Volatility spillover between the energy and AI markets: a TVP-VAR approach

1 Introduction

The rise in popularity of Large Language Models (LLMs) has transformed a number of industries worldwide. A LLM is a type of AI model which predicts natural speech (either spoken or written language) using a set of parameters refined through a training process. As the name suggests, these models tend to be very large with the most advanced models containing billions of parameters. Following breakthroughs in LLM prediction accuracy in the late 2010s, companies have raced to release bigger and better models. As the complexity, quantity, and popularity of these models increases, so does the strain on the energy market. Nvidia—one of the largest beneficiaries of the AI boom—plans to produce 1.5 million AI server units by 2027 which—if running at full capacity—would consume 85.4 terawatt-hours of electricity annually (Vries, 2023).

While increasing demand for AI models is projected to increase energy consumption across the board, data centers used for AI training do not universally use the same types of energy. Carbon intensity refers to the level of CO2 released for a given unit of energy produced. This measure varies greatly across countries, for example training an AI model in Estonia would emit more than 61 times as much CO2 as training the same model in Sweden (Wolff Anthony et al., 2020). Information regarding the type of energy consumption from AI model training and use by country is not readily available; however, the disparity in carbon efficiency (and thus energy composition) across countries indicates that the AI market may respond differently to shocks from the clean energy market compared to the traditional energy market. For example, Zhang et al. (2024) finds that the AI market is significantly more sensitive to shocks in the volatility of crude oil than to shocks in the volatility of natural gas or clean energy.

The rise of AI has also driven a higher level of interconnectedness between market sectors (Demiralay et al., 2021; Dang et al., 2024). In general, as markets grow to become more intertwined, the volatility of those markets also becomes increasingly connected (Adekoya and Oliyide, 2021). Studying the changing interdependence of market sectors allows us to better understand the rapidly changing world around us and to better predict the effect of market shocks. Volatility spillover is a term used to define the response in volatility from one market to the other. For example, if market A receives a shock and the volatility in that market increases, then market B may also experience an increase in volatility as a knock-on effect. Volatility spillover was originally formulated to quantify relationships between international markets but in recent years has also been used to describe inter-sectoral relationships within markets.

Volatility spillover studies are frequently used by investors to determine how to hedge their investments. Such studies also help inform policymakers of the risks faced by important industries, allowing them to develop infrastructure that is more resistant to market shocks. The need for such resistance is apparent given the recent instabilities introduced by COVID-19 and the Russia-Ukraine war. As policymakers and investors look to avoid financial instability in an increasingly uncertain world, volatility spillover studies provide useful information. This paper examines the changes in volatility interconnectedness of AI and Energy markets since 2018 with a particular focus on the effects of the COVID-19 pandemic and Russia-Ukraine War.

2 Literature review

The energy market's central role in the global economy means that it has experienced a large amount of volatility in the past 6 years. Xie et al. (2024) uses an elastic-net-VAR approach to show that the top 56 global energy firms exhibit strong volatility spillover characteristics (i.e., an increase in volatility in one firm is likely to lead to an increase in overall energy market volatility). Furthermore, Xie et al. (2024) found that this volatility spillover increases following extreme market shocks such as the 2008 stock market crash and the COVID-19 pandemic. Xie et al. (2024) also found that volatility spillover is more severe and longer lasting in the U.S. and Europe compared to Asia.

Similarly, a number of papers have found evidence of a structural break in the volatility interconnectedness of energy markets in response to the COVID-19 pandemic (Ha et al., 2022). Liu et al. (2024) studies the effects of COVID-19 on the volatility interconnectedness between energy markets and the AI market. This paper uses a quantile-based time-varying framework adapted from the Cross-Quantilogram (CQ) approach used in Han et al. (2016). They also apply a recursive Cross-Quantilogram method from Uddin et al. (2019). The researchers split the energy market into three main categories: natural gas, crude oil, and clean energy. Liu et al. (2024) found that volatility in the AI industry was positively correlated with volatility in the crude oil and clean energy markets, but not with volatility in the natural gas market. Liu et al. (2024)'s findings corroborate the differential effects of AI shocks across various sectors within the energy market described by Zhang et al. (2024).

The volatility spillover between the Energy and AI markets has received considerable attention in recent years. Yousaf et al. (2024) uses a VAR model with time-varying parameters (TVP-VAR) to examine the volatility interconnectedness of the energy and AI markets between 2018 and 2023. The researchers selected the top 8 companies in the AI market along with two electricity market indices. Yousaf et al. (2024) find that both the COVID-19 pandemic and the Russia-Ukraine war resulted in increased return and volatility spillover between energy and AI markets.

I extend Yousaf et al. (2024)'s work by differentiating between the oil, natural gas, and clean energy markets which allows me to analyze the volatility interconnectedness of different types of energy alongside AI market volatility. Unlike Yousaf et al. (2024) I use an AI ETF as a proxy for the AI market. This reduces the risk of capturing volatility spillovers between the energy market and technology sector because major technology stocks such as Microsoft and Nvidia consume large amounts of energy for purposes unrelated to AI (Liu et al., 2024). Finally, this paper is, to my knowledge, the first to use the bootstrapped standard error method described by Nakajima (2011) to report time-varying impulse response functions for the energy and AI markets.

The paper proceeds as follows: Section 3 contains a theoretical model, my dataset, and my empirical approach. Section 4 contains my results and post-estimation validation, and Section 4 contains my concluding remarks.

3 Data and modeling

Before estimating an empirical model, it is important to explain why we might expect the volatility of the energy and AI markets to be interdependent.

3.1 Modeling

Define the profit function of a given firm at a fixed point in time as:

Π(E)=R-C(E)(1)

where R is the firm's revenue and C(E) is the firm's cost as a function of energy prices. Then:

C(E)=C0+αE(2)

where C₀ is the company's costs without energy prices, E is the price of energy, and α is the firm's sensitivity to energy prices. Using an asset pricing framework, we can define the stock price at time t as the expected value of the profits at time t divided by the discounted value of expected future cash flow:

pt=𝔼[∑i=1∞Πt+i(1+r)i](3)

Here, r is the discount rate for the firm which is typically defined as the risk-free rate and measured using the interest rate on 3-month U.S. treasury bonds. Plugging in Equations (1) and (2) into (3) we get:

pt=𝔼[∑i=1∞(C0+αE)t+i(1+r)i](4)

I assume that energy price volatility follows a Geometric Brownian Motion. Using Ito's Lemma, we can approximate the asset price volatility:

σpt≈ασEEtr(5)

According to the relationship in (5), we expect stock price volatility to grow proportionate to increases in energy price E_*t*, energy use of the firm α, and the inverse of the discount rate r.

We now turn to the effect of stock price volatility on energy price volatility. Consider the inverse demand function of energy:

pe=α-βQ(6)

where Q is the aggregate quantity demanded of energy at the market level and can be expressed by:

Q=QAI+Q0(7)

Where Q_*AI* is the energy demanded by the market for use in AI (token generation, training, etc.), and Q₀ is all other energy demanded. Using the models for price and quantity in (6) and (7) we can write the variance of energy prices as:

σE2=β2(σAI2+σ02+2Cov(QAI,Q0))(8)

As seen in (8), the volatility of energy prices is proportionate to the volatility of the energy demand in the AI industry. In order to determine the magnitude of these relationships, we now turn to empirical evidence.

3.2 Data

I estimate the correlation between the volatility of the AI market and the volatility of the energy market using a time-varying vector autoregressive model (TVP-VAR). I use time-series data recorded on a daily basis from 05/02/2018 to 03/31/2025 and consisting of 1777 data points. The primary outcomes of interest are the volatility of the AI and Energy markets. I select Global X Robotics AI Class A (GlobalX) as a proxy for AI market volatility. The GlobalX index was publicly listed on may 2nd 2018 and is designed to track global companies whose business is focused on artificial intelligence (AI). This focus could be in creating new AI models, producing hardware for use in training AI, or using existing AI models in practical situations. The Global X ETF is superior for analysis of the AI market when compared to individual AI-related stocks due to its holistic weighting of the AI industry (Liu et al., 2024; Zhang et al., 2024). All data was collected from Yahoo Finance using the quantmod package in R.

In keeping with the existing literature, I opt to use futures rather than spot prices to measure energy markets since the futures market adjusts more quickly to changes in the expected future value (Perifanis and Dagoumas, 2018). Tiwari et al. (2023) suggests that different sectors within the energy market respond differently to market shocks. Liu et al. (2024) also finds that volatility in the AI market effects volatility in the renewable energy sector differently than the non-renewable energy sector. Therefore, I opt to divide the energy market into three categories: oil, gas, and renewable. To estimate the oil market, I use the West Texas Intermediates Crude Oil Futures (WTI) which tracks futures contracts for crude oil. For Natural Gas I select the Huber Natural Gas Spot Price Index. I select the iShares Global Clean Energy ETF as a proxy for the clean energy market which is an ETF that tracks global companies investing in public companies engaged in wind, solar, hydroelectric, and geothermal energy production.

I control for overall market volatility using the CBOE Volatility Index. VIX is the standard index used for measuring overall market volatility. The index is derived from the expected changes in the S&P 500 index over the next 30 days using S&P 500 stock options. The use of a volatility index as a control variable is well-established in the literature, for example, Wang et al. (2024) uses the FSI as a proxy for overall market volatility.

Table 1 provides descriptive data of the variables' raw values. I use the 30 day rolling volatility of these variables, that is, the standard deviation of the difference in logged returns over a 30-day moving average, presented below in (9):

σt=129∑i=t-29t(ri-r̄t)2(9)

Where t is the next 30-day period following an observation i, and r_*i* is the log return at time i calculated using the following formula:

ri=ln(PiPi-1)(10)

The transformation in (10) is supported by one of the foundational volatility spillover papers, Diebold and Yilmaz (2012). Taking the volatility of the VIX index may seem counterintuitive; however, in accordance with economic theory surrounding volatility spillover, cross-asset volatility is a result of market shocks. The volatility of the VIX index captures shocks to overall market uncertainty. Furthermore, this transformation ensures that all variables are of similar magnitude and range, resulting in more intuitive comparisons.

Table 1. Descriptive statistics.

Data from 05/02/2018 to 03/31/2025 on a daily basis. Collected from Yahoo Finance on 03/31/2025.

3.3 Empirical approach

A simple vector auto-regression model represents the time-series values of a dependent variable as a function of its' own lags, the lags of other variables in the model, and the contemporaneous values of other variables in the model. The basic VAR model proposed by Sims (1980) is expressed as follows:

yt=B1yt-1+⋯+Bpyt-p+εt, εt~N(0,Σ)(11)

Where y_*t* is a k x 1 vector of endogenous variables, B₁, ..., B_*s* are k x k coefficient matrices for each lag i, and ϵ_*t* is a k x 1 vector of reduced-form residuals that is normally distributed with a constant variance-covariance matrix, Σ.

A key assumption of the VAR model is that the relationships between variables, while dependent on prior values of the dependent variables, are otherwise independent of time. A significant amount of research has found that in financial markets, the volatility and channels of volatility transmission do in fact vary over time (Primiceri, 2005; Koop et al., 2009; Koop and Korobilis, 2010). This is particularly true in the context of an emerging technology such as AI. For instance, as investors have become more familiar with AI models and the amount of energy required to train them, we might expect a decrease in volatility spillover between the energy and AI markets over time.

Following Nakajima (2011) we can introduce time-varying effects to the VAR model in (11) in the following way:

yt=xt′β+zt′αt+εt, εt~N(0,σt2), t=1,…,n(12)

Where xt′ is the time-invariant effect of the endogenous variables on y_*t*, and zt′ is the time-dependent effect of the endogenous variables on y_*t*. Therefore, α_*t* is a p x 1 vector of time-varying coefficients. We assume that α_*t* follows a first-order random walk process:

αt+1=αt+ut, ut~N(0,Σ), t=0,…,n-1, α0=0

Furthermore, we assume that the log of σt2 – the variance of the residuals – also follows a random walk process. The TVP-VAR model is typically modeled using a Kalman Filter technique. The calculations required for this approach are outside the scope of this paper; however, Balcilar et al. (2021) provides the most common formulation of the approach used to model the TVP-VAR.

One significant advantage of the TVP-VAR model over other models such as those involving Markov-Switching is that structural changes are not necessarily assumed to occur at discrete points in time but are allowed to occur as part of continuous processes. In other words, the TVP-VAR model is able to capture gradual changes because the coefficient and variance matrices change in each time period. As Figure 1 shows, the volatility of Crude Oil Futures, GlobalX, VIX, and iShares Global Clean Energy Index increase noticeably afterMarch 2020 and February 2022. Not only do these shocks result in an immediate increase, but that increase appears to persist for up to six months.

I first estimate an unrestricted VAR to determine whether the data is heteroskedastic and thus requires a time-varying approach. The Schwarz Bayesian Criterion (SC) and Hannan-Quinn Criterion (HQ) tests suggest an optimal lag length of 2, while the Akaike Information Criterion (AIC) and Final Prediction Error (FPE) tests suggest an optimal lag length of 5 (results in Appendix A). Since the TVP-VAR model is parameter-heavy, I opt for 2 lags to avoid overfitting (Primiceri, 2005).

I test my time-series for stationarity using the Augmented Dickey-Fuller, Phillips-Perron and Box-Ljung tests. Table 2 indicates that we reject the null hypotheses for all tests and all variables at the 5% level (1% level for the Box-Ljung test) with the exception of the iShares Global Clean Energy Index. I conclude that the time-series are stationary and autocorrelated. According to Ha et al. (2022), the presence of autocorrelation supports the use of a model with time-varying parameters such as TVP-VAR.

Table 2. Stationarity and autocorrelation test results.

The Null Hypothesis for the Dickey-Fuller and Phillips-Perron tests are that the time-series follows a unit root process. The null hypothesis for the Box-Ljung test is that there is no autocorrelation present in the time-series for the specified number of lags. For all tests, the specified number of lags is 2 in keeping with the AIC, HQIC, and SBIC results. Confidence levels: * –1%, –5%, *–10%.

In order to verify ARCH effects, I estimate an unrestricted VAR model with a lag length of 2 and run the multivariate ARCH-LM test (Engle, 1982). This test yields a Chi-Squared value of 2575.4 (p-stat < 0.001). Therefore, I reject the null hypothesis of no ARCH effects and conclude that the residuals are conditionally heteroskedastic. This result provides further evidence for the use of a time-varying model (Liu et al., 2024).

I estimate the TVP-VAR model with 2 lags based on results of the optimal lag length tests. The Kalman Filtering method relies upon priors for the variance-covariance matrix. I use the Minnesota Prior (sometimes referred to as the Litterman Prior) described by Litterman (1979) which is a Normal Distribution with tunable parameter γ that determines prior shrinkage.

Time variation in the coefficient and covariance matrix is determined by forgetting factors κ₁ and κ₂ which determine how quickly past information is discounted. I opt for the standard choice in the literature which is to set both to 0.99. Finally, for the Minnesota Prior, I chose γ = 0.1 which is also standard in the literature. The forecast error variance decomposition (FEVD) horizon determines how long shocks propagate across variables. A 30 day FEVD horizon is standard in the literature as it allows for the modeling of medium-term transmission dynamics, but avoids excessive sensitivity (Diebold and Yilmaz, 2012; Balcilar et al., 2021).

4 Results

I begin by presenting the Total Connectedness Index (TCI) for each pair of variables as well as the evolution of the average TCI over time. The former allows us to analyze the volatility spillover between each variable, while the latter provides information regarding the overall connectedness of the Energy and AI markets in response to shocks such as the COVID-19 pandemic. I then present the net total connectedness and net pairwise connectedness results of the model. These results are directional in that they allow us to determine whether each variable is a net-receiver or net-transmitter of volatility in the system. Finally, I present the impulse response functions and perform a robustness check.

4.1 Average dynamic connectedness

The Average Joint Connectedness values across the entire time frame (2018–2025) are presented in Table 3. Each row corresponds to the contribution of each variable to the forecasted error variance of the column variable. Each column corresponds to the effect of the given variable on all the other variables. For example, the Crude Oil Row indicates how much volatility the Crude Oil Futures asset transmits on average to each corresponding asset on the column. The values on the diagonal display the connectedness of the variable with itself. The “NET” row displays the average effect of each asset in the corresponding column on the system. The “NPT” row indicates how many assets the asset on the column transmits volatility to on average. For example, AI's NPT value is 2, indicating that, on average, it transmits volatility to 2 other assets (Crude Oil and Natural Gas). Figure 2 displays the same information as Table 3 (average volatility transmission) in the form of a network.

Table 3. Average joint connectedness.

Results based on a TVP-VAR model with lag length 2 and 30-step-ahead generalized forecast error variance decomposition. Volatility transmission is from the entry on the row to the entry on the column.

The average TCI value is 36.51%, indicating that 36.51% of the forecast error variance of the variables is explained by cross-variable spillover—with the remaining volatility being attributable to own-variable volatility. These findings suggest that the volatility of the energy market, overall market, and AI market co-move to a significant extent.

Table 3 shows that the AI, Clean Energy, and VIX indices have positive net values, indicating that these variables are net transmitters of shocks, that is, they tend to influence other variables in the system rather than be influenced by them. The traditional energy assets—Crude Oil and Natural Gas—are net receivers of shocks. Figure 2 displays the results of this table graphically. Interestingly, we can see that the AI industry receives volatility from the overall market and from the clean energy market but transmits volatility to the traditional energy indices. Yousaf et al. (2024) similarly finds that the oil market is a net receiver of volatility from AI stocks.

4.2 Dynamic total connectedness

The average dynamic total connectedness is presented below in Figure 3. It is important to note that this graph does not allow for the analysis of interconnectedness between variables, but rather the average connectedness between all variables over time. Figure 3 shows large variation in total connectedness over time, with large spikes in March 2020 and February 2022. In late 2022, volatility connectedness appears to decrease, oscillating between 15% and 25% between 2023 and 2025. The increase in total connectedness in March of 2020 coincides both with the COVID-19 pandemic and, shortly after, the release of GPT-3 (May 2020). The COVID-19 pandemic in particular resulted in between 5 and 10% reduction in energy demand around the world and the bankruptcies of 19 energy companies in the U.S. (Jiang et al., 2021). The increase of volatility spillover immediately following the COVID-19 pandemic is supported by a large body of literature (Li, 2021; Aslam et al., 2021). The second large increase in volatility spillover beginning in February of 2022 coincides with the Russia-Ukraine war, as well as the release of ChatGPT in November, 2022. Similarly, papers such as Yang et al. (2022) find evidence for increased volatility transmission as a result of geopolitical shocks. Guo et al. (2024) uses a GARCH model and finds that both the COVID-19 pandemic and the Russia-Ukraine war resulted in significant increases in volatility spillover between energy markets and the overall market, but that COVID-19 had a greater impact. These results are supported by my findings.

The drop-off in connectedness from 2023 onward is surprising; however, this decrease may be explained by a variety of factors. First, inflation rates in many countries rose precipitously from 2020 to 2022, followed by a return to pre-COVID-19 inflation rates in 2023. According to Chiang and Chen (2023), stock market volatility is positively correlated with inflation and so the lowered inflation may explain some of this drop-off. Second, AI's increasing popularity since 2020 means that investors are likely to be more confident in their ability to project future energy consumption from the AI market, pricing in various potential shocks.

4.3 Net total and net pairwise directional connectedness

Recalling the results from Section 4.1, I found that VIX and GlobalX are net receivers of shocks, while Natural Gas, GlobalX, and Clean Energy are net transmitters of shocks. It is possible that these markets have changed their roles as net transmitters/net receivers over time. Figure 4 presents the dynamic net total directional connectedness of each index to the system. This value is calculated by subtracting the volatility an asset receives from the system (the other 4 variables) at a given time t from the volatility that same asset transmits to the system at time t. Therefore, positive values indicate the variable has a net-transmitting role in the system, while negative values indicate net-receiving roles.

The results shown in Figure 4 suggest that the role of each index varies significantly over time. The AI industry in particular is a net-receiver of shocks between 2018 and 2021; however, outside of this period is generally a transmitter of volatility. The natural gas market is a net transmitter of volatility in early 2022 but is otherwise a receiver of volatility, indicating that the market shock occurring in February of that year effect the market through natural gas. The overall market volatility is, as expected, generally a transmitter of volatility to the AI and Energy markets; however, VIX is a net receiver of volatility for about 6 months following March 2020 and again following February 2022. This result suggests that these market shocks affected the energy and AI markets disproportionately more than the overall market.

I present the net-pairwise connectedness indices in Figure 5. These graphs display the connectedness between the two listed markets. Similarly to Figure 4, a positive value indicates that the variable on the left (in the title) is transmitting a shock to the variable on the right. A negative value indicates that the variable on the left is transmitting a shock to the variable on the right (note that changing the sign of the transmission is equivalent to changing the order of the two variables).

The first column of Figure 5 shows that beginning in March of 2020 the AI market was a net receiver of volatility from the overall market and from the clean energy sector. March of 2020 marks the largest amount of volatility received by the AI market between 2018 and 2025. The AI market was also a net receiver of volatility from the clean energy market between 2023 and 2025. Aside from a short period from 2021 to 2022, the AI energy market did not receive volatility from the traditional energy markets (crude oil and natural gas).

Interestingly, the model seems to experience a structural break in June of 2020 when the AI industry switched from being a net receiver of volatility to a net transmitter of volatility. This relationship is particularly evident when considering the volatility spillover between the AI industry and the traditional energy market. This inflection point coincides with the release of GPT-3 on June 11, 2020. The release of GPT-3 fueled a large amount of both public and private investment into the AI industry. Additionally, between January and April of 2020, crude oil prices experienced a decline of more than 60% leaving the Crude Oil market more vulnerable to external shocks. The heightened sensitivity of traditional energy markets, coupled with growing public awareness of LLM models such as GPT-3 in June of 2020, may have resulted in a shift in investor strategy toward using the AI industry as a predictor of future energy demand.

4.4 Impulse response functions

Impulse response functions are key to inference for most VAR models. In essence, impulse response functions graph the response of a variable to a shock in another variable, assuming all other factor are constant. To determine the expected path, we draw parameters (coefficient, variances, and covariances) from the posterior distribution at time t, and simulate the model with random shocks over a time horizon h. Then, using the same parameters, we fix the shock of one variable to be one standard deviation and compare the results over the time horizon to the baseline. This comparison is then repeated a large number of times (10,000 in this case) and used to construct a distribution of IRFs for each horizon h and time t. Since the relationship between variables is conditional on t, the resulting IRFs are three dimensional.

I present the response functions from a one standard deviation shock in the AI market for each variable as pairs of three-dimensional heat maps. The map on the left is color graded according to the strength of the response (yellow indicates a strong positive response, blue indicates a strong negative response). The map on the right is red when the response is significant at the 5% level.

On average, shocks occurring in 2018 and 2019 are more likely to be significant than shocks occurring after 2019. This relationship was particularly noticeable for shocks from the energy markets (oil, natural gas, and clean energy) to the AI market. The most significant response from an impulse typically occurs between days 2 and 4; however, the impulse from the AI market to the natural gas market had a secondary positive response on day 12. This result was significant at the 5% level across all time periods.

As seen in Figure 6, a one standard deviation shock in the AI industry corresponds to a 0.002 increase in volatility in the clean energy market after 2 days, followed by a 0.002 decrease in volatility in the clean energy market after 4 days. This response is significant at the 5 percent level up to 2023. As seen in Figure 7, the response of crude oil to a shock in the AI industry was generally more persistent. Interestingly, the response of the crude oil market is –0.001 on day 4 (indicating a decrease in volatility) followed by a positive 0.002 response on day 5/

s As previously mentioned, the response of natural gas from a standard deviation shock in AI has two peaks: one on day 2 and one on day 10 (Figure 8). This effect was significant between 2019 and 2025 and tended to increase over time. This indicates that the natural gas futures market is becoming increasingly exposed to shocks in the AI market, possibly due to the growth of the AI industry and data centers' reliance on natural gas.

Finally, the response of the overall market volatility from a standard deviation shock in the AI market is 0.002 on day 2, followed by –0.005 on day 4 (Figure 9). These effects are significant at the 5% level between 2018 and 2020. This effect is not persistent over longer time horizons when compared to the energy market. Positive innovations in the AI market (such as the release of a new LLM model) may result in decreased expected market volatility in the long run. I report the IRF relationships between the remaining variables in Appendix B.

5 Robustness checks

5.1 30 day rolling volatility

The choice of a 30 day rolling volatility, as stated in the section 3, is standard practice in the literature; however, the 30-day rolling volatility calculation induces autocorrelation in the data and may smooth shocks. To assess the extent to which the 30 day rolling window volatility effects the results, I run the original model with 10, 20, 30, and 60 day rolling window volatility and report the results in Table 4.

Table 4. Mean and median TCI using alternative volatility windows.

Pre period: 2019–2021. Post period: 2022–2023. Results are robust to alternative rolling volatility windows.

The mean and median statistics for each model are separated into the “pre” period containing the first market shock and the “post” period containing the second market shock. In each model the 2019–2021 period exhibits a higher average TCI than the 2022–2023 period. As the rolling window increases, the pre period mean tends to increase; however, the post period mean stays around the same for each model. These results are consistent with a prolonged high volatility regime in the “pre” period and shorter, smaller shocks in the “post” period.

The no-overlap row is calculated using 10 day volatility periods with each period of 10 days being a separate observation in the model. This version of the model exhibits significantly higher volatility, a consequence of there being no smoothing. Nevertheless, the differences between the “pre” and “post” periods remain significant (post has 18.2% higher TCI). In general, the similarity of the TCI mean and median for various windows indicates that the model results are robust to the volatility window duration.

5.2 Alternative FEVD horizons

While the choice of a 30-day FEVD horizon is standard in the literature, the use of horizons which are too large lead to increased connectedness and potentially spurious results. On the other hand, horizons which are too short result in decreased connectedness and little volatility spillover. I run the original model with 10, 20, 30, and 60 day FEVD horizons to determine whether the FEVD horizon choice significantly effects the results.

As seen in Figure 10, the choice of FEVD horizon has a significant impact on the level of TCI, particularly from 2022 onward. The pattern of TCI over time; however, remains relatively the same across all FEVD horizons. Notably, the shocks occurring in March 2020 and February 2022 are present for all levels. This result suggests that the results are robust for various FEVD horizon choices, but that the exact level of TCI connectedness is sensitive to parameter changes.

5.3 Alternative AI index

In order to assess the validity of the Global X Robotics & Artificial Intelligence ETF as a proxy for the AI market, I run the original model with an alternative AI index. I replace the Global X ETF with the Invesco AI and Next Gen Software ETF which, like the Global X ETF, invests in a number of companies engaged in different aspects of the AI industry (software, hardware, implementation, etc.). The Invesco ETF is weighted more heavily toward companies based in the U.S. I run the same TVP-VAR model as before and compare the results.

The overall connectedness is 10–20 percent higher when using the Invesco ETF compared to the Global X ETF; however, the pattern of volatility spillover after the COVID-19 pandemic and the Russia-Ukraine war are similar across models (Figure 11). The net pairwise connectedness graph displays a greater deviation from the original model. As seen in Figure 12, the alternative AI ETF does not appear to affect the spillover between other indices (e.g., between crude oil and clean energy). Additionally, the volatility spillover relationship between AI and crude oil is largely consistent with the original model. Volatility spillover between AI and Clean Energy in the Invesco model is less clear: the AI ETF acts as a transmitter of volatility about half of the time and as a receiver of volatility for the other half. Notably, the Invesco model indicates that the volatility transmission from the Natural Gas market in February of 2022 was significantly longer lasting than in the original model. The Invesco ETF is weighted more heavily toward companies (Figure 11): Dynamic Total Connectedness Over Time with Invesco AI ETF Notes: Results based on a TVP-VAR model with lag length 2 and 30-step-ahead generalized forecast error variance decomposition. Each index's net volatility transmitted/received to/from the model is displayed. Positive values indicate net volatility transmitted, while negative values indicate net volatility received. Run using the Invesco AI ETF as opposed to the Global X AI ETF. The black time-series is the original model, while the red line is the alternative model. based in the United States which relies more on natural gas for energy compared to countries in Europe and Asia (Ritchie and Rosado, 2020).

6 Conclusion

This paper investigated the volatility spillover between the energy and artificial intelligence markets using a TVP-VAR approach. I found that overall volatility spillover is moderate between the energy and AI markets, and that increases in volatility spillover coincide with the COVID-19 pandemic and the Russia-Ukraine War; however, more work is needed to establish a causal relationship. AI stocks tended to be net receivers of volatility from the clean energy market; however, they tend to transmit volatility to traditional energy markets. In the periods following market shocks in March of 2020 and February of 2022, the volatility transmission from the AI market to traditional energy markets was particularly pronounced. These periods of AI volatility transmission lasted for approximately 6 months. These results coincide with the results from Liu et al. (2024) who uses a Cross-Quantilogram approach. I identify a possible structural break in June of 2020 which may be attributed to the release of GPT-3. The public hype generated by this release, coupled with the vulnerability of the traditional energy market at the time, could have resulted in the AI market becoming a net transmitter of volatility to traditional energy markets.

These results may prove useful to energy regulators and infrastructure planners who are responsible for capacity planning and grid resilience assessments. Additionally, increased monitoring of data center energy consumption may help reduce uncertainty about future energy demand and decrease market uncertainty. From an investment perspective, the AI market appears to be less vulnerable to shocks originating in traditional energy markets and is more vulnerable to shocks from the clean energy sector.

I find strong evidence to support differential volatility spillover between clean and traditional energy types and the AI market. This result is supported by Liu et al. (2024). An additional robustness test using individual stock indices rather than an ETF similar to Yousaf et al. (2024) would likely yield interesting results and could act as a robustness test. Electricity prices, rather than energy commodity prices, may also provide useful results for investors. An electricity price model would allow researchers to determine whether the volatility spillover between the energy and AI markets comes from fluctuations in investors' expectations (energy commodity prices) or from the actual cost of AI model training (electricity prices). Finally, the TVP-VAR model is a relatively new method of analysis which has gained popularity in recent years. A study comparing the results presented here to those using the same data with well- established models such as the GARCH model would provide interesting insight into the comparative accuracy of the TVP-VAR model.

Finally, it is important to note certain limitations of this study. The TVP-VAR model does not provide causal inference and so, with the absence of structural break identification techniques, it is impossible to conclusively attribute major increases in volatility spillover to real world events, notably, the COVID-19 pandemic and the Russia-Ukraine war.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frevc.2026.1772831/full#supplementary-material

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Footnotes

Edited by: Sondès Kahouli, Université de Bretagne Occidentale, France

Reviewed by: Laurentiu Guinea, Complutense University of Madrid, Spain

Imen Khemakhem, Faculty of Economics and Management, Tunisia