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Scientific Reports volume 15, Article number: 23756 (2025) Cite this article
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Driven by the goals of “carbon peak and carbon neutrality”, China’s photovoltaic industry has experienced rapid expansion, which provides a unique opportunity to study dynamic spillover effects within a structured industry framework. This study uses data from January 2017 to December 2024 to fill the research gap by exploring the complex spillover effects between the upstream, midstream and downstream of the photovoltaic industry chain. Empirical analysis based on the TVP-VAR-DY and TVP-VAR-BK models shows that: (1) Spillover effects initiated by specific markets, as well as their received impacts, exhibit significant time-varying asymmetries driven by major policy shifts and extreme events. (2) Spillover effects among key material markets are significantly higher under high-frequency trading conditions than under medium or long term. (3) Upstream silicon materials and photovoltaic modules are considered the main sources of risk transmission, while mid- and downstream links such as silver paste and photovoltaic glass are the main recipients of risk. The transmission of cross-market risks usually follows a feedback model, that is, the “upstream drive, downstream response” contagion pattern. In addition, the dynamic risk hedging strategies among key material markets in the photovoltaic industry provide empirical evidence for industry stakeholders and policymakers to implement risk management strategies.
Global warming caused by the continued increase in greenhouse gas emissions will have catastrophic consequences¹. The adoption of renewable energy is essential to avoid natural disasters and achieve net zero or negative greenhouse gas emissions². The photovoltaic (PV) industry is the most promising renewable energy technology. The International Energy Agency (IEA) and the International Renewable Energy Agency (IRENA) predict that by 2050, the installed capacity of solar photovoltaics will increase from 760 GW in 2020 to 14 TW. At present, China’s photovoltaic industry has a relatively complete industrial chain and has become the world’s largest producer and consumer of photovoltaic products. Through rapid growth and large investments to alleviate the disadvantages of fossil fuel combustion³, it has become a strategic emerging industry and an important driving force for China’s energy transformation. China’s photovoltaic module production has ranked first in the world for 16 consecutive years, accounting for more than 80% of the global market share, especially as the prices of key raw materials such as polysilicon continue to rise (see Fig. 1).
Trends in China’s polycrystalline silicon production and capacity changes.
However, the photovoltaic (PV) industry chain is currently facing severe structural challenges. The sharp fluctuations in the prices of key raw materials have increased market uncertainty⁴, regional market segmentation and imbalance between supply and demand have led to inefficient resource allocation⁵, and the lack of coordination among various links in the industry chain has hindered the improvement of overall competitiveness⁶. The prices of key materials such as polysilicon have risen, and regional market segmentation and closure have hindered market circulation, resulting in resource waste and reduced efficiency. These challenges urgently require comprehensive research to seek effective solutions. Therefore, this study explores the spillover effects between different levels of the photovoltaic industry chain and analyzes the impact of uncertain extreme events on the prices of key materials. This can optimize the risk management of the photovoltaic industry chain, stabilize the prices of key materials, enhance the resilience of the industry, and provide valuable experience for the construction of the international photovoltaic industry market.
The photovoltaic industry is a derivative industry that combines semiconductor technology with new energy demand. The upstream of the photovoltaic industry chain involves the collection and processing of crystalline silicon raw materials, the midstream involves the manufacturing of photovoltaic cells and supporting equipment, and the downstream involves the integration and operation of photovoltaic power station systems. On the one hand, the rising prices of raw materials such as photovoltaic silicon wafers and silver paste may lead to a decline in the profits of photovoltaic companies. The influencing factors may include high indirect costs, low production technology and increased competitive pressure⁷. On the other hand, the rising prices of key materials in the upstream of the photovoltaic industry chain may affect the mid- and downstream companies from processing to distribution to users⁸, and they will improve their technology to cope with the rising raw material prices and maintain profit margins⁹. As raw material prices fluctuate, the profits and losses of companies may be passed on to consumers¹⁰. These dynamic factors highlight the interconnectedness of the industry chain and the necessity of risk management strategies.
Many researchers have explored the risk spillover effects between the photovoltaic market and other energy markets¹¹ and the carbon market^12,13. At the same time, some scholars have studied the price drivers of the photovoltaic market, such as how the silver market affects the stock price of the photovoltaic solar market, and the return and volatility spillover effects and drivers of the clean energy industry (electric vehicles, solar energy, wind energy), electricity and eight energy metals under different conditions¹⁴. Existing research mainly focuses on the macro-level analysis of the spillover effects between different markets, focusing on the supply risks of raw materials such as silicon materials and metals¹⁵, the impact of technological innovation on prices, and the market-based pricing strategies of core products such as photovoltaic glass and solar cells¹⁶. However, there is a lack of analysis of the time-frequency spillover effects of cross-level price fluctuations within the market, and time lags and cyclicalities are often ignored, as well as the relationship between external policy shocks and the industrial chain. This paper studies the micro-dynamic spillover effects of the upstream, midstream and downstream photovoltaic material markets, and combines time-frequency analysis to fully understand the internal dynamics of the photovoltaic industry chain, and solves the problem of how to improve the stability of the photovoltaic industry chain through dynamic risk management strategies.
The main contributions of this paper are reflected in the following three aspects: First, based on the micro level, the time-frequency spillover effects of market price fluctuations in the upstream, midstream and downstream of the photovoltaic industry chain are studied to deal with the problems of drastic market price fluctuations and market instability in the industry chain. Second, based on the TVP-VAR-DY and TVP-VAR-BK models, the time-frequency spillover effects between different markets are measured from the new perspectives of time-frequency domain, time delay and periodicity. Not only can the dynamic change path of the size and direction of the risk spillover effect be obtained, but also the spillover effect at a specific time point can be analyzed to determine its periodicity and optimal time delay. Third, based on uncertain external factors such as the dual carbon goals and the COVID-19 pandemic, their impact on the market risk spillover effect of the photovoltaic industry chain is explored, providing new methods and strategies for effective risk management in the face of external uncertainties, promoting the stability and sustainable development of the industry chain, and enriching the theoretical research on industry chain risks.
Photovoltaic power generation is a technology that uses the photovoltaic effect of semiconductor interfaces to directly convert solar energy into electrical energy. It is a safe, clean and efficient energy system. At present, most scholars’ research focuses on the photovoltaic industry^17,18,19, as shown in Fig. 2. Research on the photovoltaic industry chain mainly includes two perspectives: value chain and supply chain. On the one hand, the value chain of distributed photovoltaic power generation usually includes various links in the upstream, midstream, downstream and auxiliary links^20,21. The complete value chain covers all activities required for an enterprise to develop products or services, from the production stage of the manufacturer to the consumption stage of the final consumer²². Most scholars analyze the knowledge spillover effect between the solar photovoltaic value chain from the perspective of technological innovation²², as well as competitive factors in technology, economy, management, politics, photovoltaic market and significant regional competitive advantages^23,24. On the other hand, the planning of photovoltaic supply chain operations is centered on the integration of production, sales, and transportation, and mainly focuses on the research of renewable energy and sustainable development as well as silicon, metal and other material markets^25,26,27. Some scholars have studied the supply chain risk mechanism¹⁵. Key metals used in the battery production process, such as lithium, cobalt, and graphite, are very scarce resources, and photovoltaic demand fluctuates greatly, facing the uncertainty of consumer and market demand, which increases the decision-making risk²⁸. In addition, some scholars have considered the price impact of government subsidy policies and studied the pricing issues between supply chains^29,30,31.
The relevant literature number of the photovoltaic industry.
Previous studies on the industrial chain have mainly focused on the price drivers and other influencing factors of each link. First, industrial chain activities are divided into upstream, midstream and downstream^32,33. The upstream includes the extraction of silica³⁴, the production of silicon ingots and silicon wafers^35,36. The midstream includes the production of photovoltaic glass³⁷, photovoltaic cells³⁸, photovoltaic brackets³⁹ and inverters⁴⁰. Second, the market price of upstream enterprises is affected by factors such as technological innovation⁴¹, process improvement⁴², dynamic pricing⁴³ and consumer confidence⁴⁴. Upstream companies have a certain level of technology and high investment costs. In order to reduce technical barriers and supply risks, they often form international alliances, strengthen technical cooperation, and provide raw materials for mid- and downstream companies^33,45. Due to the research and development of green technologies and innovations in the energy field, a large number of key upstream raw materials (silicon, silver, zinc, copper, etc.) still face greater short-term supply and price decision risks²⁸. Furthermore, midstream enterprises adopt market-oriented strategies and set prices based on factors such as product quality, technological differentiation, and service level to stimulate consumer demand³². Downstream enterprises produce photovoltaic system balance components, such as photovoltaic power stations, and make profits through product assembly, maintenance, and service provision²³. When a certain link experiences large fluctuations, controlling the intermediate link enterprises can reduce the scope of impact on other links and adjust risk prevention strategies in a timely manner^46,47,48. In China, with the introduction of the grid power subsidy policy, the profitability of downstream enterprises has improved, alleviating the problem of overcapacity in the photovoltaic and solar energy industries and boosting the domestic market^28,49.
In addition, under the influence of extreme uncertain events such as the COVID-19 pandemic, the development trend of the industrial chain has changed^50,51,52. The variability of the COVID-19 pandemic has an impact on the transportation scheduling and capacity issues of the renewable energy industry chain⁵³. At the same time, the impact on upstream companies is greater than that on downstream companies⁵⁴. Continuously assessing the impact of uncertainty and focusing on internal improvements in the industrial chain will enable the renewable energy industry to respond to risks flexibly^25,45. In terms of research methods, some scholars have constructed time-varying total volatility and paired volatility spillover indices based on the TVP-VAR-SV and DY models¹³. The COVID-19 pandemic has had a significant impact on the spillover effect of the solar market⁵⁵. The return and volatility spillover effects and their driving factors in clean energy, electricity, and metal material markets such as solar energy have been explored⁵⁶. There is a moderate degree of spillover effect among the three, with the solar energy market acting as the transmitter of the spillover effect and the electricity market acting as the receiver of the spillover effect. When extreme events such as the COVID-19 pandemic occur, the spillover effect will increase sharply. It can be seen that the research on the impact of uncertain events mainly focuses on the one-way and static impact on market risk transmission from a macro perspective.
However, existing research mainly focuses on the static structure and single event impact of the photovoltaic industry chain, and analyzes price fluctuations from the perspective of the macro industry chain. There is a lack of dynamic spillover effect analysis of price fluctuations in the photovoltaic industry chain market from the multi-dimensional perspectives of time-frequency domain, time delay and periodicity, making it difficult to capture the risk transmission intensity and optimal response cycle at a specific time point. At the same time, there is also a lack of linkage analysis between policy intervention (such as carbon neutrality) and industrial chain risk spillover effects, especially how to improve the stability of the industrial chain through dynamic risk management strategies under policy linkage. Therefore, this paper uses the TVP-VAR-DY and TVP-VAR-BK models to reveal the dynamic path, periodic characteristics and optimal time delay of risk spillover between key material markets in different links (upstream, midstream and downstream, as shown in Fig. 3), providing a precise time window for risk warning in each link of the industrial chain. In combination with the dual carbon goals and external shocks such as the epidemic, a phased dynamic risk management framework is proposed, thereby expanding the research dimension of industrial chain risk spillover.
The links of the photovoltaic industry chain.
The rolling window model is among the most commonly used methods. However, traditional rolling window settings may result in sample loss and unstable model outputs. DY spillover index model is highly sensitive to outliers⁵⁷. To overcome these limitations, Antonakakis et al. integrated the TVP-VAR-SV model with the DY spillover index⁵⁸, resulting in the TVP-VAR-DY model. The construction of this model involves the following key steps:
The TVP-VAR(p) model is expressed as follows:
Here, (:{y}_{t}) is an N×1 vector, where (:{B}_{t}) denotes the parameter matrix and (:{varSigma:}_{t}) denotes the time-varying variance-covariance matrix. The TVP-VAR(p) model is then estimated using the Kalman filter algorithm. H-step ahead forecasts are conducted, followed by the implementation of the Generalized Forecast Error Variance Decomposition (GFEVD), as follows:
(:{A}_{ij}) represents the response function. Based on the Generalized Forecast Error Variance Decomposition (GFEVD), the spillover effect from variable (:i) to variable (:j) is defined by the following formula:
(:{varSigma:}_{jj,t}) denotes the time-varying standard deviation of the (:j)-th error term, and (:{theta:}_{i}) is an indicator vector. To ensure comparability of the variance decomposition matrix, normalization is applied.
The Total Spillover Index (TSI) is calculated by summing all non-diagonal elements in the normalized variance decomposition matrix and dividing the result by the total number of variables.
Additionally, TO and FROM respectively represent the influence a single variable exerts on others and the influence it receives from them.
By combining the TO and FROM indices, the net spillover index (NET) for variable i relative to other variables is obtained.
The Net Pairing Directional Spillover Index (NPDS), which captures the net spillover between pairs of variables, is calculated using the following formula.
The market’s response to economic shocks differs across frequencies. Therefore, analyzing spillover effects between variables at multiple frequencies is essential. Building on Diebold and Yilmaz⁵⁹, Baruník and Křehlík⁶⁰ developed a method to calculate the spillover index across different frequencies. Subsequently, Barunik and Ellington⁶¹ integrated the BK spillover approach with the TVP-VAR model, proposing the TVP-VAR-BK model. This framework reveals spillover effects across frequencies and deepens the understanding of economic interrelations. The construction of the TVP-VAR-BK model involves the following steps:
The frequency response function is defined as follows:
Where (:i=sqrt{-1}). The general causal spectrum over frequencies (:omega:in:(-pi:,:pi:)) is defined as follows:
Formula (11) describes how the shock caused by variable i contributes to the spillover effect on variable j at frequency ω. The frequency band is defined as (a, b), where a < b and a, b∈(-π,π). At frequency d, the GFEVD is: (:i) affects the spillover effect on variable (:j) at frequency (:omega:). At frequency (:d), the GFEVD is defined as:
Here (:{W}_{i,t}left(omega:right)=frac{{theta:}_{i}^{{prime:}}{A}_{h}left({e}^{-iomega:}right){varSigma:}_{t}{A}_{h}^{{prime:}}left({e}^{-iomega:}right){theta:}_{i}}{frac{pi:}{2}{int:}_{-pi:}^{pi:}left({theta:}_{i}^{{prime:}}{A}_{h}left({e}^{-iomega:}right){varSigma:}_{t}{A}_{h}^{{prime:}}left({e}^{-iomega:}right){theta:}_{i}right)domega:}). Similarly, normalization is applied to ensure comparability across frequency bands:
Accordingly, the frequency-domain TSI, TO, FROM, and NPDS are calculated using the following formulas:
Tr{⋅} represents the trace operator.
This study first adopts the Minimum Variance Portfolio (MVP) model, introduced by Markowitz⁶², to evaluate the performance of risk-hedging portfolios in the photovoltaic industry chain. The MVP approach minimizes the overall variance of the investment portfolio, and the corresponding portfolio weights are computed as follows:
In Eq. (19), (:{omega:}_{{sum:}_{t}}) denotes an n×1 weight vector, I is an unit vector, and (:{sum:}_{t}) represents the n×n conditional variance-covariance matrix at time t. The net pairwise risk spillover index captures bidirectional interactions among variables in a multivariate setting and serves as a foundation for optimizing portfolio allocations. Accordingly, this study introduces the Minimum Net Pairwise Spillover Portfolio (MCoP1):
(:{NPDS}_{t}) denotes the net pairwise directional connectedness matrix at time t. The pairwise net spillover index considers only interactions within a bivariate system and may overlook the potential influence of third-party variables on these relationships. The risk spillover index can serve as a proxy for measuring asset interactions in a multivariate system and can also be employed for portfolio optimization. Based on the above considerations, this study further proposes the Minimum Spillover Portfolio (MCoP2):
(:{TCI}_{t}) denotes the total spillover index matrix at time t.
The performance of the three portfolios is evaluated using the Sharpe Ratio (SR). The Sharpe Ratio, introduced by Sharpe⁶³, measures the excess return of a portfolio relative to its risk. Also known as the reward-to-volatility ratio, it is calculated as follows:
Where, (:{r}_{p}) denotes the return of the portfolio, assuming a zero risk-free rate, and (:varleft({r}_{p}right)) represents the variance of the portfolio. The Sharpe Ratio provides a metric for evaluating a portfolio’s return relative to its risk. It facilitates portfolio comparison, with the optimal portfolio being the one with the highest SR value-that is, the highest return for a given level of risk.
Capital markets, characterized by high-frequency trading, rapid responsiveness, and efficient information aggregation, can promptly reflect potential inter-firm linkages and the transmission pathways of systemic risk. Therefore, they offer distinct advantages in revealing supply chain structures, industrial co-movement mechanisms, and risk spillover effects^64,65,66. Based on this, the study uses the closing prices of A-share listed companies representing key segments of the photovoltaic industry chain, ranging from upstream to downstream, as the research sample. These segments include silicon materials (Si), silver paste (SP), photovoltaic cells (CELL), inverters (INV), PV brackets (PB), PV backsheets (PBS), PV glass (PG), PV modules (PM), and PV power stations (PPS).
All A-share companies are manually screened. Firms were included if they had a clearly defined core business in the photovoltaic industry chain and derived at least 20% of their revenue from related business in each of the past two annual reports. Firms with ST or ST* status or with prolonged suspensions that compromise data continuity were excluded. Missing closing prices due to non-trading days or temporary suspensions were imputed using the last available closing price. Following Zhao et al.⁶⁷, weighted averages are applied to construct representative market indices for each segment. To address potential heteroscedasticity, the raw data were log-transformed and differenced at the first order. Considering the global rise in environmental awareness and stricter policies since 2017, which have driven solar capacity to grow faster than all fossil fuels combined-the sample period is set from January 2017 to December 2024.
Return series.
Figure 4 displays the time series of returns for each variable, and Table 1 reports the corresponding descriptive statistics. The descriptive statistics show that all variables have positive mean returns, indicating an overall upward trend during the sample period. Notably, inverters (INV) and photovoltaic power stations (PPS) exhibit relatively higher average returns (0.0017 and 0.0013, respectively), suggesting potential investment advantages. However, photovoltaic backsheet (PBS), despite having the highest mean return (0.0019), also exhibits the largest standard deviation (0.0357) and the highest maximum value (0.4399), indicating substantially higher volatility and risk relative to other segments of the value chain.
Regarding skewness and kurtosis, most return distributions are right-skewed, though the overall skewness values remain modest, implying relatively symmetrical volatility. Only PBS (skewness = 1.52; kurtosis = 14.72) shows pronounced right skewness and leptokurtic behavior, indicating a higher probability of extreme positive return events. The Jarque-Bera (JB) test and the Augmented Dickey-Fuller (ADF) unit root test both reject the null hypotheses at the 1% significance level, confirming that all variables deviate significantly from normality and are stationary. These properties justify their suitability for subsequent time series modeling and empirical analysis.
The VAR model’s lag order is set to 1 based on the AIC, BIC, and HQIC criteria (see Appendix A for details). Following Tiwari et al.⁶⁸ the forecast horizon for variance decomposition is set to 100 steps. Time-domain total spillover effects between markets are calculated using the TVP-VAR-DY method, as reported in Table 2.
The total spillover effect within the photovoltaic industry chain reaches 75.00%, indicating substantial risk transmission among its segments. More than half of the volatility observed during the sample period originates from cross-segment spillovers within the photovoltaic industry chain. This may be attributed to the fact that firms’ market performance is often regarded as a barometer of broader industry development. When significant information arises in one segment, investors tend to adjust expectations across others, leading to co-movements in prices, trading volumes, and related indicators. The dissemination of public information further amplifies systemic responses.
Upstream silicon materials (Si) and photovoltaic modules (PM) exhibit the highest net spillover effects — 12.42% and 15.26%, respectively — indicating that they serve as primary risk transmitters within the system, exerting strong spillover impacts on downstream segments. In contrast, silver paste (SP), PV backsheet (PBS), and PV glass (PG) primarily act as risk recipients, with net values of −17.44%, −14.99%, and − 5.09%, respectively, reflecting greater exposure to volatility transmitted from other segments. Midstream components-photovoltaic cells (CELL) and inverters (INV) — also exhibit strong spillover capacities, with TO values reaching 87.34 and 84.96, respectively, underscoring their central roles in the transmission of information and risk. Overall, risk spillovers within the photovoltaic industry chain are primarily concentrated in the upstream and module segments, whereas midstream and downstream segments tend to function as passive recipients.
To systematically analyze the spillover characteristics of the photovoltaic industry chain across different frequency domains, this study employs the TVP-VAR-BK approach to quantify risk spillovers in the short-, medium-, and long-term bands. Following Deng and Xu⁶⁹, the time domain is divided into three frequency intervals: short-term (1–5 days), medium-term (5–22 days), and long-term (more than 22 days). The spillover results for each frequency domain are summarized in Table 3.
The risk spillover effects of the photovoltaic industry chain in the high-, medium-, and low-frequency bands are 60.91%, 9.37%, and 4.72%, respectively. The sum of these spillover effects constitutes the total spillover in the time domain. Spillover effects among markets are significantly higher in the high-frequency domain than in the medium- and low-frequency domains, indicating that risk spillovers within the photovoltaic industry chain are predominantly driven by high-frequency components—that is, they are mainly concentrated in the short term⁷⁰. This phenomenon can be attributed to the fact that market participants typically operate with short investment horizons, favoring short-term speculation and trading, which in turn accelerates cross-market risk transmission over short periods⁷¹.
Across frequency bands, the total spillover effect shows a declining trend from the short to the long term, suggesting that climate policy uncertainty exerts relatively limited long-term (low-frequency) shocks on energy and metal markets. This provides empirical support for investors seeking diversification and stability in long-term returns⁷².
To intuitively capture the inter-market linkage structure, this study adopts a complex network analysis approach to construct the spillover network of the photovoltaic industry chain, thereby characterizing its risk transmission pathways. As shown in Fig. 6, across both time and frequency domains, silver paste (SP), PV brackets (PB), PV backsheets (PBS), and PV glass (PG) consistently function as primary receivers of risk spillovers, whereas downstream markets persist as key transmitters of risk.
Network characteristics further suggest that inter-market connectivity is more pronounced in the time domain and the short-term frequency band. Risk transmission within the photovoltaic industry chain occurs primarily in the short term, and the network roles of various nodes remain relatively stable across both short- and medium-to-long-term frequency domains. Overall, risk spillovers are concentrated in the upstream and module segments, while the midstream and downstream segments primarily act as passive recipients. This pattern reflects a typical ‘’upstream-driven, downstream-responsive’’ risk contagion mechanism embedded in the structure of the photovoltaic industry chain.
Net Pairing Directional Risk Spillover Network in Time and Frequency Domain. Note: Node size represents the net pairwise spillover effect of the corresponding variable, while edge thickness and arrow direction indicate the magnitude and direction of the spillover effects. Additionally, blue nodes represent net transmitters, and yellow nodes represent net receivers.
While the static spillover analyses in Tables 2 and 3 capture the direction and average intensity of spillovers among variables over the sample period, they do not reflect temporal variations in spillover effects across markets. Consequently, this section explores the dynamic evolution of spillover indices among the variables.
As shown in Fig. 6, the total spillover effect within the photovoltaic industry chain exhibits significant time variation, fluctuating between 60% and 85%, and is closely linked to factors such as policy changes and profit distribution. Following the introduction of the ‘’531 New Policy’’ in 2018, structural shifts in market expectations led to a sharp increase in the spillover index between 2018 and 2019, prompting substantial adjustments in the business models of photovoltaic enterprises.
Since 2019, the upstream silicon materials sector has experienced accelerated consolidation, with leading firms gaining pricing power and rapidly expanding their market share. This heightened industry concentration has sustained a high spillover index, reflecting the rapid transmission of upstream volatility to midstream and downstream segments. Since 2022, a sharp increase in silicon material prices has compressed profit margins in the midstream module and downstream power station segments, leading to a gradual rise in the spillover index. This trend reflects a chronic risk accumulation and transmission mechanism driven by internal profit redistribution pressures across the industry chain. In 2024, under the continued advancement of the ‘’dual-carbon’’ goals, the photovoltaic industry entered a new phase of capacity expansion. In particular, renewed fluctuations in upstream silicon material prices, coupled with escalating international trade tensions, further amplified market volatility and contributed to a continued rise in the spillover index.
From a frequency-domain perspective, the total spillover effect in the time domain closely mirrors the evolutionary trajectory of short-term spillovers within the photovoltaic industry chain. Moreover, short-term spillovers are markedly stronger than those in the medium- and long-term frequency bands, indicating that interactions among key materials are primarily concentrated in the short term, with spillover intensity diminishing over time and gradually stabilizing. The heterogeneity of spillover effects across frequency domains highlights differences in investor preferences and behavior, suggesting a tendency to prioritize short-term market performance⁷³.
Dynamic total risk spillover effects in time and frequency domain. Total spillover effect (black shaded area); short-term spillover effect (red shaded area); medium-term spillover effect (blue shaded area); long-term spillover effect (green shaded area).
To analyze the roles, relative positions, and time-varying characteristics of individual markets within the photovoltaic industry chain, this section presents trend graphs of net spillover effects across both the time and frequency domains, as illustrated in Fig. 7.
Across both the time domain and the high-frequency band, net spillover trends remain largely consistent, exhibiting considerable volatility across markets. Upstream silicon materials (Si) consistently act as a positive source of risk spillovers, suggesting that under conditions of high industry concentration and reduced subsidies, their cost fluctuations are rapidly transmitted downstream. In the midstream segment, photovoltaic cells (CELL) and inverters (INV)—driven by rapid technological advancements and the pursuit of high conversion efficiency and intelligent technologies—have gradually emerged as new sources of risk spillovers, exerting considerable transmission pressure on both upstream and downstream segments. Downstream photovoltaic power stations (PPS), affected by the phase-out of subsidies and shorter project development cycles, face increased uncertainty in cash flow and expected returns, and consequently exhibit pronounced risk spillover characteristics.
Overall, the withdrawal of subsidies has reinforced the upstream segment’s dominance in price formation, while technological upgrades have amplified market volatility in the midstream. Together, these factors contribute to the short-term and concentrated nature of risk transmission across the photovoltaic industry chain.
Dynamic net spillover effects in time and frequency domain.
This section analyzes the net pairwise risk spillovers within the photovoltaic industry chain. Figure 8 presents the net pairwise risk spillover values, where values below zero indicate that a market is a net receiver of risk spillovers, while values above zero indicate that it is a net transmitter to specific markets.
Throughout the development of the photovoltaic industry chain, net pairwise risk spillovers exhibit a distinct chain — like structural pattern. Specifically, midstream segments such as photovoltaic cells (CELL) and modules (PM) exhibit strong risk transmission to downstream photovoltaic power stations (PPS), indicating that manufacturing segments exert significant influence over end-use applications. In contrast, upstream raw materials such as silicon (Si) and silver paste (SP) generate positive net spillovers toward multiple midstream segments, reflecting the significant influence of raw material prices and supply-demand dynamics on midstream operations. In the short term, spillover effects from upstream materials to midstream segments are further amplified, suggesting that raw material price fluctuations have strong immediate transmission effects in the spot market-particularly under the combined impact of subsidy phase-out and market-oriented reforms.
From a medium- to long-term perspective, midstream non-core segments — such as inverters, brackets, and photovoltaic glass — exhibit relatively weaker spillover capacity, whereas modules (PM), driven by rapid technological advancements, display greater spillover volatility over the same horizon. Moreover, technological advancements and policy shifts have collectively reshaped risk transmission pathways across different stages, reinforcing feedback effects from midstream to upstream segments. Overall, while the photovoltaic industry chain exhibits increasingly integrated dynamics, inter-segment risk spillovers remain highly time-varying.
Dynamic net pairing risk spillover effects.
Building on the analysis of time-varying spillover effects in the photovoltaic industry chain presented in Sect. Analysis of dynamic risk spillover effects (see Figs. 6, 7 and 8), this section focuses on formulating and optimizing hedging strategies for risk management. The preceding analysis reveals significant time-varying spillover effects across different segments of the photovoltaic industry chain over short-, medium-, and long-term horizons. This finding provides a theoretical foundation for developing dynamically adjustable portfolio strategies. Accordingly, this section integrates the net and total spillover indices of each segment in the industry chain to construct an optimal investment portfolio, aiming to balance risk minimization with return stability.
This section focuses on the implementation of bilateral hedging strategies. The objective is to construct an optimal investment portfolio based on long and short market positions, estimate hedge ratios, and evaluate the effectiveness of the strategy in mitigating risk and enhancing returns. Through quantitative analysis, this section systematically demonstrates the feasibility and practical relevance of bilateral hedging in the context of the photovoltaic industry chain.
Specifically, Panel A of Table 4 summarizes the optimal hedge ratios for key material pairs, offering empirical support for the design of precise hedging strategies. The results show that optimal hedge ratios across materials in the photovoltaic industry chain range from 0.22 to 0.91, indicating substantial hedging potential among various asset combinations. For example, the Si/SP (silicon and silver paste) pair yields a hedge ratio of 0.3, implying that for every $1 invested in silicon, a $0.3 short position in silver paste is sufficient to partially hedge against market risk. This relatively low hedge ratio reflects reduced hedging costs and indicates high risk management efficiency.
In addition to hedge ratio analysis, the study further examines the risk — return characteristics of bilateral portfolios. Panel B of Table 4 reports the optimal weight allocations for each portfolio and assesses their effectiveness in risk mitigation. The results indicate that when two markets are combined into a hedging portfolio, overall volatility declines significantly relative to the unhedged case, with reductions ranging from 2 to 69%, highlighting the strong hedging effectiveness of bilateral portfolios. Therefore, bilateral hedging strategies demonstrate considerable effectiveness in mitigating overall risk across the photovoltaic industry chain.
This section constructs portfolios based on three investment strategies — Minimum Variance Portfolio (MVP), Minimum Net Pairwise Spillover Portfolio (MCoP1), and Minimum Spillover Portfolio (MCoP2) — and systematically compares their relative performance and risk management effectiveness.
As shown in Fig. 9, the cumulative returns of the three strategies exhibit notable differences in their risk-return profiles. The MVP strategy demonstrates relatively low volatility and stable, albeit modest, returns, reflecting a high degree of robustness. MCoP1 outperforms MVP in most periods, indicating that it effectively controls net systemic risk spillovers while generating considerable excess returns, thereby exhibiting strong risk-adjusted performance. MCoP2 achieves the highest cumulative returns, with overall performance significantly exceeding that of the other two strategies. This highlights its superior capacity to suppress cross-market risk transmission and exploit favorable structural investment opportunities within the spillover network.
Cumulative returns.
This section further examines and compares the return-to-volatility ratio, namely the Sharpe ratio, as reported in Table 5. The Minimum Spillover Portfolio (MCoP2) consistently records the highest Sharpe ratio across most periods. Notably, prior to the implementation of the ‘’531’’ policy, MCoP2 achieved a Sharpe ratio of 3.8545, significantly outperforming other strategies and indicating robust risk-adjusted return capacity in the absence of policy disruptions. However, following the policy’s implementation, its Sharpe ratio declined to 1.4902, and the differences among strategies narrowed, reflecting heightened market uncertainty resulting from the policy shock. After the announcement of the carbon neutrality policy, the Sharpe ratios of all three strategies increased significantly, suggesting that the policy’s development incentives improved overall market performance, with MCoP2 continuing to outperform.
During the pre- to mid-pandemic phases, the average Sharpe ratios of all strategies gradually increased, indicating strong adaptability to volatile market conditions. In contrast, during the post-pandemic phase, all three strategies exhibited negative Sharpe ratios, reflecting heightened market risk and severe return drawdowns. Strategy effectiveness declined markedly, with MVP performing the worst-recording a Sharpe ratio of −1.2194. Overall, spillover-based strategies outperform the traditional minimum variance approach in terms of risk-adjusted returns across most periods, demonstrating superior market responsiveness and portfolio allocation value.
To assess the robustness of the spillover effect results within the photovoltaic industry chain, this study conducts robustness checks by substituting the TVP-VAR model with a conventional VAR model, modifying the forecast horizon, and adjusting Kalman filter parameters. The results of the robustness checks are largely consistent with those shown in Fig. 10, confirming the empirical findings’ stability.
Robustness test.
Note: Rolling Window represents the dynamic risk total spillover index calculated after replacing the original TVP-VAR model with the VAR model. Forecast means setting the forecast period to 50, and Parameter means adjusting the Kalman filter smoothing parameter to 0.95.
This study conducts a systematic analysis of risk spillover dynamics and investment strategies within the photovoltaic industry chain, leading to the following key conclusions: First, the photovoltaic industry chain exhibits pronounced short-term risk spillover effects, with a total spillover rate reaching 75%. Upstream silicon materials and photovoltaic modules are identified as the primary sources of risk transmission, whereas mid- to downstream segments such as silver paste and photovoltaic glass primarily act as risk recipients. Second, the spillover structure is highly time-varying, shaped by policy shocks (e.g., the ‘’531’’ policy) and price fluctuations. Complex network analysis reveals the interconnectivity and directional nature of risk transmission among segments, reflecting a typical ‘’upstream-driven, downstream-responsive’’ contagion pattern. Finally, investment strategies based on spillover effects — such as the Minimum Spillover Portfolio (MCoP2) — consistently outperform the traditional Minimum Variance Portfolio (MVP) in terms of risk–return efficiency. Additionally, bilateral hedging strategies demonstrate notable advantages in reducing portfolio volatility and controlling costs, underscoring their practical relevance as effective risk management instruments within the photovoltaic industry chain. Based on the main conclusions, this paper puts forward the following policy implications:
First, drawing on the experience of the drastic fluctuations in the industrial chain under the impact of the “531” policy, enterprises need to establish a dynamic policy response mechanism. Encourage enterprises in silicon materials, batteries, inverters and other links to focus on carbon neutral technology research and development, and deepen cooperation through strategic alliances, joint laboratories and other forms. Regulatory authorities maybe should improve the standard system for the entire life cycle of photovoltaic products, guide enterprises to collaborate and innovate in areas such as green manufacturing and recycling, and avoid disorderly market competition caused by policy adjustments.
Second, in view of the high energy consumption and long cycle characteristics of the upstream silicon material link, combined with the requirements of carbon neutrality for the transformation of the energy structure, support polysilicon enterprises to carry out low-carbon technology research, such as promoting water electrolysis to produce hydrogen to reduce carbon emissions. Simultaneously promote the “zero-carbon” transformation of photovoltaic industrial parks, and use distributed photovoltaic and energy storage systems to achieve energy self-sufficiency in the park. Investors could focus on the layout of the carbon neutral industry chain, give priority to supporting enterprises with green certification and low-carbon technology reserves, and help the industry accelerate towards the “double low” goal.
In addition, referring to the short-term impact of the “531” policy on market supply and demand, policy formulation needs to focus on stability and foresight. Local regulatory authorities should combine carbon neutrality policies to scientifically guide the regional layout of the photovoltaic industry chain. In areas such as Sichuan and Yunnan, which are rich in hydropower resources, high-energy-load silicon material industries should be developed based on the advantages of clean energy. In the eastern coastal areas, focus on the technological upgrades of component manufacturing, system integration and other links to form a gradient collaborative model of “raw material production in the west – technology transformation in the east”.
Finally, establish a risk early warning mechanism for the linkage of “policy – market – enterprise”, and formulate an industry chain emergency plan in advance for potential shocks such as the decline of electricity price subsidies and the tightening of carbon emission quotas in the process of promoting carbon neutrality policies. Regulatory authorities maybe should improve the photovoltaic product price monitoring platform, track the cost fluctuations of each link in real time, and strictly investigate and punish market-disrupting behaviors such as price gouging and malicious dumping in accordance with the law. Encourage enterprises to hedge policy and market risks through financial instruments such as carbon trading to enhance the overall risk resistance of the industry chain.
Future research will consider employing Threshold Vector Autoregression (TVAR) and other advanced nonlinear models to improve the capacity of existing frameworks in capturing complex nonlinear dynamics and addressing sudden structural shifts. In addition, the scope of analysis will be expanded to incorporate a broader set of markets and an extended sample period. Further research will examine the asymmetric nature of risk spillovers in the photovoltaic industry chain, with an emphasis on decomposing market fluctuations into positive and negative components and analyzing their respective impacts.
Data sets generated during the current study are available from the corresponding author on reasonable request.
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