liquidity shocks directly destabilized industry stock markets, as evaporating investor confidence and potential bank runs precipitated a sharp spike in systemic risk.

In contrast, the 2015 crash catapulted industry risks from moderate levels to record peaks, marked by an abrupt, explosive surge. Unlike other crises, risk transmission during this episode was exceptionally rapid, amplified by the prevailing one-sided market sentiment, which accelerated risk accumulation and sudden unwinding. Following the 2020 COVID-19 outbreak, systemic risks rose moderately across industries, yet the impact paled in comparison to the 2008 and 2015 crises. This underscores that catastrophic events—financial crises, market collapses, and pandemics—consistently amplify financial risks throughout the industrial landscape.

To provide a comprehensive analysis of industry-specific risk exposures,

Table 2. Descriptive statistics of industry systemic financial risk index $∆CoVaR.$

	Full Sample		Financial Crisis		Stock Market Crash		Pandemic
	Mean	SD	Mean	SD	Mean	SD	Mean	SD
Energy	1.0545	(0.5018)	1.8424	(0.4702)	2.1928	(0.6683)	1.2147	(0.1621)
Materials	1.1804	(0.4968)	1.7504	(0.4806)	2.5038	(0.8800)	1.5835	(0.2118)
Industrials	1.1342	(0.5032)	1.6473	(0.4914)	2.5909	(0.8796)	1.5683	(0.1943)
Consumer Discretionary	1.0885	(0.4985)	1.6356	(0.5079)	2.4725	(0.8016)	1.5829	(0.1752)
Consumer Staples	0.9426	(0.4516)	1.3864	(0.4533)	2.1329	(0.7782)	1.3648	(0.1524)
Health Care	0.9381	(0.4860)	1.2223	(0.4974)	2.3131	(0.7517)	0.8977	(0.0789)
Financials	1.0530	(0.4780)	1.8396	(0.5283)	1.8457	(0.4795)	1.3453	(0.1088)
Information Technology	1.1749	(0.4868)	1.5988	(0.5037)	2.5815	(0.7157)	1.8044	(0.1240)
Telecommunication Services	1.0028	(0.5311)	1.5057	(0.5539)	2.3257	(0.7670)	1.5873	(0.1292)
Utilities	0.8850	(0.5482)	1.2713	(0.3969)	2.4633	(0.9376)	1.0294	(0.1984)
Real Estate	1.1377	(0.5129)	1.8466	(0.4606)	2.3099	(0.6612)	1.4177	(0.1794)

presents the mean values and standard deviations of ΔCoVaR across four distinct market regimes: the full sample period, the 2008 Global Financial Crisis, the 2015 stock market crash, and the COVID-19 pandemic. The Materials sector (highest full-sample mean at 1.1804) and Information Technology (1.1749) emerge as the most systemically risky industries, while Utilities (0.8850) and Health Care (0.9381) demonstrate the greatest resilience. This ranking holds during normal periods but shifts dramatically under stress. Notably, extreme events significantly amplify risk across all sectors—during the 2008 financial crisis, Real Estate (1.8466), Energy (1.8424), and Financials (1.8396) suffered the most severe contagion, whereas the 2015 stock market crash drove Industrials (2.5909) and Information Technology (2.5815) to record risk levels, nearly doubling their full-sample averages.

These findings demonstrate that both internal and external factors influence the systemic risk of industry markets, with external shocks having a more pronounced and severe impact. The significant influence of extreme events on industry financial risk indices aligns with societal perceptions and macroeconomic data, validating the effectiveness and reliability of the constructed systemic risk indicator in measuring the magnitude and fluctuation of systemic risk within Chinese industry stock markets.

The Granger causality test results in

Table 3. Granger causality result of industry systemic financial risk index $∆CoVaR.$

Sector	Energy	Materials	Industrials	Consumer Discretionary	Consumer Staples	Health Care	Financials	Information Technology	Telecommunication Services	Utilities	Real Estate
Energy		3.09 **	2.05 *	1.67	2.00 *	1.71	0.69	3.00 *	4.92 ***	0.22	3.22 **
Materials	6.25 ***		1.51	3.91 **	2.10 *	3.87 **	0.65	7.63 ***	5.36 ***	4.99 ***	6.64 ***
Industrials	4.90 ***	1.09		3.54 **	2.20 *	3.02 *	0.88	7.87 ***	4.91 ***	5.10 ***	6.69 ***
Consumer Discretionary	4.55 ***	2.33 *	1.23		2.81 *	1.98 *	2.98 *	3.16 **	2.83 *	4.80 ***	2.84 *
Consumer Staples	4.23 ***	3.42 **	3.88 **	5.28 ***		2.15 *	2.67 *	3.60 **	1.17	3.15 **	3.37 **
Health Care	4.71 ***	2.40 *	2.07 *	1.7	9.04 ***		2.43 *	0.97	2.45 *	5.92 ***	1.88 *
Financials	3.94 **	3.12 **	2.87 *	1.21	1.42	2.48 *		2.77 *	0.25	0.54	0.54
Information Technology	3.87 **	3.39 **	4.46 ***	6.31 ***	12.32 ***	5.54 ***	3.41 **		3.77 **	5.93 ***	4.64 ***
Telecommunication Services	1.66	2.48 *	2.31 *	5.78 ***	3.36 **	5.90 ***	5.22 ***	5.48 ***		4.97 ***	4.06 **
Utilities	5.38 ***	4.52 ***	4.56 ***	4.73 ***	2.93 *	3.87 **	1.26	5.70 ***	0.92		1.57
Real Estate	2.94 *	2.75 *	2.37 *	7.96 ***	8.35 ***	6.35 ***	3.09 **	6.58 ***	2.63 *	7.47 ***

Notes: The J-B statistic is used to test whether the yield series follows a normal distribution; the ADF is used to test whether the yield series is stationary.* p < 0.1, ** p < 0.05, *** p < 0.01.

demonstrate a complex network of systemic risk spillovers across Chinese industries. The information technology industry is the main risk transmitter, with a high level of risk output, and there is a relatively obvious one-way transmission phenomenon in consumer staples (12.32 ***). Interestingly, while the Financials sector receives strong risk inflows from Consumer Discretionary (2.98 *), Consumer Staples (2.67 *), Telecommunication Services (5.22 ***) and Real Estate (3.09 **), it simultaneously transmits risks to Energy (3.94 **), Materials (3.12 **) and Industrials (2.87 *), revealing its dual role as both risk recipient and transmitter. The Energy sector shows a distinctive pattern as a net risk absorber, being significantly influenced by Materials (6.25 ***) but exhibiting limited outward spillovers. These findings highlight an asymmetric risk transmission structure where Information Technology serve as primary risk sources, while Energy act as risk sinks, with Financials functioning as a crucial intermediary node in China’s systemic risk network.

4.2. Static Spillover Effects Analysis of the Full Sample

Following Baruník and Křehlík [5], this paper adopts a 100-day forecast horizon (H) and 120-day rolling window to quantify systemic financial risk spillovers across Chinese industry markets under three frequency bands: short- (1–5 days), medium- (5–22 days), and long-term (22–250 days) (The three frequency bands were chosen to align with standard equity-market trading cycles: 1–5 days corresponds to a one-week horizon (five trading days per week), 5–22 days approximates a one-month horizon (around 22 trading days per month), and 22–250 days represents a one-year horizon (roughly 250 trading days per year)).

Table 4. Short-term static spillover effects estimation results.

	Energy	Materials	Industrials	Consumer Discretionary	Consumer Staples	Health Care	Financials	Information Technology	Telecommunication Services	Utilities	Real Estate	From
Energy	18.00	12.00	10.67	10.00	6.67	7.33	5.33	9.33	6.00	8.00	6.67	7.93
Materials	7.66	14.35	12.92	12.44	7.66	9.09	4.31	11.96	4.78	8.13	6.70	11.65
Industrials	6.49	12.43	14.05	12.43	7.57	9.73	4.32	12.97	4.86	8.11	7.03	10.27
Consumer Discretionary	5.44	11.56	12.24	14.29	8.84	10.88	4.08	13.61	4.76	7.48	6.80	8.09
Consumer Staples	5.10	10.19	10.83	12.74	17.20	12.10	3.82	10.83	3.82	7.01	6.37	8.54
Health Care	4.69	10.16	11.72	13.28	9.38	17.19	3.13	14.06	3.91	7.03	5.47	6.85
Financials	8.16	9.18	10.20	10.20	7.14	7.14	15.31	10.20	5.10	6.12	11.22	5.35
Information Technology	4.42	11.50	12.39	13.27	7.08	11.50	2.65	19.47	5.31	7.08	5.31	5.83
Telecommunication Services	7.08	9.73	10.62	10.62	6.19	7.96	3.54	13.27	19.47	7.08	4.42	5.93
Utilities	7.04	11.97	11.97	11.97	7.75	9.15	3.52	11.97	4.93	13.38	6.34	8.06
Real Estate	6.06	10.10	11.11	12.12	7.07	8.08	7.07	10.10	4.04	6.06	18.18	5.25
To	5.61	9.45	10.24	10.82	6.78	8.62	3.84	11.14	4.41	6.69	6.16	Total: 83.75%
Net	−2.32	−2.2	−0.03	2.73	−1.76	1.77	−1.51	5.31	−1.52	−1.37	0.91

,

Table 5. Estimated results of mid-term static spillover effects.

	Energy	Materials	Industrials	Consumer Discretionary	Consumer Staples	Health Care	Financials	Information Technology	Telecommunication Services	Utilities	Real Estate	From
Energy	17.49	11.66	10.76	10.31	6.73	7.62	5.38	9.87	5.61	8.07	6.50	8.03
Materials	7.33	14.17	12.67	12.50	7.83	9.50	4.17	12.50	4.50	8.17	6.67	11.22
Industrials	6.21	12.24	13.75	12.81	7.72	9.98	4.14	13.37	4.71	8.29	6.78	9.99
Consumer Discretionary	5.54	11.55	12.47	14.55	8.78	10.85	3.70	13.86	4.39	7.39	6.93	8.04
Consumer Staples	5.06	10.13	10.76	12.87	16.46	11.81	3.80	11.39	4.01	7.17	6.54	8.63
Health Care	4.66	10.36	11.40	12.95	9.84	17.36	2.85	14.51	3.89	6.74	5.44	6.96
Financials	7.99	9.38	10.42	10.76	7.29	7.64	14.93	10.42	4.51	6.25	10.42	5.38
Information Technology	4.75	11.28	12.76	13.35	7.12	11.57	2.67	19.29	5.04	6.82	5.34	5.93
Telecommunication Services	7.37	9.63	10.76	10.76	6.23	8.78	3.40	13.31	17.56	7.08	5.10	6.35
Utilities	6.88	11.47	12.16	12.16	8.03	9.40	3.67	12.39	4.59	13.07	6.19	8.27
Real Estate	6.02	10.03	11.04	12.04	7.69	8.03	7.02	11.04	3.68	6.35	17.06	5.43
To	5.58	9.48	10.27	10.98	6.94	8.86	3.8	11.44	4.12	6.67	6.1	Total: 84.23%
Net	−2.45	−1.74	0.28	2.94	−1.69	1.9	−1.58	5.51	−2.23	−1.6	0.67

and

Table 6. Estimated results of long-term static spillover effects.

	Energy	Materials	Industrials	Consumer Discretionary	Consumer Staples	Health Care	Financials	Information Technology	Telecommunication Services	Utilities	Real Estate	From
Energy	14.89	11.74	10.96	10.50	8.12	7.24	5.64	9.51	5.07	8.79	7.55	8.02
Materials	6.92	13.76	12.51	12.21	9.13	9.38	4.17	11.75	4.42	8.42	7.34	10.09
Industrials	5.87	12.02	13.33	12.49	9.04	9.79	4.19	12.81	4.66	8.43	7.36	9.07
Consumer Discretionary	5.31	11.54	12.36	13.79	9.96	10.37	3.98	13.07	4.29	7.87	7.46	8.22
Consumer Staples	4.95	10.53	11.30	12.60	15.84	11.39	4.01	11.21	3.96	7.70	6.53	9.11
Health Care	4.28	10.82	11.62	12.46	11.56	15.10	3.17	13.52	3.70	7.55	6.23	7.83
Financials	7.36	9.45	9.99	10.61	9.06	7.36	14.25	9.76	4.57	6.51	11.08	5.4
Information Technology	4.53	11.16	12.40	12.90	9.18	11.04	3.04	17.36	4.71	7.07	6.63	6.5
Telecommunication Services	6.62	9.78	10.98	10.60	7.70	8.26	3.97	12.37	15.96	7.51	6.25	6.49
Utilities	6.77	11.35	12.21	11.76	9.11	9.52	3.82	11.35	4.58	12.67	6.87	8.37
Real Estate	5.83	10.67	11.27	12.19	8.48	8.08	6.76	10.67	3.91	7.02	15.11	6.24
To	5.27	9.71	10.41	10.76	8.18	8.5	3.97	10.77	4.04	7.04	6.69	Total: 85.35%
Net	−2.75	−0.38	1.34	2.54	−0.93	0.67	−1.43	4.27	−2.45	−1.33	0.45

present the static spillover effects of industry financial risks under extreme conditions from short-term, medium-term, and long-term perspectives. The diagonal values represent the self-impact of lagged effects, while off-diagonal values represent directional spillovers of financial risks between two markets. To improve readability, we have presented the level of risk spillover between the two markets in heatmaps (Figure 2). “To” represents outgoing spillovers from one industry to other markets, while “From” represents incoming spillovers received by one industry from others. “Net” represents the net risk spillover level for a given industry, calculated as “To” minus “From”. The bolded Total Connectedness (TC) value in the bottom right corner represents the total risk spillover level for that frequency band. The total spillover indices within the three frequency bands depict the proportion of spillovers in the short, medium, and long term, indicating the extent to which overall industry systemic financial risk fluctuations are driven by cross-market spillovers at each time horizon. The overall extreme risk across industries is high, with total spillover indices reaching 79.30% (short-term), 84.50% (medium-term), and 85.60% (long-term). This indicates that over 79% of the variation in systemic risk within the sample period is attributable to cross-market spillover effects of systemic risk, while less than 21% originates from within the system itself.

Specifically, from the perspective of receiving systemic financial risk (“From”), Energy (8.00% short-term), Materials (10.09% long-term), and Utilities (8.37% long-term) are the primary risk recipients across horizons. This indicates that these industries are more susceptible to risk contagion following extreme shocks. Materials ranks among the top three receivers in all horizons (short-term: 2nd at 11.65%; medium-term: 1st at 11.22%), reflecting its downstream susceptibility. Materials typically has a certain degree of cost-passing capability, enabling it to pass on some of the pressure from rising raw material prices to downstream enterprises. The demand for Energy products is relatively inelastic, meaning that even during economic downturns, basic energy needs persist. Additionally, Energy is typically highly concentrated and often receives government policy support, such as energy security strategies and green energy subsidies. The demand for Telecommunications Services and Utilities is relatively stable, with strong monopolistic characteristics, and is less affected by economic cycles. Therefore, these industries possess strong risk-resistance capabilities.

From the perspective of transmitting systemic financial risk (“To”), Information Technology dominates across all horizons (short-term: 11.96%; medium-term: 13.86%; long-term: 11.35%), followed by Industrials and Consumer Discretionary, consistently serving as major risk sources during extreme events. Information Technology exceeds 11% outward spillovers in all periods, underscoring its heightened systemic role. The Financials sector consistently demonstrates low spillover activity (Net: –1.51% short-term; –0.14% long-term), indicating enhanced stability and risk resilience during systemic financial risk. Information Technology is characterized by rapid technological iteration, high valuations, significant market volatility, and high sensitivity to changes in the macroeconomic environment, resulting in high risk. Demand for Consumer Discretionary is highly sensitive to economic cycles, and external shocks can easily lead to insufficient demand, triggering the risk of overcapacity. Industrial is highly correlated with the macroeconomic cycle. During an economic downturn, demand and prices for industrial products are impacted, making it prone to exporting risks.

In summary, Consumer Discretionary, Industrials, Healthcare, and Information Technology industries are more prone to extreme risks due to their characteristics of high demand volatility, intense market competition, high policy risks, and rapid technological updates. On the other hand, Energy, Materials, Consumer Staples, Financials, Telecom Services, Utilities, and Real Estate industries are more likely to absorb extreme risks due to their characteristics of inelastic demand, policy support, high industry concentration, and cost-shifting capabilities.

4.3. Dynamic Spillover Effects Analysis of Industry Risk

To compare the time-varying characteristics of financial risk spillover effects across different frequency domains, this paper employs a rolling window approach to investigate the dynamic spillover effects of industry financial risks in both the time and frequency domains, focusing on total spillover levels, net spillover levels, and network spillover relationships. The total spillover level represents the overall magnitude of extreme financial risk spillover effects across the 11 industry markets. The net spillover level indicates whether an individual industry, in the time and frequency domains, is a net transmitter of extreme risk to other industries or a net recipient of extreme risk from other markets. Positive or negative values in the network spillover represent, respectively, the level of risk spilled from or received by an individual financial market to/from other markets in the time and frequency domains.

Figure 3 (comprising three subplots for short-, medium-, and long-term horizons) illustrates the spillover levels of industry financial risk in China across different time scales. The magnitude of risk spillover effects varies substantially across frequencies, with short-term fluctuations showing the highest volatility (0–35 range), medium-term peaks reaching up to 45, and long-term levels maintaining the highest sustained values (10–80 range).

Firstly, from a time-domain perspective on the total spillover index, the interconnectedness of risk spillovers across industries increased significantly during and before the financial crisis, peaking at approximately 27 in the short-term band. As the impact of the crisis subsided, the interconnectedness gradually weakened. Before the 2015 stock market crash, the degree of risk spillover among industries steadily climbed and remained at a high level, before rapidly declining after the crash. In 2017, against a backdrop of renewed deleveraging efforts and tightening liquidity in China, frequent credit events such as debt defaults occurred, propelling medium-term interconnectedness to a new high of 34. Since the outbreak of the COVID−19 pandemic in 2020, the total spillover level initially increased rapidly. However, it has subsequently declined over 40% by 2024, contrasting with the continued development of the pandemic. This suggests that China’s sustained implementation of monetary and fiscal policies aimed at stabilizing the market and economy, by providing ample liquidity, has effectively mitigated extreme risk spillover effects while reducing systemic risk levels.

Secondly, from a frequency-domain perspective on the total spillover index, although risk spillover levels across different frequencies exhibit relatively synchronized trends in the time domain, there are substantial differences in their magnitudes and persistence. Cross-industry extreme risk spillover effects are primarily driven by long-term extreme risk spillovers, which consistently maintain the highest levels (>50 throughout most periods). Short-term spillover effects are mainly driven by noise trading, such as herding behavior and investor sentiment, while long-term spillovers are more influenced by economic fundamentals and persistent uncertain events. Therefore, cross-industry spillover effects of extreme risk in China are characterized by long-term (low-frequency) drivers, which demonstrate greater persistence and contribute to approximately 60–80% of total spillovers, with more persistent and enduring real impacts.

Additionally, this paper examines the net spillover effect of industry risk, with the analysis results shown in Figure 4. As depicted in Figure 4, the net spillover effect of industry risk exhibits notable time-varying and heterogeneous characteristics across different horizons, while also displaying a trend of co-movement among industries that remains consistent across various time periods. At certain key points—such as the financial crisis, European debt crisis, 2015 stock market crash, U.S.–China trade war, and the onset of the COVID−19 pandemic—the net spillover and total spillover effects reveal similar patterns, both demonstrating substantial fluctuations. Specifically, industries demonstrate synchronized regime shifts during crises: the 2015 market crash triggered simultaneous transitions to net transmission in Real Estate (+2.8 mid-run) and Financials (+1.5 short-run), while the U.S.–China trade war forced Technology into abrupt net reception (−4.2 long-run). In terms of spillover direction, all industries are shown to alternately emit and absorb risk during extreme events, with these shifts becoming more pronounced following major shocks. The impact of the COVID-19 pandemic in 2020 stands out for its severe and persistent effect across industries, with the Energy, Materials, Consumer Staples, and Real Estate sectors experiencing particularly notable volatility. Notably, after the onset of the pandemic, Energy shifted from a net receiver to a net transmitter of risk, a transition also observed in Materials, Finance, Real Estate, and Health Care. More specifically, COVID-19 induced unprecedented sectoral realignments: Energy’s transformation into a net transmitter (+4.8 short-run) reflected supply chain disruptions, while Financials’ shift (+1.9 net) revealed liquidity redistribution pressures. Crucially, Utilities consistently functioned as a system stabilizer with near-zero net spillovers across horizons, whereas Industrials acted as a crisis amplifier, exhibiting high-magnitude spillovers (>|5.0|) in all events. These findings suggest that industry risk spillover effects are likely to undergo significant shifts over time and in response to specific events, underscoring the importance of monitoring systemic risk with attention to its time-varying characteristics.

In summary, the heterogeneous spillover profiles across horizons reflect distinct underlying drivers: in the short run, liquidity shocks, noise trading, and shifts in investor sentiment precipitate rapid but fleeting risk transmissions, particularly in high-beta, retail-driven sectors; over the medium term, policy actions and credit-cycle dynamics extend the duration of spillovers, most notably in Financials and Real Estate as stimulus or tightening measures filter through credit markets; and in the long run, fundamental linkages—such as capital-intensive cycles and global supply-chain dependencies—sustain and propagate risk over months, especially in sectors like Energy and Materials.

The transmission of market sentiment and risk contagion among industries has resulted in a complex network of risk spillovers, forming an industry-wide risk spillover network. In this paper, we apply complex network methods to depict extreme risk transmission relationships between pairs of industries, aiming to clarify the structural characteristics of risk spillover. This method treats each industry within the national economy as a node in a complex network, considers the risk spillover relationships as network edges, and uses variance contributions calculated through variance decomposition as the adjacency matrix of the volatility spillover network. We construct an extreme risk spillover network among Chinese industries by treating each sector as a node and using variance-decomposition contributions as the weighted edges, yielding an 11-node, 55-edge graph (Figure 5).

First, the average pairwise spillover coefficients in the long run exceed those in the short and mid runs, indicating that under extreme conditions, long-term risk contagion within the industrial system becomes more pronounced. Second, across all three horizons, Consumer Discretionary, Industrials, Healthcare, and Information Technology consistently act as net transmitters of extreme risk, while Energy, Materials, Consumer Staples, Financials, Telecom Services, Utilities, and Real Estate primarily serve as net receivers. Third, the sign distribution of the spillover coefficients varies over time: there are 20 positive vs. 35 negative pairs in the short run, 25 positive vs. 30 negative in the mid run, and 21 positive vs. 34 negative in the long run. In each case, fewer than half of the industry pairs register positive spillovers, and this proportion declines further over longer horizons, suggesting that as the horizon lengthens, industries are increasingly on the receiving end of extreme shocks, while their outward transmission weakens.

Finally, when examining individual pairwise strengths, Energy consistently exhibits its strongest risk transmissions toward Consumer Discretionary, Industrials, and Materials, and these three sectors remain among the top five recipients of shocks from Energy in every frequency band. This highlights the pervasive and enduring influence of the Energy sector in propagating extreme risk—particularly over the long term—and underscores the need to monitor risk buildup in this sector. Conversely, Telecom Services transfers significant risk to Information Technology, Consumer Discretionary, and Healthcare under extreme conditions, though these reception patterns shift as one moves from short to mid and long horizons, with Consumer Staples, Financials, Healthcare, and Consumer Discretionary emerging as key receivers in the latter periods.

4.4. Robust Test

Table 7. Descriptive statistics of industry systemic financial risk index $\mathrm{M}\mathrm{E}\mathrm{S}.$

	Full Sample		Financial Crisis		Stock Market Crash		Pandemic
	Mean	SD	Mean	SD	Mean	SD	Mean	SD
Energy	1.1406	(0.5844)	1.9578	(0.5861)	2.3611	(0.7084)	1.5841	(0.1620)
Materials	1.1725	(0.5598)	1.9659	(0.5836)	2.3174	(0.7076)	1.6342	(0.1678)
Industrials	1.1900	(0.5637)	1.9700	(0.5981)	2.3770	(0.7149)	1.6796	(0.1717)
Consumer Discretionary	1.1847	(0.5598)	1.9563	(0.6087)	2.3742	(0.7230)	1.6827	(0.1674)
Consumer Staples	1.0741	(0.5631)	1.8247	(0.5812)	2.3346	(0.7297)	1.5605	(0.1744)
Health Care	1.0443	(0.5649)	1.7664	(0.6848)	2.3049	(0.7131)	1.2323	(0.1349)
Financials	1.1569	(0.5399)	1.9184	(0.5439)	2.2722	(0.6793)	1.5670	(0.1550)
Information Technology	1.0737	(0.5446)	1.8823	(0.6379)	2.1698	(0.6778)	1.4885	(0.1843)
Telecommunication Services	1.0052	(0.5276)	1.6864	(0.5804)	2.1753	(0.6746)	1.4608	(0.1633)
Utilities	1.1033	(0.5760)	1.8791	(0.5892)	2.3217	(0.6874)	1.6077	(0.1642)
Real Estate	1.0794	(0.5527)	1.8262	(0.5474)	2.2787	(0.7167)	1.5073	(0.1822)

reports the MES-based systemic risk measures for each industry over the full sample and three extreme-event windows (the 2008–2009 Global Financial Crisis, the 2015–2016 stock-market crash, and the 2020 pandemic), presenting both means and standard deviations. Over the full sample, Energy, Materials, Consumer Discretionary, and Financials exhibit the highest average MES values (approximately 1.14, 1.17, 1.18, and 1.16, respectively), indicating that these sectors are most sensitive to systemic market shocks. In each event window, MES levels rise sharply: during the financial crisis, Energy’s MES increases from 1.14 to 1.96; in the stock-market crash, it climbs further to 2.36; and although it recedes somewhat in the pandemic period, it remains elevated at about 1.58. These patterns perfectly mirror those obtained under ΔCoVaR (Table 2): the same industries in the same windows display high concentration and volatility of systemic risk, confirming the robustness of our results to the choice of risk metric.

Figure 2 depicts the total spillover index over short-, medium-, and long-run horizons as computed with ΔCoVaR, while Figure 6 shows the analogous dynamics when MES replaces ΔCoVaR. In the short run, both metrics peak sharply during 2008–2009 and in 2015, and they exhibit a marked uptick at the onset of the 2020 pandemic; thereafter, they gradually subside and remain relatively stable through 2023–2024. In the medium run, both ΔCoVaR and MES capture a sustained high-spillover regime in the latter stage of the financial crisis and a pronounced extreme in 2015, whereas pandemic-period medium-run spillovers are milder but more volatile. In the long run, both plots display a “three-peak” pattern—2008–2009, 2014–2016, and 2020—with nearly identical peak magnitudes and durations, indicating that the long-run contagion dynamics are unaffected by the choice of systemic-risk measure.

Taken together, both the cross-sectional summary statistics and the multi-frequency dynamic spillover trajectories demonstrate that MES and ΔCoVaR yield highly consistent conclusions: the Energy, Materials, and Consumer Discretionary sectors bear the greatest systemic exposure during major market shocks; risk events amplify inter-industry spillovers and reshape their distribution across short, medium, and long horizons; and, overall, the MES-based results strongly validate the robustness of our earlier ΔCoVaR findings.

5. Conclusions and Policy Recommendations

First, by applying the ∆CoVaR index within a DCC-GJR-GARCH framework to 11 Chinese industry indices, we provide a granular, industry-level assessment of systemic risk under extreme shocks. Second, integrating the Baruník–Křehlík frequency-domain spillover methodology, we decompose contagion into short- (1–5 days), medium- (5–22 days), and long-term (22–250 days) horizons, uncovering distinct transmission mechanisms: rapid, sentiment-driven spillovers in the short run; policy and credit-cycle effects in the medium run; and fundamental, supply-chain-driven persistence in the long run. Third, we validate all findings with a MES-based robustness check, demonstrating that our network structure—where Energy, Materials, Consumer Discretionary, and Financials are most sensitive to systemic market shocks.—remains stable across risk metrics and crisis episodes. Empirically, we find that (1) extreme-risk spillovers synchronize across industries but exhibit pronounced time-varying peaks during the 2008 GFC, the 2015 crash, and the COVID-19 pandemic; (2) net spillover roles shift over time, with post-pandemic intensification in sectors such as Energy, Materials, Healthcare, and Finance; and (3) long-term spillovers dominate overall connectedness, highlighting the lasting impact of fundamentals and structural linkages.

Based on these findings, we propose the following targeted policy recommendations to mitigate and prevent systemic financial risks. First, regulators should implement a real-time, multi-horizon tail-risk monitoring platform that integrates ∆CoVaR and MES metrics across short (1–5 days), medium (5–22 days) and long (22–250 days) horizons, leveraging both coherence and leading indicators to enhance early-warning capabilities. Second, a sector-specific macroprudential framework should be established. A joint regulatory framework should be developed from an industry perspective to monitor capital flows across industries, regulate cross-industry financial cooperation, and avoid speculative activities and bubble formation, thereby mitigating the negative impact of risk spillovers. Finally, emphasis should be placed on identifying the formation mechanisms of new risk sources and transmission pathways of financial risk in the post-pandemic era. Authorities must conduct annual “Industry Transmission Reviews” to map emerging risk nodes and supply-chain vulnerabilities, refine policy tools, and stabilize market expectations so as to forestall the build-up and sudden release of new systemic shocks.

Regarding the shortcomings of this paper, as a study focused on the Chinese market, it fails to compare the risk spillover characteristics of the Chinese market with those of other major economies. This makes it difficult to reveal the uniqueness of the risk transmission mechanism in China’s financial markets, thereby reducing the international influence of the study. In the future, we can conduct more comparative analyses.