How Do Carbon Market and Fossil Energy Market Affect Each Other During the COVID-19, Russia–Ukraine War and Israeli–Palestinian Conflict?

Abstract

Despite the close linkage between carbon markets and fossil fuel markets, minimal research has investigated their co-movement dynamics during times of heightened geopolitical instability and public health crises, including the COVID-19 pandemic, Israeli–Palestinian conflict, and the Russia–Ukraine war. Most studies use conditional mean regression models for testing linear Granger causality, which falls short in assessing time-varying causal relationships. This paper employs a time-varying Granger causality framework to examine the dynamic linkages between fossil fuel markets and carbon markets across multiple time horizons. This methodology enables the evaluation of causal relationships that evolve over time, providing deeper insights into how the carbon market interacts with traditional fossil fuel markets. The study examines causal linkages among carbon, coal, and oil prices from 2 January 2018 to 11 July 2025, using data from Wind Database. The findings reveal a short-lived yet highly significant bidirectional causality between the carbon and fossil fuel markets during the COVID-19 period, whereas a sustained and highly significant bidirectional causal relationship emerges after the onset of the Russia–Ukraine war. During the outbreak of the Israeli–Palestinian conflict, this linkage continued without major disruptions or directional shifts. Furthermore, the recursive evolution approach, based on variable sub-window sizes, detects additional evidence of significant bidirectional causal relationships among carbon, coal, and oil prices. These discoveries can serve as valuable inputs for investors and policymakers, enabling them to make informed decisions that protect their interests and ensure market stability. Additionally, coal prices showed greater persistence than oil prices in these bidirectional causal links.

1. Introduction

1.1. Research Background and Significance

Geopolitical risks, encompassing wars, terrorist attacks, and national tensions, alongside global health crises like the COVID-19 pandemic, constitute a pivotal factor in shaping investment decisions and serve as a primary cause of volatility in both the carbon and fossil fuel markets [1]. COVID-19 caused unprecedented disruptions to global supply chains, energy demand patterns, and economic activity, leading to significant market fluctuations [2]. Following the outbreak of a fresh wave of Israeli–Palestinian conflict on 7 October 2023, the stock markets of both Palestine and Israel witnessed significant declines, coinciding with a substantial surge in global panic and economic uncertainty [3]. Furthermore, the escalating nature of the conflict has propelled an increase in global crude oil and natural gas prices. Meanwhile, the enduring conflict between Russia and Ukraine has inflicted substantial damage on the world economy and imparted considerable uncertainty to international trade. Russia and Ukraine occupy a prominent position as major suppliers and exporters of global energy commodities. Consequently, the conflict has exerted a detrimental influence on the prices of energy commodities, particularly crude oil, natural gas, and coal. In light of these developments, examining the carbon and fossil fuel markets during the periods of the COVID-19 pandemic, the Russia–Ukraine war, and Israeli–Palestinian conflicts assumes significant economic importance. Such an investigation holds the potential to unveil valuable insights into the intricate dynamics shaping these markets and their sensitivity to geopolitical disruptions, thereby informing more informed and strategic investment decisions.

Fossil fuels, particularly those utilized in industries and electricity generation, constitute the primary source of carbon emissions [4]. Carbon emissions trading significantly influences energy production and consumption. Meanwhile, enterprises strive to optimize the balance between energy costs and carbon emissions to maximize profits [5]. Changes in energy prices can substantially affect energy use, subsequently influencing carbon allowance demand [6]. During the COVID-19 pandemic, several scholars investigated the link connecting carbon and fossil fuel markets [7]. However, in the wake of recent geopolitical conflicts, much of the focus has shifted to examining the interplay between fossil fuels and renewable energy sources. Little attention has been paid to whether the interplay of fossil fuel and carbon prices has undergone any changes in such a volatile environment. While much of the existing literature acknowledges a strong dynamic coexistence of these markets, with patterns varying over time, none have utilized the tvgc approach to explicitly examine their time-varying dynamics under different market conditions influenced by geopolitical conflicts and public health crises.

1.2. Research Objectives and Hypotheses

This study employs a time-varying Granger causality (TVGC) framework to investigate the dynamic bidirectional causal linkages between carbon prices and key fossil fuel prices during periods of heightened geopolitical tension and public health crises, specifically the COVID-19 pandemic, Russia–Ukraine war, and Israeli–Palestinian conflict. Based on the identified gap, this study aims to answer the following research questions. First, how do the bidirectional causal linkages between carbon prices and fossil fuel prices evolve during major geopolitical and public health crises? Second, do these causal linkages differ significantly across these crisis types in terms of their intensity and persistence? Third, which fossil energy source exhibits a stronger and more persistent causal relationship with carbon prices during these turbulent periods? To empirically address these questions, we posit the following hypotheses:

H1. 

Geopolitical crises and public health crises strengthen their causal transmission to the carbon market through the price channel of fossil energy.

H2. 

The impact of the Israeli–Palestinian conflict is less than that of the Russia–Ukraine war and COVID-19.

H3. 

Bidirectional carbon–fossil fuel causality strengthens during crises, with coal exhibiting greater persistence than oil.

Understanding the relationship linking carbon prices and fossil fuel prices is economically and environmentally significant. First, manufacturing companies are increasingly seeking to lower their dependence on fossil fuels to mitigate greenhouse gas emissions and boost efficiency [8,9]. Secondly, the global energy landscape remains uncertain, influenced by various factors including public health crises, geopolitical conflicts, climate change, and exchange rate fluctuations [10]. Examining interactions between carbon and fossil fuel markets during these conflicts is crucial for ensuring effective environmental regulatory procedures. This, in turn, can aid in reducing carbon emissions, appropriately adjusting energy consumption structures and implementing optimal carbon reduction strategies.

1.3. Research Contribution

The first core contribution of this study is the application of the time-varying Granger causality test ( TVGC) to analyze carbon and fossil energy prices. This approach enables us to gain a more nuanced understanding of the dynamic relationship between these two key market indicators. To ensure the robustness of our findings, we have employed three detection methods within the framework of the time-varying Granger test: the forward expanding Wald test, the rolling Wald test, and the recursive expanding Wald test [11,12,13,14]. Each of these methods offers a unique perspective on causality, allowing us to triangulate our results and arrive at a more comprehensive conclusion. One of the key advantages of the tvgc is its ability to pinpoint causality within a specific time period. This is particularly useful in the context of public health crises and geopolitical conflicts, as it allows us to observe changes in causality that may occur in response to such events. By analyzing the data through this lens, we can gain valuable insights into how these conflicts impact the global energy market. Furthermore, the flexibility of the tvgc program allows us to adjust the window size during the detection process. This means that we can zoom in on particular time frames to identify more precisely the duration of causal relationships. Such temporal precision is indispensable for analyzing how carbon and fossil energy prices interact, a process that is both complex and volatile.

The second key contribution is the analysis of causal relationship changes during the specific contexts of COVID-19, the Russia–Ukraine war, and the Israeli–Palestinian conflict. In recent years, both the Russia–Ukraine war and the Israeli–Palestinian conflict have caused significant disruptions in the international energy market. These conflicts have led to supply shortages and commodity price shocks that have, in turn, posed serious threats to the stability of the financial system. Given the far-reaching economic and political implications of these events, it is crucial to understand how they have influenced the interdependence of carbon and fossil energy prices.

The third key contribution is that we pioneer the integration of crisis typology theory with advanced time-varying econometrics. By conceptualizing distinct crisis modalities, such as transient health shocks like COVID-19 versus sustained geopolitical conflicts like the Russia–Ukraine war, we uncover how the duration and nature of crises fundamentally modulate the causality regimes between carbon and fossil energy markets. This theoretical–methodological synergy reveals dynamics—such as the shift from short-lived to entrenched bidirectional causality—that static linear frameworks inherently overlook.

Our study provides a rigorous analysis of the causality between these two markets in the context of these geopolitical conflicts and public health crises. We believe that this research has vital practical significance for investors, policymakers, and other stakeholders who are seeking to navigate the increasingly volatile and interconnected global energy landscape. For investors and other market participants, understanding how carbon and fossil energy prices interact causally can inform more effective hedging and risk diversification strategies. By anticipating how these markets may respond to geopolitical events and public health crises, they can make more informed decisions about where and when to allocate their capital. Similarly, policymakers can use this information to develop more targeted and effective policies that mitigate the systemic risks posed by these interconnected markets. By monitoring the direction of causality, they can identify potential vulnerabilities and take proactive measures to prevent the transmission of risks between markets. In this way, our research contributes to the broader goal of enhancing the resilience and stability of the global financial system.

The manuscript is structured as follows: Section 2 reviews the existing literature on carbon–energy linkages. Section 3 details data sources from Wind and the time-varying Granger causality framework. Section 4 presents empirical results demonstrating crisis-specific causality patterns. Section 5 concludes with policy recommendations and research limitations.

2. Literature Review

Some researchers have delved into the intricate relationship between carbon prices and energy prices. Their findings reveal that energy prices, particularly those of fossil fuels like natural gas and coal, exert a significant influence on carbon prices [15,16,17,18]. This influence stems from the fact that the utilization of fossil fuels is a primary contributor to carbon emissions. Fossil fuels are extensively utilized in various aspects of human production and daily life, ranging from transportation and energy generation to industrial manufacturing. Scholars have also elucidated how fossil fuel switching impacts carbon prices for power companies, citing the effect of fuel switching and carbon demand aggregation. Energy prices, particularly those of fossil fuels, have a notable impact on carbon prices. This impact is primarily attributed to the carbon emissions resulting from fossil fuel usage. Consequently, in the context of power companies, the transition from one fossil fuel to another can have implications for carbon prices, necessitating consideration of both fuel switching and carbon demand aggregation effects [19,20].

The carbon market exerts a substantial influence on energy prices. The carbon emissions trading mechanism seeks to enhance energy structure and efficiency, thereby reducing carbon emissions and influencing the traditional energy market. Research by Lin and Li [21] demonstrates that the output of the energy sector is more sensitive to the price of the carbon emissions trading system (ETS) compared to other industries. Yu et al. [22] employed both linear and nonlinear Granger causality to distinguish between different time scales, revealing the linkage mechanisms between the two markets. There exists a notable bidirectional influence relationship between the carbon market and the energy market. Through the carbon emissions trading mechanism, the carbon market can affect energy prices, and the output of the energy sector is highly sensitive to carbon prices. Therefore, studying the linkage mechanisms between these two markets is crucial for a comprehensive understanding of their relationship.

The COVID-19 pandemic has profoundly impacted the global energy system. Existing research mainly explores the sharp decline in fossil energy demand and price fluctuations caused by the pandemic, as well as the potential impetus for the development of renewable energy [23]. Meanwhile, there are also studies focusing on the short-term impact of the stagnation of economic activities at the beginning of the epidemic on the carbon market, particularly on elements such as carbon prices [24]. However, the time-varying characteristics of the dynamic interaction between the carbon market and the fossil energy market during the epidemic period have not been deeply explored in the existing literature.

The Russia–Ukraine war has been a hotly discussed topic in recent years. For the study of the influence of the Russia–Ukraine war on energy, the first strand of the literature focused on renewable energy. The war between Russia and Ukraine led to an increased emphasis on renewable energy [25]. Some scholars studied clean energy stock prices during the Russia–Ukraine war and argued that renewable energy companies benefited during the Russia–Ukraine war [26,27]. The second strand of the literature investigated traditional sources of energy. Most studies explored energy security during the war. Ozawa [28] proved Europe’s energy dependence on Russia became especially relevant. A number of scholars [29,30] introduced that European countries have determined to reuse fossil fuels to reduce the risk of insufficient gas supplies. In addition, some scholars have studied the influence of the Russia–Ukraine war on the carbon market. Bun [31], who has been tracking unaccounted greenhouse gas emissions from the war in Ukraine since 2022, believes that total greenhouse gas emissions are likely to decrease due to higher energy and fertilizer prices and reduced fossil energy use. The above literature studies the issues of renewable energy transition and energy security caused by the Russia–Ukraine war, but there are few studies on the time-varying interaction between the carbon market and fossil energy market.

The Israeli–Palestinian conflict escalated dramatically after the October 2023 attacks, triggering severe humanitarian crises including widespread famine in Gaza. From a political science perspective, such conflicts exemplify how asymmetric power dynamics weaponize resource access; Israel’s control over Gaza’s supply routes directly constrained fuel distribution, exacerbating energy insecurity. By 2025, 92% of Gaza’s population relied on humanitarian aid for basic energy needs, reflecting the conflict’s entrenched impact on energy–poverty nexuses. Most of the previous research has focused on climate change and energy security. There has been very little research on energy in the context of the new Israeli–Palestinian conflict. Cui & Maghyereh [3] research the higher-order moments of geopolitical risk for energy. There has been no study of the linkage between carbon and energy markets in the Israeli–Palestinian conflict.

The causal mechanisms between carbon prices and fossil fuels diverge significantly for crude oil versus coal. Crude oil impacts carbon prices indirectly via transportation and industrial demand elasticity; price spikes during conflicts may temporarily reduce consumption but spur long-term substitution with renewables [32]. Conversely, coal, as a primary electricity source, exhibits direct causality: coal price surges directly raise carbon costs due to higher emission intensity, especially in regions reliant on coal-fired power [33]. Recent evidence confirms this asymmetry—compared with the indirect effect of oil, geopolitical events will have a greater impact on the direct effect of coal [34].

Scholars have employed various models and methodologies to explore the link connecting two markets. While the VAR framework captures joint dynamics [35], and Granger causality identifies predictive relationships [36], cointegration analyses extend to both linear and nonlinear frameworks. Particularly, the ARDL approach introduced by Kilinc-Ata [37] provides robust cointegration assessment without pre-testing integration orders, especially valuable for environmental–economic systems. Beyond causality, the NARDL method captures asymmetric responses to positive or negative shocks [38]. Modern techniques include the PCMCI algorithm [39], which addresses high-dimensional causal networks with noise resilience, overcoming traditional Granger limitations. Volatility modeling further employs GARCH variants and copulas [40,41] to cluster volatility and model tail dependencies.

While existing studies confirm that carbon and fossil energy prices exhibit bidirectional causality in stable periods [42], this relationship is predominantly linear and static. Geopolitical conflicts and public health crises introduce nonlinear shocks by disrupting supply chains, altering energy demand, and amplifying market uncertainty. For instance, during the Russia–Ukraine war, fossil energy shortages intensified carbon price volatility via ‘fuel-switching effects’ [43]. Crucially, time-varying Granger causality (TVGC) methods reveal that these events transform short-term causalities into sustained bidirectional linkages, which standard linear models fail to capture [4,44]. Thus, analyzing conflict periods is not redundant but essential to uncover dynamic mechanisms, such as how crisis-induced policy shifts rewire carbon–energy interdependencies.

X. Ma et al. [45] analyze the interaction between geopolitical risk and the carbon and crude oil markets from a multi-timescale perspective. Yang et al. [46] use a vector error correction model (VECM) to explore the connection linking oil prices and carbon emissions. Ding et al. [33] use BK spillover measures and Tao et al. [47] use a DY approach to explore spillovers across carbon and fossil energy markets. Alkathery & Chaudhuri [48] use multivariate GARCH models to detect co-movement in these markets. Jiang et al. [49] apply the Granger causality method on quantiles to investigate bidirectional causality linking carbon prices and fossil fuels. However, merely considering temporal relationships or merely studying linkages across markets may not capture the true workings of connectivity when markets are hit by multiple events. Moreover, it is less clear whether there is a random influence among their prices from a time-varying perspective.

The time-varying Granger test ( TVGC) model is widely used to detect time-varying relationships between energy and other variables. Ren et al. [44] have used time-varying Granger tests to detect the impact of climate policy uncertainty on traditional energy. Huo et al. [50] use this method to detect the discontinuous effects of policy uncertainty on renewable energy. Dogan et al. [51] apply this method to investigate the causal relationship between bitcoin, clean energy, and carbon emissions allowances. Compared with other methods, this method can identify the causal relationship between different time periods and time points, so it is more convenient to study the change in the causal relationship in different periods.

3. Materials and Methods

3.1. Data

This paper aims to analyze the time-varying causal relationship during COVID-19, the Russia–Ukraine war, and the Israeli–Palestinian conflict. But, more importantly, it analyzed the Israeli–Palestinian conflict and the Russia–Ukraine war. The acute phase of the COVID-19 pandemic began in December 2019 and had largely subsided by the time of this study. The Russia–Ukraine war erupted in February 2022, and the Israeli–Palestinian conflict erupted in October 2023, both of which were ongoing at the time of writing.

The utilization of fossil energy prices encompasses the futures settlement prices of crude oil and coal, alongside the futures settlement prices of EUA (European Union Allowance) products. Referencing of the recent literature ensures the relevance and recency of the data and methodologies employed. The European Climate Exchange (ECX), traded on the Intercontinental Exchange (ICE), serves as the source for providing EUA futures settlement prices, offering a reliable and transparent platform for pricing emissions allowances. In the computation of fossil fuel costs, continuous settlement prices of ICE Rotterdam coal futures and Brent crude oil futures are employed, providing a comprehensive view of energy market dynamics. The sample dates are selected from 2 January 2018 to 11 July 2025, the data frequency is once a day, and 1442 observations in total are taken from the point where the three futures cross.

In this study, ‘carbon price’ specifically refers to the futures settlement prices of European Union Allowances (EUA) traded on the Intercontinental Exchange (ICE). This variable represents the market value of carbon emission rights within the EU Emissions Trading System (ETS), serving as a proxy for global carbon pricing dynamics due to its liquidity and policy influence.

Our data is mainly focused on the European market, but it can also reflect certain characteristics of the global market: EUA carbon futures, Brent crude oil futures, and ICE Rotterdam coal futures. This selection ensures representation of interconnected yet regionally distinct markets, which is critical for generalizing findings beyond single economies. The period covering January 2018 to July 2025 captures pre-COVID and post-COVID transitions, full phases of the Russia–Ukraine war from February 2022 to the present, and the Israeli–Palestinian conflict since October 2023, enabling a comparative analysis of non-crisis vs. crisis intervals.

3.2. Methodology

To accurately identify shifts in carbon–fossil energy price causality during the COVID-19 pandemic, Israeli–Palestinian conflict, and Russia–Ukraine war, this paper adopts an innovative time-varying Granger causality test developed by Shi et al. [52]. The approach includes forward expanding window, rolling window, and recursive evolution window-based procedures for checking causality.

While complex models including but not limited to TVP-VAR and wavelet coherence exist, the standard VAR is the ‘necessary foundation’ for TVGC testing [52]. This simplicity ensures computational stability when recursively estimating 1442 subsamples, whereas more parameterized models risk overfitting in rolling windows [44]. Our triad of algorithms further mitigates model dependency by cross-validating causality transitions.

Our research design adopts a three-phase sequential exploration beginning with the crisis typology framework categorizing events by duration and scale, followed by TVGC Triangulation applying forward, rolling, and recursive tests to detect causality regimes, and concluding with Theory–Method Integration linking crisis attributes to causality patterns through persistence metrics. Through this framework, Phase 1 obtains a typology of crisis events that contextualizes their fundamental attributes. Phase 2 generates time-varying causality regimes across different testing algorithms, enabling robustness checks. Phase 3 yields integrated insights on how crisis attributes quantitatively modulate causality patterns.

3.2.1. Granger Causality

Consider the original, without loss of generality, bivariate VAR model given by the following:

$$y_{1t}={\varphi }_0^{(1)}+{\displaystyle \sum _{i=1}^p{\varphi }_{1i}^{(1)}}{y}_{1t-i}+{\displaystyle \sum _{i=1}^p{\varphi }_{2i}^{(1)}}{y}_{2t-i}+{\epsilon }_{1t}$$

(1)

$$y_{2t}={\varphi }_0^{(2)}+{\displaystyle \sum _{i=1}^p{\varphi }_{1i}^{(2)}}{y}_{1t-i}+{\displaystyle \sum _{i=1}^p{\varphi }_{2i}^{(2)}}{y}_{2t-i}+{\epsilon }_{2t}$$

(2)

where p is the optimal lag order of the VAR model determined by the Bayesian Information Criterion (BIC) and ${\epsilon }_{\mathrm{i}t}$ are the residual terms. On the basis of the historical information of $y_{1t}$, adding the p-order lag of $y_{2t}$ into the model, if the prediction ability of the former improves, means that $y_2$ Granger causes $y_1$. The null hypothesis for the absence of Granger causality from $y_2$ to $y_1$ is $H_0={\mathit{\varphi }}_{21}^{(1)}=\dots ={\mathit{\varphi }}_{2i}^{(1)}=0$. In general, testing whether the null hypothesis holds involves testing the joint significance of ${\mathit{\varphi }}_{2i}^{(1)}(i=1,\dots ,p)$ via a Wald test.

After recasting the system in matrix notation, the original bivariate VAR (p) equation can be reduced to the following form:

$$y_t=\prod x_t+{\epsilon }_t$$

(3)

where $y_t=(y_{1t},y_{2t})\prime$, $x_t=(1,{y^{\prime }}_{t-1},{y^{\prime }}_{t-2},\dots ,{y^{\prime }}_{t-p})\prime$, and ${\prod }_{2\times \left(2\mathrm{p}+1\right)}=({\Phi }_0,{\Phi }_1,\dots ,{\Phi }_p)$ with ${\Phi }_0=({\mathit{\varphi }}_0^{(1)},{\mathit{\varphi }}_0^{(2)})\prime$ and ${\Phi }_i=\left(\begin{array}{cc}{\mathit{\varphi }}_{1i}^{(1)}& {\mathit{\varphi }}_{2i}^{(1)}\\ {\mathit{\varphi }}_{1i}^{(2)}& {\mathit{\varphi }}_{2i}^{(2)}\end{array}\right)$ for $i=1,\dots ,p$.

The null hypothesis that $y_2$ is not the Granger cause of $y_1$ is expressed as $R_{1\to 2}\pi =0$, where $R_{1\to 2}$ is the representation of the coefficient restriction matrix and $\pi$ is the row vectorization of $\Pi$.

Moreover, $w_{1\to 2}$ is a representative of the Wald statistic of the heteroskedastic consistent with the null hypothesis, defined as follows:

$$w_{1\to 2}=T\left(R_{1\to 2}\widehat{\pi }\right)\prime {\left[R_{1\to 2}\left({\widehat{V}}^{-1}\widehat{\Sigma }{\widehat{V}}^{-1}\right){R^{\prime }}_{1\to 2}\right]}^{-1}\left(R_{1\to 2}\widehat{\pi }\right)$$

(4)

where $\widehat{V}=I_n\otimes \widehat{Q}$ with

${\widehat{\epsilon }}_t={\mathit{y}}_t-\widehat{\Pi }{\mathit{x}}_t$. It is worth noting that the subscript n of ${\mathit{I}}_n$ on the right side of the definition of $\widehat{\mathit{V}}$ refers to the number of variables in the original VAR model, which is equal to two in this context.

The above framework can only be applied to the Granger causality test, where stationary economic variables are used to estimate the VAR model. To account for the possibility of Granger causality tests for integrated variables, Toda & Yamamoto [53] and Dolado & Lütkepohl [54] advocated for estimating a Lag-Augmented VAR (LA-VAR) model as follows:

$$y_{1t}={\mathit{\alpha }}_0^{(1)}+{\mathit{\alpha }}_1^{(1)}t+{\displaystyle \sum _{i=1}^p{\varphi }_{1i}^{(1)}}{y}_{1t-i}+{\displaystyle \sum _{i=1}^p{\varphi }_{2i}^{(1)}}{y}_{2t-i}+{\epsilon }_{1t}$$

(5)

$$y_{2t}={\mathit{\alpha }}_0^{(2)}+{\mathit{\alpha }}_1^{(2)}t+{\displaystyle \sum _{i=1}^p{\varphi }_{1i}^{(2)}}{y}_{1t-i}+{\displaystyle \sum _{i=1}^p{\varphi }_{2i}^{(2)}}{y}_{2t-i}+{\epsilon }_{2t}$$

(6)

where $t$ represents a time trend, $p$ is the optimal lag order of the original VAR model, and ${\mathit{\epsilon }}_{it}$ represents the residual term. In contrast, the LA-VAR model adds an additional d-order lag to the original VAR model, which increases the ability to obtain the maximum possible integration order of the variables in the system. Therefore, the original model can be re-expressed as VAR (m+d) in this case. Since the coefficients associated with the additional d were not taken into account in the test constraints, the Granger causality test within the framework of LA-VAR could also be continued as previously described. More generally, when $y_t$ is an n-dimensional vector, the LA-VAR model has the following form:

$$y_t={\rho }_0+{\rho }_{1}t+{\displaystyle \sum _{i=1}^p{\theta }_i}{y}_{t-i}+{\displaystyle \sum _{i=p+1}^{p+d}{\theta }_j{y}_{t-j}}+{\mathit{\epsilon }}_t$$

(7)

3.2.2. Recursive Testing Algorithms

To ensure that Granger causality does not create fragility when considering period substitution, and to accurately identify changing dates, recursive estimation methods are required. We obtain relevant information and use it for inference by computing the Granger causality test statistical series for different times. Three algorithms can compute and generate a series of Wald test statistics from the subsample of the data, namely the forward expanding window, rolling window, and recursive evolving window tests. The advantage of these three test algorithms is that the exogenous detection of Granger causality change points can be converted to endogenous. Consider a sample y with a total of T observations. Assume that $h_1$ and $h_2$ represent the quantile start and end points of each regression subsample ($0<h_i<1$), and $h_w=h_2-h_1$. Based on the LA-VAR model, the Wald statistic obtained from each regression sample is expressed as $w_{h_1}^{h_2}$. Let ${\mu }_1=⌊h_{1}T⌋$, ${\mu }_2=⌊h_{2}T⌋$, and ${\mu }_w=⌊h_{w}T⌋$, where the function $⌊h_{i}T⌋$ represents taking the integer part of the product and defines ${\mu }_0=⌊h_{0}T⌋$ as the minimum number of regression sample observations needed to estimate the VAR model. The start and end points of the regression subsample for calculating the Wald statistic are $y_{⌊h_{1}T⌋}$ and $y_{⌊h_{2}T⌋}$, respectively.

The forward expanding window algorithm [55] can be said to be a standard forward recursion [56]. For this algorithm, the starting point of the subsample for calculating the Wald statistic is fixed to the first observation (i.e., ${\mu }_1=1$). Then, the regression window size is gradually expanded from the smallest length until the final test statistic is computed using all sample observations. Notably, this procedure is equivalent to moving ${\mu }_2$ from ${\mu }_0$ to $T$, and the starting point of each regression subsample is the first observation.

The size of the regression window is fixed for the rolling window algorithm [57]. The window length is assumed to be equal to ${\mu }_0$ in this paper, advancing one test result at a time, and computing the corresponding Wald statistic for each regression window. The starting point of the window is moving from the first observation to $T-{\mu }_0+1$, and the ending point is ${\mu }_2={\mu }_1+{\mu }_0-1$. That is, when the end point of the regression sample moves from ${\mu }_0$ to the last data $T$, the window period points follow, and there is always a fixed size ${\mu }_0$ in between.

For the recursive evolving window algorithm, the end point of the regression window is the same as the rolling window process, namely ${\mu }_2=\left\{{\mu }_0,\dots ,T\right\}$. However, the starting point of the window is not the same as in the rolling program, which is a fixed distance from the ending point, covering all possible values from 1 to ${\mu }_2-{\mu }_0+1$. The fractional observations of interest h provide the common endpoint for all sub-windows, and the algorithm tests every possible regression sample. We apply the observations of interest to each point in the sample data and repeat the process until the minimum window size ${\mu }_0$. The end result is that, for each observation of interest, we obtain a corresponding set of Wald statistics series ${\left\{w_{h_1,h_2}\right\}}_{h_2=h}^{h_1\in \left[0,h_2-h_0\right]}$. The test statistic is defined as the sup-norm of the Wald statistic at each observation $s{w}_h(h_0)=\underset{h_2=h,h_1\in \left[0,h_2-h_0\right]}{\sup }\left\{w_{h_1,h_2}\right\}$. At this time, for each observation of interest, the null hypothesis of the absence of Granger causality should be inferred according to the sup Wald statistic $s{w}_h(h_0)$.

4. Results and Discussion

Before the analysis begins, it is important to clarify that ‘carbon’ in this section refers to carbon emission allowances. In order to observe the movements of the three variables over different periods, we draw a price trend chart, and the time series trends of the three prices are depicted in Figure 1.

From Figure 1, it can be found that there are strong trends in three prices. The prices of these commodities have been uneven since the beginning of 2020, which may be a consequence of the COVID-19 pandemic. This is due to the special nature of the COVID-19 crisis; it not only restricted the mobility of people at home and abroad, but also caused a surge in the number of countries facing energy security risks in terms of trade restrictions, etc. However, coal prices only started to trend upward in late 2021. Especially during the Russia–Ukraine war, the upward trend in coal prices was pronounced, and the price of oil and carbon gradually showed a rising tendency. After that, coal prices began to decline from September 2022, while oil and carbon prices showed volatility. During the Israeli–Palestinian conflict, the three fluctuated slightly.

The purpose of this paper is to investigate the changes in the causality between oil, coal, and carbon. Accordingly, this study is based on a three-variable VAR model including oil, coal, and carbon, namely $y_t=\left(oi{l}_t,coa{l}_t,carbo{n}_t\right)$. In this case, we used the other variables when examining the causal relationship between each energy price pair. We expect to reduce the impact of other sub-category prices on judging the relationship to enhance the reliability and accuracy of the results.

The advantage of using the three LA-VAR-based detection algorithms introduced earlier is that filtering behaviors such as logarithm and detrend processing are not required to be performed on the observation series in advance. Nevertheless, tests for time-varying Granger causality do require information about the largest possible order of integration of the variables. To this end, we follow the work of Shi et al. [58] by applying the augmented Dickey–Fuller (ADF) test for each data sequence.

Table 1. ADF unit root test results for oil, coal, and carbon prices.

	Test Statistics		Test Statistics
$oi{l}_t$	−2.201	$\Delta oi{l}_t$	−28.010
$coa{l}_t$	−2.180	$\Delta coa{l}_t$	−25.820
$carbo{n}_t$	−1.866	$\Delta carbo{n}_t$	−25.868
	1%	5%	10%
Critical value	−3.430	−2.860	−2.570

provides the detection statistics and their respective finite sample critical values. It can be found that all data time series are $I\left(1\right)$. According to this, we not only incorporate a constant term and a time trend into the regression, but also set the value of the lag enhancement parameter to the unit, as shown in Equation (6).

To complete the study of the causal relationship between oil, coal, and carbon prices using forward, rolling, and recursive evolving algorithms, the optimal lag order of the original VAR model must be determined. In this paper, we utilize BIC to select the optimal lag order, and the maximum lag order is 12. The optimal lag order was chosen to be 4, which is used in all subsample regressions. The minimum window size is set to include 72 observations (approximately 2.5 months). Each subsequent graphical result contains the value of the Wald test statistics and their corresponding 90th and 95th quantiles. When the value of the Wald statistic exceeds the critical value of the sample, it is considered that there is a causal relationship between the economic variables; otherwise, it indicates that the null hypothesis of no causal relationship cannot be rejected.

4.1. The Causality from Oil and Coal to Carbon Prices

The three algorithms consistently indicate that the causal effects of coal and oil prices on carbon prices are time-varying and dynamic. As can be seen from the Figure 2 and Figure 3, the impact of coal and oil prices on carbon prices continued to be significant during the Israeli–Palestinian conflict and the Russia–Ukraine war. Chen et al. argue there are higher-order moments of geopolitical risk for energy. Accordingly, when geopolitical conflicts occur, they can have an impact on energy and carbon markets and enhance their connectivity.

However, the results of the rolling window test are not continuous. During the Russia–Ukraine war, the rolling window test did not find a causal relationship between oil and carbon prices. It can be seen that the rolling window test is not sensitive enough to test causality and detects fewer causality relationships. Shi et al. have also mentioned that of the three methods, the rolling window test is the least sensitive.

The recursive evolving algorithm detected the largest number and longest duration of causal events between carbon and the prices of the other two energy products, highlighting its superior sensitivity in capturing transient and evolving linkages. In recursive testing technology, both coal and oil prices had a longer and more pronounced effect on carbon prices during the Russia–Ukraine war. This finding strongly supports H1, confirming that geopolitical crises amplify the causal transmission from fossil fuel markets to the carbon market through price channels. The heightened and sustained causality during the war likely stems from the profound supply disruptions and surging energy insecurity, particularly in Europe, which significantly altered energy consumption patterns and intensified the cost pass-through to carbon allowances. Furthermore, the observed heterogeneity in the impact of coal versus oil aligns with H3. From Figure 2, we can draw the conclusion that coal has a stronger and more lasting causal effect, which can be attributed to its dominant position in power generation in Europe during the gas shortage crisis triggered by the war. Coal price surges directly translated into higher carbon costs due to its higher emission intensity, as theorized earlier and supported by Ding et al. [33] and Moulim et al. [18]. In contrast, oil’s impact, while significant during the conflict, was relatively shorter-lived and exhibited smaller fluctuations, as shown in Figure 3. This reflects its more indirect transmission mechanism primarily through demand elasticity in transportation and industry, where short-term consumption cuts during price spikes may occur, but long-term substitution dynamics play a larger role, as suggested by Nguyen et al. [25]. Figure 1 visually corroborates this, showing the sharpest rise in coal prices coinciding with the war’s onset, with carbon and oil prices also rising significantly but with different volatility patterns. Due to the increased demand for energy during the war, energy prices rose rapidly, and excessive consumption of energy would also lead to an increase in carbon emissions, thus increasing carbon prices. At this time, the energy market would have a significant impact on the carbon market.

Furthermore, our analysis reveals that the Russia–Ukraine war established persistent bidirectional causality between coal and carbon prices as shown in Figure 2. This reflects Europe’s accelerated shift to coal-fired power amid fossil energy supply disruptions, where coal price surges directly elevated carbon costs due to higher emission intensity. Crucially, this coal-driven linkage remained robust during the subsequent Israeli–Palestinian conflict from October 2023 to July 2025, though with reduced volatility. In stark contrast, COVID-19 induced only transient causality, peaking during the 2020 lockdowns as shown in Figure 2 and Figure 3 but vanishing by year-end as economies reopened. This demonstrates how geopolitical conflicts forge enduring market interdependencies fundamentally distinct from pandemic demand shocks.

4.2. The Causality from Carbon to Coal and Oil Prices

The findings of this study align with those reported by Tan and Wang [59] and Kun Duan et al. [20]. Causality exists linking fossil fuel price changes and carbon price variations. This relationship indicates that fluctuations in the cost of fossil fuels have a direct influence on carbon emission pricing. As fossil fuel prices rise or fall, so too do the costs associated with carbon emissions, reflecting the interconnected nature of energy markets and environmental policies. However, the effect of carbon prices on coal and oil prices is less pronounced. The carbon price significantly impacted coal prices before and after the COVID-19 outbreak and during the Russia–Ukraine war, as shown in Figure 1. It can be observed in Figure 4 that after the outbreak of the Israeli–Palestinian conflict, the impact of carbon prices on coal and oil prices exhibits less intense fluctuations compared to the period of the Russia–Ukraine war. This observation partially supports H2 regarding the potentially lesser duration and intensity of impacts from the Israeli–Palestinian conflict. The milder causal fluctuations likely stem from the relatively more localized nature of the Israeli–Palestinian conflict compared to the Russia–Ukraine war. While causing regional turmoil and global uncertainty, the Israeli–Palestinian conflict did not involve major global energy producers on the scale of Russia, thus causing less severe and widespread disruptions to global fossil fuel supply chains. This interpretation aligns with the finding that the conflict had a smaller impact on international markets than the COVID-19 pandemic. This may be because the countries involved in the Israeli–Palestinian conflict have less impact on world fossil energy supply and demand than the Russia–Ukraine war. The Israeli–Palestinian conflict has also had a smaller impact on international markets than the COVID-19 pandemic.

Regarding the bidirectional causality, the recursive test successfully detected significant causality running from carbon prices to fossil fuel prices during both conflicts, reinforcing H3 about strengthened bidirectional links during crises, as also illustrated in Figure 5. The failure of the forward and rolling tests to consistently capture this carbon-to-fossil-fuel effect underscores the importance of employing sensitive methods like the recursive evolving window to detect potentially shorter-lived or evolving causal directions, especially in turbulent periods.

5. Conclusions and Policy Recommendations

5.1. Practical Implications

In this paper, we explore the impact of the COVID-19 outbreak, Israeli–Palestinian conflict, and Russia–Ukraine war on the linkage between traditional energy and carbon prices based on the time-varying Granger causality tests. First, we selected two energy prices and carbon price to conduct Granger causality tests. Second, after determining the optimal lag order of the VAR model and the maximum possible order of variable integration, we applied the tvgc tests to examine the causal effects between the two commodity prices. The tvgc technique includes three algorithms. Among them, the advantage of the recursive evolving test is that it can more accurately capture any changes in causality than other methods. Finally, we present results for energy–carbon price causality and obtain several practical findings.

First, a significant causal nexus exists between carbon prices and fossil energy prices after the outbreak of public health crises and geopolitical conflicts, with this nexus peaking immediately following the conflict, which proves H1. Second, following the Israeli–Palestinian conflict outbreak, the causal linkage between the variables is less pronounced than during the Russia–Ukraine war, which proves H2. Third, the crisis intensified the bidirectional causal link for carbon and fossil fuels, with coal demonstrating greater persistence than oil, which proves H3. Furthermore, the Russia–Ukraine war has created a continuous two-way causal relationship, which persists in the Israeli–Palestinian conflict without any directional change. This stands in sharp contrast to the brief connection with COVID-19, demonstrating that geopolitical conflicts have structurally reshaped the carbon energy market beyond the transient health crisis. Dynamic and time-varying causality has characterized the energy–carbon price relationship in recent years. Overall, the outbreaks of the Israeli–Palestinian conflict and Russia–Ukraine war rendered the bidirectional causal interplay between energy and carbon prices the most significant.

Identifying how the causality between energy and carbon prices changed during the Russia–Ukraine war has significant implications for investors and policymakers. Based on the above empirical results, we make several recommendations. For policymakers, they need to fully evaluate the risk transmission and connectedness between the carbon market and fossil energy markets following geopolitical conflict outbreaks. In today’s world of frequent geopolitical conflicts, policymakers should reasonably distinguish between market disturbances caused by investor sentiment and fluctuations caused by fundamental changes. Governments should establish a cross-market risk early-warning mechanism that integrates carbon and fossil energy price volatility, regardless of geopolitical conditions. This includes setting dynamic carbon quota adjustment rules linked to energy security indicators and systemic stress thresholds. Market regulators ought to mandate disclosure of carbon-hedging strategies by energy-intensive firms to enhance transparency during both stable and crisis periods. For investors, it should be clear that, under varying market conditions, the interplay between fossil fuel and carbon prices exhibits distinct patterns, becoming particularly pronounced in the wake of geopolitical conflicts. In the absence of such external shocks, while bidirectional causality dominates during conflicts, no significant causal linkage persists in stable periods without external shocks. Therefore, investors should incorporate time-varying carbon–energy causality regimes into portfolio construction, allocating assets to green bonds during stable periods while increasing carbon futures hedging ratios when geopolitical tensions escalate. When comprehending the relationship between carbon prices and fossil fuel prices, investors must acknowledge their dynamic nature under different market scenarios. Close monitoring of the interdependent structures among assets is essential. By making informed predictions about energy prices and strategically adapting their portfolios, investors can optimize their returns.

5.2. Limitations and Future Research

The generalizability of this study is limited by its geographical concentration on European carbon markets (EUA). Subsequent work must therefore broaden the empirical scope to include major emerging systems like China’s ETS and integrate data beyond July 2025 to capture the influence of recent crises, particularly development trajectories from the ongoing Israeli–Palestinian conflict.