# Measuring financial stability in the presence of energy shocks

Javier Sánchez-García, Raffaele Mattera, Salvador Cruz-Rambaud, Roy Cerqueti

► To cite this version:

Javier Sánchez-García, Raffaele Mattera, Salvador Cruz-Rambaud, Roy Cerqueti. Measuring financial stability in the presence of energy shocks. Energy Economics, 2024, 139, pp.107922. 10.1016/j.eneco.2024.107922. hal-05115049

HAL Id: hal-05115049

https://univ-angers.hal.science/hal-05115049v1

Submitted on 16 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

# Measuring financial stability in the presence of energy shocks

Javier Sánchez-García<sup>a,b,*</sup>, Raffaele Mattera<sup>c</sup>, Salvador Cruz-Rambaud<sup>a</sup>, Roy Cerqueti<sup>c,d</sup>

## ARTICLE INFO

JEL classification:

C32
C43
C53
E44
G15
G17

Keywords:

Energy market
Financial stress
Dynamic Factor Model (DFM)
Composite indicators
Macro-financial linkages
Real-time macroeconomics

## ABSTRACT

The Russia-Ukraine conflict highlighted how important energy is for the surveillance of economies worldwide. Both war and economic sanctions inevitably affected energy-related commodity prices. Although shocks in energy commodities are known to have an effect on financial stability, this information is not included in existing financial stability indicators. In this paper, we first provide empirical evidence on the existing relationship between energy-related commodities and financial stability in the EU, UK and US, as well as their importance in the forecast of economic downturns. Based on this evidence, we propose a new composite indicator of financial stability which incorporates relevant information from the energy markets. The suitability of the new composite indicator is assessed by its ability to track financial, economic, and energy crises.

## 1. Introduction

Commodities play a prominent role in the global economy, with their demand and supply influencing various sectors. In particular, changes in the prices of energy commodities can have absolutely relevant consequences, affecting not only the energy industry, but also other sectors of the economy, such as transportation, manufacturing, and construction. For example, huge fluctuations in the prices of energy commodities lead to changes in inflation rates and employment (Abbas and Lan, 2020; Wang et al., 2022), which have an impact on both households and firms. In terms of financial intermediaries, fluctuations in commodity prices have an impact on institutions exposed to these assets, e.g., through loans to commodity producers or exposure to commodity derivatives (Geman, 2009). In addition, interest rates and financial market conditions are known to react to shocks in energy-related commodities (Akram, 2009; Tang et al., 2010). Furthermore, movements in energy commodity prices can have geopolitical implications, such as the relationships between energy-producing and energy-consuming countries (Lee et al., 2021; Li et al., 2023b). In the end, energy commodity shocks are known to be related to volatility in the stock market (Creti et al., 2013; Olson et al., 2014; Ahmed and

Huo, 2021). All these aspects have a potentially significant impact on the financial stability of a country.

Therefore, in recent years, there has been an increasing interest in studying the link between financial stability and energy commodities (Nazlioglu et al., 2015; Flori et al., 2021; Battiston et al., 2021). The COVID-19 pandemic and the Ukranian war have caused significant disruptions in energy supply and demand, thus generating huge shocks in energy prices (Gil-Alana and Monge, 2020; Jia et al., 2021; Sokhanvar and Bouri, 2023).

Although there is a great deal of evidence in this respect, the current approaches to measuring financial stability do not include such information. Given the impact of a pandemic and a war on energy prices and financial stability, it is essential to account for such a relationship when computing composite indices of financial stability. An additional example in this respect is given by the oil shock in the 1980s, which represents another instance of motivating the inclusion of certain commodity parameters in the computation of financial stability indices. The current indicators adopted in the literature have been constructed for tracking purposes and are not forward-looking. As shocks in commodities affect future stability conditions, including such

<footnote><sup>a</sup> Department of Economics and Business, University of Almería, Spain</footnote>

<footnote><sup>b</sup> Mediterranean Research Center of Economy and Sustainable Development (CIMEDES), Spain</footnote>

<footnote><sup>c</sup> Department of Social and Economic Sciences, Sapienza University of Rome, Italy</footnote>

<footnote><sup>d</sup> GRANEM, University of Angers, France</footnote>

<footnote>* Corresponding author at: Department of Economics and Business, University of Almería, Spain.</footnote>

<footnote>E-mail addresses: jsg608@ual.es (J. Sánchez-García), raffaele.mattera@uniroma1.it (R. Mattera), scruz@ual.es (S. Cruz-Rambaud), roy.cerqueti@uniroma1.it (R. Cerqueti).</footnote>
information in the stability measures can help to understand whether we are at the early start of a recession, thus adopting a forward-looking perspective in the measurement.

In this paper, we first provide empirical evidence about the existing connection between the return and risk of energy-related commodities and financial stability in EU, UK, and US. In particular, considering a Granger causality analysis, we show that both returns and volatility of commodities affect financial stability. Supported by this evidence, we propose three new composite indicators of financial stability – one for each region – that incorporate energy-relevant information, i.e., returns and volatilities from the commodities market.

The starting point of our analysis is the Country Index of Systemic Stress (CISS) (Hollo et al., 2012), which aggregates five market-specific subindicators and fifteen individual financial stress measures. After showing that CISS is affected by energy commodities' shocks, we propose to augment the index by incorporating the energy-related commodity variables as new sub-indicators.

Therefore, the first contribution of the paper is the selection of energy-related commodities as new sub-indicators to be included in the new proposed index. The second contribution lies in the two-step methodology adopted for the construction of the composite index, based on Dynamic Factor Models (DFM, Forni et al., 2005; Doz et al., 2012). First, we construct a composite index related to the commodity market, which we call the commodity market factor. The commodity market factor measures the latent dynamics that explain commodity risk and tracks energy-related crises. This factor is then used to provide an adjustment to the baseline financial stability index (Morales and Estrada, 2010). The amount of adjustment varies over time and depends on the empirical distribution function of both financial stability and the commodity factor.

Previous articles dealing with the construction of financial stress indices evaluate their performances in terms of tracking known crises events (e.g., see Hollo et al., 2012; Louzis and Vouldis, 2012; Oet et al., 2015; Duprey et al., 2017). Therefore, in this paper, we also evaluate the suitability of the novel composite index in a similar way. The results show that the newly developed composite index is equally good as the benchmark CISS index (Hollo et al., 2012) for tracking financial crises, while it better recognizes crises related to energy-related crises such as the war in Ukraine and the COVID-19 pandemic that generated different effects in the commodity and stock markets (e.g., see Amar et al., 2021).

The remainder of the paper is structured as follows. Section 2 introduces the literature related to the topic under study. Sections 3 and 4 provide empirical instances that motivate the use of energy commodities in the framework of financial stability measurement. More specifically, Section 3 shows that energy commodities affect financial stability whilst, following a slightly different perspective, Section 4 provides evidence that energy-related commodity information can help in predicting the occurrence of a recession. Section 5 describes the procedure adopted for the construction of the new indicator and discusses the performance of the developed index in tracking both financial and energy crises. Section 6 concludes with final remarks.

## 2. Related literature

As global markets become increasingly interconnected, fluctuations in business and credit cycles have profound impacts on financial stability, influencing macroeconomic indicators, investment decisions, and overall economic performance. In fact, increasing interconnection means larger complexity as the origin and end of a shock are more difficult to trace. Similarly, it is translated into a higher transmission of negative phenomena through the financial system, which can result in cascade effects, panic runs, and ultimately in financial crises such as the Great Recession of 2007–2009.

These arguments have motivated an expansion of the literature on the determinants of financial instability in recent years. As Donath

et al. (2008) specify, financial stability is considered the joint stability of key financial institutions operating within financial markets. This is equivalent to the absence of systemic risk, understood as the risk that a negative event will have significant adverse consequences on the financial system as a whole through propagation effects (Eboli, 2004; Billio et al., 2012). The events that can alter financial stability (or equivalently, trigger systemic risk) are many, and so are the literature streams that consider them.

Due to its strategic importance for world economic activity, commodities have played a prominent role in financial stability analyses. For example, price fluctuations in commodities are known to have a significant effect on the financial conditions of developing and in-development nations that depend on their exports to refinance their debt (Abaidoo and Agyapong, 2022; Abaidoo et al., 2023; Mupunga and Ngundu, 2020; García and Mejía, 2018). Similarly, commodity price movements can have a significant effect on banks' positions, threatening financial stability in low-income countries, especially those that maintain a fixed exchange rate regime and a high share of primary goods in production (Eberhardt and Presbitero, 2021).

Another significant channel through which commodity prices can induce systemic risk is climate-related menaces. Flori et al. (2021) find that network-oriented topological indicators that relate commodity prices with financial stability show that these two hold a significant nexus. Dafermos et al. (2018) show that this connection functions by climate change leading to a rise in defaults, which negatively impacts bank leverage and causes a decrease in asset prices. Furthermore, financial instability triggered due to climate-related factors strengthens their negative impacts on economic growth. In the context of clean asset prices, Reboredo and Ugolini (2018) demonstrate, by using a multivariate vine-copula dependence framework, that significant fluctuations in energy prices had an equal effect on the returns of clean energy stocks from 2009 to 2016.

The aforementioned complexity increase of the international financial system (Bargigli et al., 2015), due to, among other factors, the increase in interconnectedness because of financial globalization, has resulted in an exponential increase in the literature of volatility spillovers (Baele, 2005; Ng, 2000; Christiansen, 2007; Katsiampa et al., 2019; Karali and Ramirez, 2014; Diebold and Yilmaz, 2012; Iqbal et al., 2024; Guan et al., 2024; Hu and Borjigin, 2024; Ben Ameur et al., 2024; Bouteska et al., 2023). Many of these studies are aimed at finding and quantifying those spillovers between energy prices or markets and financial markets (Yadav et al., 2023; Bouteska et al., 2023; Feng et al., 2023; Naeem et al., 2023; Zhao et al., 2023). Another prominent line of research is directed towards renewable energy and green stocks due to the increased interest in the topic (Hanif et al., 2023a,b; Li et al., 2023a; Umar et al., 2024). Yet, it should be mentioned that these kinds of analysis often focus on finding when, where, and how volatility jumps from one market to another, and not on finding the structural determinants of systemic risk.

Network models, on the other hand, are designed to unveil the complex characteristics of the financial system, as well as how shocks originate and can propagate causing banking and financial crises (Sánchez-García and Cruz-Rambaud, 2023a,b; Billio et al., 2012; Gofman, 2017; Berndsen et al., 2018; Battiston et al., 2012; Allen et al., 2012; Hautsch et al., 2015; Cont et al., 2010; Fukker and Kok, 2024; Caccioli et al., 2024; Capponi and Weber, 2024; Sánchez-García and Cruz-Rambaud, 2023c,d). Regarding energy, Uddin et al. (2023) find that the renewable energy sector is the highest transmitter of uncertainty in global energy markets, the effect being amplified by the COVID-19 pandemic. Lautier and Raynaud (2012) show that crude oil is at the core of the complexity of the energy markets. Eventually, Wang et al. (2024) demonstrate that systemic financial risk increases considerably during oil crises, that this effect is concentrated on banks, and that it has long-term negative effects on economic output.

Thus, despite the recognized importance of energy and commodity price shocks for financial stability, existing financial stability indicators
do not track for their impact. Neither are specific analyses that directly use financial stability indicators, such as the CISS, to the extent of our knowledge. These are the main arguments that motivate this research article.

### 3. Do energy commodities affect financial stability?

In this section, we provide the motivation for the development of novel composite indicators, showing that both returns and volatility of energy-related commodities affect financial stability.

#### 3.1. Data and methodology

To measure financial stability, we employ the Composite Indicator of Systemic Stress (CISS) in the financial system, provided by the European Central Bank (ECB). The index is observed at the daily frequency during the time period October 2006–August 2022. This indicator includes 15 raw market-based financial stress measures that are split by employing fundamental portfolio theory in five categories: financial intermediary sector, money markets, equity markets, bond markets, and foreign exchange markets. Therefore, the aggregated index considers the dynamic cross-correlations between the five indices. Note that energy markets (and, more generally, commodities) are excluded from the index calculation. Details about the calculation of the index can be found in Hollo et al. (2012).

The energy data consists of the daily feature prices of natural gas, WTI crude, Brent crude, low-sulphur gasoil, ultralow sulphur (ULS) diesel, and gasoline observed in the aforementioned time span (October 2006–August 2022). This choice is based on the widespread use and significance within energy markets of these energy commodities, which reflect diverse aspects of the energy sector. For instance, we notice that the well-known Dow Jones-UBS Commodity Index, which is the industry benchmark for commodities investing (Dunsby and Nelson, 2010), includes a subselection of the energy commodities considered here. Furthermore, as also highlighted by different previous studies (e.g., see Koch, 2014; Sanders and Irwin, 2014; Demirer et al., 2018), the analysis of these future prices offers valuable insights into different segments of the energy market. These commodities, moreover, are notably related to the considered financial markets of the US, UK, and EU (e.g. see Algieri and Leccadito, 2017; Ayadi et al., 2021). The use of future prices allows accounting for investors' perception of the time to come, and thus represents a better data source for forward-looking analyses (Chinn and Coibion, 2014; Qiao and Han, 2023). Table 1 shows the main descriptive statistics of the variables included in the study.

From Table 1 it can be seen that Europe has the highest mean, median and maximum values of financial stress, being the median more than a 50% higher than the rest of the countries. Since Europe has had more financial stress episodes than the United States, such as the European Debt Crisis (Constancio et al., 2012; Beker, 2014; De Bruyckere et al., 2013), this outcome is not strange. The European data are also 52% more volatile than the one of the US and 25% more volatile than the UK.

All data show positive skewness coefficients, denoting that periods of financial stability are more frequent than periods of financial instability. This is more true for the US, then for the UK, and lastly for the EU, the difference between the US and the UK being much higher (47%) than the one of the UK and the EU (11%). Additionally, all empirical distributions are leptokurtic, that is, they have fat tails with values of very low and very high financial stress being relatively frequent, this being much more true for the US whose Empirical Distribution Function (EDF) tails are 220% fatter than those of the UK.

The CISS is an indicator that assumes values that fall in the interval [0, 1]. When CISS = 0, systemic financial stress is at its lowest level. On the other hand, when CISS = 1, it is at its highest value. The energy time series have been considered in logarithms in order to get rid of the scale of the series and to achieve variance stationarity. Before econometric

<table><caption>**Table 1**
Summary statistics of the variables.</caption><thead><tr><th>Variable</th><th>Mean</th><th>Median</th><th>Minimum</th><th>Maximum</th></tr></thead><tbody><tr><td>UK CISS</td><td>0.13</td><td>0.06</td><td>0.00</td><td>0.74</td></tr><tr><td>EU CISS</td><td>0.20</td><td>0.13</td><td>0.00</td><td>0.93</td></tr><tr><td>US CISS</td><td>0.12</td><td>0.03</td><td>0.00</td><td>0.89</td></tr><tr><td>Natural gas</td><td>4.08</td><td>3.56</td><td>1.48</td><td>13.57</td></tr><tr><td>WTI crude</td><td>72.12</td><td>69.47</td><td>1.10</td><td>145.29</td></tr><tr><td>Brent crude</td><td>77.44</td><td>72.52</td><td>19.33</td><td>146.08</td></tr><tr><td>Low-sulphur gasoil</td><td>679.24</td><td>622.25</td><td>190.75</td><td>1522.5</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>221.58</td><td>205.3</td><td>61.04</td><td>513.54</td></tr><tr><td>Gasoline</td><td>211.82</td><td>204.11</td><td>41.18</td><td>427.62</td></tr></tbody><thead><tr><th></th><th>Std. Dev.</th><th>C.V.</th><th>Skewness</th><th>Ex. kurtosis</th></tr></thead><tbody><tr><td>UK CISS</td><td>0.16</td><td>1.19</td><td>1.47</td><td>1.49</td></tr><tr><td>EU CISS</td><td>0.21</td><td>1.04</td><td>1.32</td><td>1.37</td></tr><tr><td>US CISS</td><td>0.17</td><td>1.42</td><td>2.17</td><td>4.77</td></tr><tr><td>Natural gas</td><td>2.00</td><td>0.49</td><td>1.71</td><td>3.25</td></tr><tr><td>WTI crude</td><td>23.44</td><td>0.32</td><td>0.24</td><td>-0.66</td></tr><tr><td>Brent crude</td><td>25.64</td><td>0.33</td><td>0.25</td><td>-1.02</td></tr><tr><td>Low-sulphur gasoil</td><td>225.71</td><td>0.33</td><td>0.46</td><td>-0.45</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>70.45</td><td>0.31</td><td>0.47</td><td>-0.31</td></tr><tr><td>Gasoline</td><td>65.55</td><td>0.30</td><td>0.32</td><td>-0.53</td></tr></tbody><thead><tr><th></th><th>5% perc.</th><th>95% perc.</th><th>IQ range</th><th>Missing obs.</th></tr></thead><tbody><tr><td>UK CISS</td><td>0.00</td><td>0.51</td><td>0.20</td><td>0</td></tr><tr><td>EU CISS</td><td>0.00</td><td>0.64</td><td>0.29</td><td>0</td></tr><tr><td>US CISS</td><td>0.00</td><td>0.51</td><td>0.16</td><td>0</td></tr><tr><td>Natural gas</td><td>1.99</td><td>8.02</td><td>1.79</td><td>0</td></tr><tr><td>WTI crude</td><td>39.50</td><td>107.68</td><td>39.92</td><td>0</td></tr><tr><td>Brent crude</td><td>41.91</td><td>117.20</td><td>47.03</td><td>0</td></tr><tr><td>Low-sulphur gasoil</td><td>358.50</td><td>1032.3</td><td>377.88</td><td>0</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>119.83</td><td>326.42</td><td>118.89</td><td>0</td></tr><tr><td>Gasoline</td><td>118.27</td><td>318.34</td><td>107.29</td><td>0</td></tr></tbody></table>

analyses, the first differences were calculated for all series to ensure mean stationarity.

For Europe, the highest peaks in the CISS correspond to the period that going from August 2007 to April 2010, and from May 2010 to October 2010 (the Great Recession), from July 2011 to August 2012 (European Debt Crisis), from December 2015 to August 2016 (Europe's Migration Crisis), from September 2020 to November 2020 (the COVID-19 pandemic), and from March 2022 onward (inflationary crisis derived from the Russia-Ukraine armed conflict). In the case of the United States, the highest peaks correspond to the period going from November 2007 to February 2011 (Great Recession), from 2020 to July 2020 (COVID-19 pandemic), and from April 2022 onward. The biggest peaks for the UK coincide with those of Europe.

The volatilities of the energy commodities time series were estimated by filtering the series with a GARCH(1,1) model. The periods of highest volatility for the series coincide with the COVID-19 in 2020–2021 and the inflationary crisis in 2021–2022. Remarkably, these periods coincide with some of the time intervals during which the CISS has been at its highest levels.

Our goal is to test whether financial stability can be driven by energy shocks. If this is the case, we should include information from the energy market in an index that measures overall financial stability. In our framework, we test this hypothesis by means of Granger causality. We notice that although Granger causality does not mean causality (Kilian and Lütkepohl, 2017), it does rule out strict exogeneity (Kilian and Lütkepohl, 2017). Therefore, if we find that energy returns and volatility Granger-cause the CISS, we must reject that the latter is strictly exogenous to the former. In other words, finding evidence of Granger causality from the energy returns and volatility to the CISS is a necessary condition for our analysis of the impact of energy prices on financial stability to be relevant.

For testing the existence of Granger causality, we consider the following vector autoregression (VAR):

$$y_t = \alpha + A_1 y_{t-1} + A_2 y_{t-2} + \dots + A_p y_{t-p} + u_t \quad (1)$$
<table><caption>**Table 2**
Granger causality analysis of the returns of energy markets on the financial stability of the European Union. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30, 3855)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>1.2837</td><td>0.1383</td></tr><tr><td>WTI crude</td><td>3.5316</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.2010</td><td>0.2083</td></tr><tr><td>Low-sulphur gasoil</td><td>1.8800</td><td>0.0026</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>0.8093</td><td>0.7586</td></tr><tr><td>Gasoline</td><td>0.9421</td><td>0.5566</td></tr><tr><td>All lags</td><td>11.528</td><td>0.0000</td></tr></tbody><tfoot><tr><td colspan="3"><hr></td></tr><tr><td>R<sup>2</sup> = 0.1661</td><td>Adjusted R<sup>2</sup> = .1207</td><td>F(210, 3855) = 9.1055</td></tr><tr><td>p-value(F) = 0.00</td><td>β̂ = 0.0003</td><td>DW statistic D = 1.9993</td></tr></tfoot></table>

<table><caption>**Table 3**
Granger causality analysis of the returns of energy markets on the financial stability of the United States. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30, 3855)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>1.5760</td><td>0.0240</td></tr><tr><td>WTI crude</td><td>3.5168</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.5390</td><td>0.0307</td></tr><tr><td>Low-sulphur gasoil</td><td>0.90057</td><td>0.6222</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>1.7828</td><td>0.0055</td></tr><tr><td>Gasoline</td><td>1.1631</td><td>0.2477</td></tr><tr><td>All lags</td><td>5.3730</td><td>0.0000</td></tr></tbody><tfoot><tr><td colspan="3"><hr></td></tr><tr><td>R<sup>2</sup> = 0.1745</td><td>Adjusted R<sup>2</sup> = 0.1295</td><td>F(210, 3855) = 12.8861</td></tr><tr><td>p-value(F) = 0.0000</td><td>β̂ = 0.0005</td><td>DW statistic D = 1.99</td></tr></tfoot></table>

where $\alpha = (\alpha_1, \alpha_2, \dots, \alpha_k)'$ is the vector of independent terms, $A_1, A_2, \dots, A_p$ are the $k \times k$ matrices of coefficient parameters with $A_h = (a_{ij}^{(h)})_{i,j=1,\dots,k}$, $\forall h = 1, \dots, p$, $y_t = (y_{1t}, y_{2t}, \dots, y_{kt})'$ is the vector of random variables at time $t$, and $u_t = (u_{1t}, u_{2t}, \dots, u_{kt})$ is the perturbation term that follows a stochastic white noise process of dimension $k$, such that $u_t \sim (0, \Sigma_u)$, being $\Sigma_u = E(u_t u_t')$ its variance–covariance matrix. Notice that, since we use logarithmic differential series, we rule out any potential deterministic trends.

To discard strict exogeneity from energy prices to financial stability, we need to reject the null hypothesis of no global significance of the lags of the energy commodities returns and volatility to the CISS.

## 3.2. Results

The results of the Granger causality tests of the log-returns of the commodity prices are offered in Tables 2–4.

For the European Union (Table 2), the West Texas Intermediate (WTI) crude and the low sulphur gasoil prices Granger cause the CISS. Since the Euro Area imports significant amounts of fossil fuels, its financial system is exposed to the largest oil price setting index of the world, the WTI. Additionally, the tests reveal exposures to low sulphur gasoil. The Durbin-Watson test points to no autocorrelation, but robust Heteroskedasticity and Autocorrelation Corrected (HAC) errors were employed to ensure that the inference is robust to potential autocorrelation of order higher than one. The model is substantially significant.

In the case of the United States (Table 3), the WTI and the Brent crude oil Granger-cause the CISS. These results reveal how the financial stability of the United States – an energy intensive country with vast reserves of natural gas and crude oil, as well as enormous refining capabilities – is strongly affected by oil prices. The price of the ultra-low-sulphur diesel additionally Granger-causes the CISS. Again, no evidence of autocorrelation is found.

For the United Kingdom (Table 4), the financial system is not exogenous to the prices of WTI and Brent crude oil. These results imply exposures to North American and European oil prices. Moreover, no autocorrelation is found.

Although the financial systems studied in this paper reveal particular exposures to diesel and gasoline prices, what remains clear

<table><caption>**Table 4**
Granger causality analysis of the returns of energy markets on the financial stability of the United Kingdom. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30, 3855)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>0.9652</td><td>0.5200</td></tr><tr><td>WTI crude</td><td>7.9103</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.5961</td><td>0.0209</td></tr><tr><td>Low-sulphur gasoil</td><td>1.1344</td><td>0.2806</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>1.1226</td><td>0.2949</td></tr><tr><td>Gasoline</td><td>1.1175</td><td>0.3012</td></tr><tr><td>All lags</td><td>10.830</td><td>0.0000</td></tr></tbody><tfoot><tr><td colspan="3"><hr></td></tr><tr><td>R<sup>2</sup> = 0.1868</td><td>Adjusted R<sup>2</sup> = 0.1426</td><td>F(210, 3855) = 22.6839</td></tr><tr><td>p-value(F) = 0.0000</td><td>β̂ = -0.0017</td><td>DW statistic D = 2.0031</td></tr></tfoot></table>

<table><caption>**Table 5**
Granger causality analysis of the volatility of energy markets on the financial stability of the European Union. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30, 3853)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>1.3932</td><td>0.0756</td></tr><tr><td>WTI crude</td><td>4.1234</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.2820</td><td>0.1396</td></tr><tr><td>Low-sulphur gasoil</td><td>2.2705</td><td>0.0001</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>1.4527</td><td>0.0530</td></tr><tr><td>Gasoline</td><td>1.7538</td><td>0.0068</td></tr><tr><td>All lags</td><td>9.6231</td><td>0.0000</td></tr></tbody><tfoot><tr><td colspan="3"><hr></td></tr><tr><td>R<sup>2</sup> = 0.1702</td><td>Adjusted R<sup>2</sup> = 0.1250</td><td>F(210, 3853) = 17.3074</td></tr><tr><td>p-value(F) = 0.0000</td><td>β̂ = -0.0003</td><td>DW statistic D = 1.9992</td></tr></tfoot></table>

is the significant exposure that the financial system has to oil price fluctuations. The WTI index, considered as the main reference for oil price setting in the world, Granger-causes the CISS of the Euro area, United States, and United Kingdom. This means that no financial system is exogenous to oil prices. However, the returns of natural gas and gasoline do not show any signs of Granger causality with respect to the three financial systems studied.

We now focus on energy price volatility shocks.

In Table 5, the results regarding the Granger causality of the volatility of the energy prices to the CISS of the Euro area are presented. The model shows no symptoms of autocorrelation and is substantially significant considering the *F* test. When dealing with oil price volatility, again the WTI Granger-causes the CISS of Europe. However, what changes from the log-returns is that, now, the low-sulphur gasoil, the Ultra-Low-Sulphur (ULS) diesel and the gasoline volatilities Granger-cause financial stability. This suggests that the relationship between energy markets and financial stability is stronger in light of volatility, as a larger number of energy commodities show association with CISS. While the non-strict exogeneity of the financial system of Europe to gasoline, gasoil, and diesel returns could not be rejected, volatility shocks on the three main fossil fuels do exert an effect on financial stability. This result is interesting, since it signals that incremental price increases or decreases may not constitute a financial threat, but sudden events that generate volatility shocks to the prices of fossil fuels, such as the COVID-19 pandemic or the recent war in Ukraine, may. Finally, the volatility of natural gas also Granger-causes the CISS. Similarly, although the financial system of the Euro area does not seem to be exposed to trends in the price of natural gas, it is exposed to volatility shocks. This leads to a similar conclusion: drastic events that can cause sudden variations in the price of natural gas can put financial stability at risk.

In the case of the United States (Table 6), the econometric model also presents the desired properties of absence of autocorrelation and significance of the *F* test. In this case, the volatility of natural gas does not Granger-cause the CISS, but the volatility of the WTI and Brent crude do. Similarly, the volatility shocks to low-sulphur gasoil also Granger-cause the financial stability index.

For the United Kingdom, the results are presented in Table 7. Again, the model presents the desired properties. The volatility of the WTI crude as well as the one of the low-sulphur gasoline are Granger causal.
<table><caption>**Table 6**
Granger causality analysis of the volatility of energy markets on the financial stability of the United States. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30,3853)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>0.5617</td><td>0.9740</td></tr><tr><td>WTI crude</td><td>6.4845</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.4020</td><td>0.0718</td></tr><tr><td>Low-sulphur gasoil</td><td>1.7095</td><td>0.0094</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>1.2281</td><td>0.1830</td></tr><tr><td>Gasoline</td><td>1.3324</td><td>0.1066</td></tr><tr><td>All lags</td><td>5.1047</td><td>0.0000</td></tr><tr><td>R<sup>2</sup> = 0.1719</td><td>Adjusted R<sup>2</sup> = 0.1267</td><td>F(210, 3853) = 102.5984</td></tr><tr><td>p-value(F) = 0.0000</td><td>β̂ = -0.0003</td><td>DW statistic D = 2.0005</td></tr></tbody></table>

<table><caption>**Table 7**
Granger causality analysis of the volatility of energy markets on the financial stability of the UK. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Variable</th><th>F(30,3853)</th><th>p-value</th></tr></thead><tbody><tr><td>Natural gas</td><td>0.9424</td><td>0.5561</td></tr><tr><td>WTI crude</td><td>5.4068</td><td>0.0000</td></tr><tr><td>Brent crude</td><td>1.1475</td><td>0.2653</td></tr><tr><td>Low-sulphur gasoil</td><td>1.8401</td><td>0.0035</td></tr><tr><td>Ultra-low-sulphur diesel</td><td>1.1222</td><td>0.2954</td></tr><tr><td>Gasoline</td><td>2.0819</td><td>0.0005</td></tr><tr><td>All lags</td><td>10.775</td><td>0.0000</td></tr><tr><td>R<sup>2</sup> = 0.1874</td><td>Adjusted R<sup>2</sup> = 0.1431</td><td>F(210, 3853) = 54.4273</td></tr><tr><td>p-value(F) = 0.0000</td><td>β̂ = 0.0003</td><td>DW statistic D = 1.9992</td></tr></tbody></table>

From the econometric analysis carried out in this section, it is possible to conclude that financial stability is not exogenous to energy prices and energy price shocks. Oil prices and oil price volatilities Granger cause the CISS through the WTI crude oil in all the countries studied in this paper. Therefore, there is robust evidence that the WTI index is one of the main explainers of financial stability between the energy sources considered. In the case of natural gas, the log-returns are never Granger causal, whereas the volatility is for Europe. This reveals a particular exposure of the financial system to price shocks in natural gas due to, among other factors, supply-demand disruptions due to the war in Ukraine.

## 4. Predicting the probability of a recession

In order to assess to what extent energy markets add relevant information to financial stability indicators, we conducted a forecasting evaluation exercise. With this approach, we estimate dynamic Logit models with the form

$$P(Y_t = 1) = \frac{1}{1 + \exp\{-f(X_t)\}}$$ $$f(X_t) = \beta_0 + \beta_1 X_{1t} + \beta_2 X_{2t} + \dots + \beta_k X_{kt} + \epsilon_t$$

where $Y_t \in \{0, 1\}$ is a binary variable, so that $Y_t = 1$ if the economy goes through a recession, and $Y_t = 0$ if not. The recession periods are the ones stipulated by the NBER for the US and by the OECD for the UK and EU, and these are available to the public at the Federal Reserve Economic Data webpage.

Both the OECD and the NBER define recessions as turning points in business cycles, starting at peaks and ending at troughs. However, they employ different methodologies. The OECD uses a standardized “growth cycle” approach, utilizing deviation-from-trend data series and GDP as a benchmark. In contrast, the NBER operates a Business Cycle Dating Committee (BCDC) for the US, which defines recessions based on significant decreases in economic activity across sectors lasting more than a few months. The committee considers depth, diffusion, and duration criteria, allowing for differentiation between contractions and recessions. We believe that in these kinds of evaluations, counting with a specialized committee of experts that is able to provide their criteria adds value to mere statistical indicators. However, while a similar

<table><caption>**Table 8**
Dynamic Logit model statistics for the European economy. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Statistic</th><th>CISS</th><th>CISS+E</th><th>Performance</th></tr></thead><tbody><tr><td>McFadden R<sup>2</sup></td><td>0.0816</td><td>0.3960</td><td>Δ384%</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.0810</td><td>0.3930</td><td>Δ385%</td></tr><tr><td>Log-likelihood</td><td>-2448.61</td><td>-1610.32</td><td>Δ34%</td></tr><tr><td>Akaike criterion</td><td>4901.22</td><td>3236.64</td><td>Δ34%</td></tr><tr><td>Schwarz criterion</td><td>4913.86</td><td>3287.18</td><td>Δ35%</td></tr><tr><td>Hannan-Quinn</td><td>4905.70</td><td>3254.53</td><td>Δ34%</td></tr><tr><td>'Correctly predicted'</td><td>69.1%</td><td>81.9%</td><td>Δ18%</td></tr><tr><td>Likelihood ratio test χ<sup>2</sup>(1)</td><td>435.35</td><td>2111.94</td><td>Δ384%</td></tr><tr><td>Sample size (T)</td><td>4095</td><td>4095</td><td>—</td></tr></tbody></table>

committee exists for the Euro Area, it lacks daily quantitative indicators like the NBER, leading to the decision to use NBER for the US and OECD for the Euro Area and the UK for consistent analyses. However, we also include analyses for the US that employ the OECD indicators as a robustness test, with qualitatively similar results.

For the empirical estimates of $f(X_t)$, denoted hereafter by $\hat{f}(X_t)$, we consider two models for each country:

$$\hat{f}_1(X_t) = \hat{\beta}_0 + \hat{\beta}_1 \text{CISS}_t \quad (2)$$

$$\hat{f}_2(X_t) = \hat{\beta}_0 + \hat{\beta}_1 \text{CISS}_t + \sum_{i=2}^{7} \hat{\beta}_i Z_{it} \quad (3)$$

where $Z_{it}$ includes the price of the six energy commodities by order, i.e., natural gas, WTI crude oil, Brent crude oil, low sulphur gasoil, ULS diesel, and gasoline. We call the models (2) and (3) CISS and CISS+E, respectively, and compare their performance in correctly predicting that the economy is in recession.

We do not perform any transformation of the variables to achieve mean-variance stationarity. The main reason for this is that we are not interested in statistical inference but in forecasting performance, particularly, in how well the models predict past recessions. For this reason, we do not include information related to inferences. However, some authors have presented theoretical results showing that binary outcome models are robust to nonstationary processes (Park and Phillips, 2000; Chang et al., 2005).

Figs. 1–4 present empirical evidence on the predictive performance of CISS (2) and CISS+E (3), i.e., models of CISS plus energy markets. The blue line shows the predictive performance of the CISS, whilst the blue line displays CISS+E. The grey bars are the recession dates, where $Y_t = 1$.

As shown in all figures, including energy markets significantly increases the predictive performance of the model. In all three economies, CISS+E assigns more probability to those dates when the economy is in a recession. This is especially true for the European economy in all three main recessions of the sample period (2008–2009, 2012–2013, 2018–2020). But it is also true for the British and North American economies, especially during the Great Recession (2008–2009).

Equally relevant is that the CISS+E model assigns fewer ‘false positives’ in all three cases. For example, in the US, CISS+E assigns a lower probability in 2012, when the economy, in fact, did not enter a recession phase. Similarly, this result holds for the model of the UK. Of particular relevance is that, for the economy of the Eurozone, the CISS+E model eliminates the noise that is present for the CISS only model, which assigns $P(Y_t = 1) > 0.2 \forall t$, that is, the probability of a recession is always greater than 0.2.

Tables 8, 9, 10, and 11 compare the core statistics of the model corresponding to the CISS with those of the CISS plus energy markets model.

In all cases, including energy markets in the model with the CISS+E significantly (sometimes drastically, as in the case of the European economy) improves the relevant statistics. The McFadden regular and adjusted R<sup>2</sup> statistics experiment increases that range from 36% to
<figure><img src="image_4.png" /><figcaption>Fig. 1. Europe recession probabilities against actual recessions. Grey bars: OECD recession dates. Red line: CISS and energy markets. Blue line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. United States of America recession probabilities against actual recessions. Grey bars: NBER recession dates. Red line: CISS and energy markets. Blue line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. United Kingdom recession probabilities against actual recessions. Grey bars: OECD recession dates. Red line: CISS and energy markets. Blue line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 4. United States of America recession probabilities against actual recessions (2). Grey bars: recession dates. Red line: CISS and energy markets. Blue line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 9**

Dynamic Logit model statistics for the British economy. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Statistic</th><th>CISS</th><th>CISS+E</th><th>Performance</th></tr></thead><tbody><tr><td>McFadden R<sup>2</sup></td><td>0.3574</td><td>0.4909</td><td>Δ36%</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.3562</td><td>0.4862</td><td>Δ36%</td></tr><tr><td>Log-likelihood</td><td>-1097.48</td><td>-869.47</td><td>V20%</td></tr><tr><td>Akaike criterion</td><td>2198.97</td><td>1754.94</td><td>V20%</td></tr><tr><td>Schwarz criterion</td><td>2211.60</td><td>1805.48</td><td>V18%</td></tr><tr><td>Hannan-Quinn</td><td>2203.44</td><td>1772.83</td><td>V19%</td></tr><tr><td>'Correctly predicted'</td><td>90.5%</td><td>92.4%</td><td>Δ2%</td></tr><tr><td>Likelihood ratio test χ<sup>2</sup>(1)</td><td>1220.72</td><td>1676.74</td><td>Δ36%</td></tr><tr><td>Sample size (T)</td><td>4095</td><td>4095</td><td>-</td></tr></tbody></table>

<table><caption>**Table 10**

Dynamic Logit model statistics for the North American economy. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Statistic</th><th>CISS</th><th>CISS+E</th><th>Performance</th></tr></thead><tbody><tr><td>McFadden R<sup>2</sup></td><td>0.5124</td><td>0.7363</td><td>Δ44%</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.5109</td><td>0.7304</td><td>Δ43%</td></tr><tr><td>Log-likelihood</td><td>-666.59</td><td>-360.52</td><td>V85%</td></tr><tr><td>Akaike criterion</td><td>1337.19</td><td>737.04</td><td>V45%</td></tr><tr><td>Schwarz criterion</td><td>1349.82</td><td>787.58</td><td>V42%</td></tr><tr><td>Hannan-Quinn</td><td>1341.66</td><td>754.94</td><td>V43%</td></tr><tr><td>'Correctly predicted'</td><td>93.5%</td><td>98.1%</td><td>Δ7%</td></tr><tr><td>Likelihood ratio test χ<sup>2</sup>(1)</td><td>1401.02</td><td>2013.16</td><td>Δ44%</td></tr><tr><td>Sample size (T)</td><td>4095</td><td>4095</td><td>-</td></tr></tbody></table>

<table><caption>**Table 11**

Dynamic Logit model statistics for the North American economy with the OECD recession probabilities. Inference corresponds to robust HAC errors.</caption><thead><tr><th>Statistic</th><th>CISS</th><th>CISS+E</th><th>Performance</th></tr></thead><tbody><tr><td>McFadden R<sup>2</sup></td><td>0.0440</td><td>0.0722</td><td>Δ46%</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.0433</td><td>0.0693</td><td>Δ46%</td></tr><tr><td>Log-likelihood</td><td>-2595.34</td><td>-2518.71</td><td>V3%</td></tr><tr><td>Akaike criterion</td><td>5194.68</td><td>5053.42</td><td>V3%</td></tr><tr><td>Schwarz criterion</td><td>5207.31</td><td>5103.96</td><td>V2%</td></tr><tr><td>Hannan-Quinn</td><td>5199.15</td><td>5071.31</td><td>V3%</td></tr><tr><td>'Correctly predicted'</td><td>65.6%</td><td>65.8%</td><td>Δ1%</td></tr><tr><td>Likelihood ratio test χ<sup>2</sup>(1)</td><td>239.01</td><td>392.27</td><td>Δ46%</td></tr><tr><td>Sample size (T)</td><td>4095</td><td>4095</td><td>-</td></tr></tbody></table>

385%. These improvements are also reflected in related statistics, such as log-likelihood and the AIC, BIC, and HQ criteria. The cases that are correctly predicted, i.e., $\hat{P}(Y_t = 1) > 0.5$ when $P(Y_t = 1)$, also improve with the CISS+E model, especially in the case of the EU, where this statistic goes from 69.1% to 81.9%. Finally, the empirical statistic $\chi^2$

of the likelihood ratio test experiments (drastic in the European case) increases, thus severely increasing the chances of rejecting the null hypothesis of no global significance of the model.

## 5. A novel composite index for financial stability

In what follows, building on the results provided by model (3), we present the methodology adopted for the development of a novel CISS indicator that is adjusted to include information from the energy market. We call this indicator adj-CISS. Then, we show the main empirical results associated with the adj-CISS indices for the three countries, i.e., US, UK and EU.

### 5.1. Methodology

Composite indicators are used to measure concepts that cannot be captured by a single variable, as occurs with financial stability. As argued by Morales and Estrada (2010), an important issue when developing financial stability measures is the absence of consensus on its definition. Financial stability, indeed, has main sources, ranging from those related to financial institutions and, more broadly, the stock market to those based on macroeconomic aggregates. In what follows, given the empirical instances presented in the previous sections, we also incorporate information related to the energy market in the financial stability index calculation.

Composite indicators aggregate several sub-indicators into a single meaningful variable measuring the latent concept of interest. In general, the construction of a composite index requires many preliminary steps (Greco et al., 2019). One of the most important is the framework definition along with the selection of the sub-indicators to be considered and the definition of their weights.

In this paper, we consider the CISS as a base indicator of financial stability because it is available for many countries, making them comparable in terms of financial stability. As explained more detailedly in Section 2, the CISS aggregates five market-specific sub-indicators and fifteen individual financial stress measures. Given that the framework behind the CISS is the measurement of financial stability, according to previous sections, we include energy-related commodities as new information in the index. In particular, we propose to adjust the baseline composite indicator CISS_t with the information related to the commodity market, which we call CM_t:

$$ \text{adj-CISS}_t = (1 - \delta)\text{CISS}_t + \delta\text{CM}_t \quad (4) $$

with $\delta \in [0, 1]$ being the degree of adjustment to the baseline indicator.
We notice that, in accordance with the original setting introduced by Hollo et al. (2012), the proposed adjustment mechanism (Eq. (4)) adopts a portfolio perspective, where we choose a suitable share δ to be allocated in the new term CM. Hence, the proposed framework shares the same economic intuitions as the CISS. In particular, we consider the CISS as the primary index of interest, and recognize the interconnectedness of financial markets and the commodity markets. The diversification strategy involves weighting the CISS with the CM index within the portfolio.

The consequence of this interpretation is twofold. First of all, by incorporating the CM index we introduce diversification benefits. This helps to mitigate the specific risks associated with the financial stability index, particularly those influenced by movements in commodity prices. As a result, the portfolio – i.e. the composite index – becomes more resilient to market shocks and fluctuations. Second, the inclusion of the CM index enables a more comprehensive analysis of financial stability. By examining the interactions between financial markets and commodity markets, we gain insights into the broader macroeconomic dynamics that can affect financial stability. This holistic perspective enhances our ability to assess and manage systemic risks.

Given the economic and financial interoperability of (4), two main issues can be however highlighted. First, the definition of commodity market information CM<sub>t</sub> and, second, the determination of the optimal degree of adjustment δ.

Let us focus on the first issue. Since the relationship between volatility and financial stability is negative – meaning that increasing volatility is associated with lower stability – the most reasonable choice is to consider the volatility of the energy commodities as the main adjustment mechanism to CISS. The volatility of the commodities can be easily estimated by means of GARCH models. However, considering all the volatilities contemporaneously in (4) there arises a relevant problem of signal distortion, which should be avoided. To overcome this issue, we constructed a synthetic measure of “energy market volatility” that is used to proxy the quantity CM<sub>t</sub> in (4). Different approaches can be used for this task. For example, an optimal synthesis can be defined on the basis of correlation (Hollo et al., 2012) or, if a reasonable dependent variable is available, regression analysis (Sorić et al., 2016; Mattera et al., 2022b). While the latter has its main drawback in the lack of a suitable dependent variable, the main issue related to correlation-based approaches is that correlations could be statistically nonsignificant or, more generally, even significant correlations would not imply causality. Therefore, nowadays both approaches are scarcely employed (Greco et al., 2019), and an often considered alternative for the synthesis of many time series is the factor model (e.g., see Gelper and Croux, 2010; Morales and Estrada, 2010; Charles et al., 2018; Mattera et al., 2022a).

Following a factor model, we assume that all K volatilities at a given time t, $z_{k,t}$ ($k = 1, 2, \dots, K$), can be explained by a common component $f_t$:

$$z_{k,t} = \lambda_k f_t + e_{k,t}, \quad (5)$$

with $\lambda_k$ is the kth factor loading and $e_{k,t}$ is the kth idiosyncratic component. Accordingly, the common (latent) component $f_t$ can be used as an indicator of financial stability. Stock and Watson (2002) demonstrate that, under regularity conditions, the Principal Component (PC) estimator allows for a consistent estimation of $f_t$. However, in a time series framework, it would be relevant to also include p lagged factors in (5):

$$z_{k,t} = \sum_{i=0}^{p} \lambda_{k,i} f_{t-i} + e_{k,t}. \quad (6)$$

Notice that (6) can be seen as a static factor model with p + 1 static factors. The model in Eq. (6) is called Dynamic Factor Model, and the common part of the model is $\chi_t = \lambda' F_t$, where $F_t = (f_t, f_{t-1}, \dots, f_{t-p})'$ and $\lambda$ is the matrix of dimension k × p with the generic element $\lambda_{h,q}$; $h = 1, \dots, k$; $q = 1, \dots, p$. For a more in-depth discussion of the

technical properties of dynamic factor models, we refer the reader to Forni et al. (2005). A common solution to estimate latent factors is the Dynamic Principal Component estimator (Brillinger, 2001). In this paper, however, we adopt a more recent approach developed by Doz et al. (2011, 2012) in the estimation of the latent factor. The estimated factor is the term $f_t$ in (6), which we call CM<sub>t</sub>.

The second issue relies on the determination of the adjustment δ. Our aim is to adjust the baseline CISS in the presence of shocks in energy prices, assuming that a constant δ in (4) is clearly reductive. Ideally, the degree of adjustment should vary over time, i.e.,

$$\text{adj-}\text{CISS}_t = (1 - \delta_t)\text{CISS}_t + \delta_t \text{CM}_t, \quad (7)$$

and $\delta_t$ should be larger since the larger volatility in the commodity market is in the right tail of its distribution for each time t. Starting from this intuition, we propose a simple data-driven approach for choosing the amount of adjustment dynamically. Let us define $\Phi_1(\cdot)$ as the empirical cumulative distribution function (ECDF) of the volatility of the energy market and $\Phi_2(\cdot)$ as the ECDF of the CISS of a given country. The use of $\Phi_1(\cdot)$ and $\Phi_2(\cdot)$ allows us to focus on the right tail of the distribution of both time series, i.e., large values of instability. A suitable weighting approach is given by

$$\delta_t = \frac{\Phi_1(\text{CM}_t)}{\Phi_2(\text{CISS}_t)} \quad (8)$$

The intuition behind (8) is easy. When $\Phi_1(\text{CM}_t) > \Phi_2(\text{CISS}_t)$, the volatility in the commodity market is particularly large, the adjustment should be considerable. The larger the ratio, the larger the amount of adjustment. Vice versa, when $\Phi_1(\text{CM}_t) < \Phi_2(\text{CISS}_t)$ the role of the commodity market is clearly less relevant and needs to be less weighted. In the extreme case in which the volatility of the commodity market at time t is on the left of its distribution, i.e., low volatility conditions, while the CISS is in the right tail, it makes no sense to provide a high weighting to the commodity market for measuring financial stability. On the contrary, if national markets are in a tranquil period – thus being in the left tail of the distribution – while there is a huge crisis in the energy markets, not considering information from the energy market biases the perception about the overall levels of financial stability. By adopting this approach in the adjustment determination, we explore several sources of heterogeneity, as the adjustment coefficients virtually differ across both time and countries.

## 5.2. Empirical results

To be effective in practice, we need the novel composite indicator to increase in presence of energy-related commodity shocks. In what follows, we evaluate the performance of the composite indicator in this regard. The temporal evolution of the adjusted CISS (7) is shown in Fig. 5, while a Country specific comparison between the baseline CISS and its adjusted version results are shown in Figs. 6–8.

We interestingly notice that the novel composite index tracks the baseline CISS indicator well during the 2008 financial crisis. This means that the adjustment is not very large. However, we observe a huge spike in the indicator in 2020, that is, during the COVID-19 pandemic. The baseline CISS also increases, but by a low amount compared with the financial crisis. This is the effect of a high adjustment $\delta_t$ during 2020. Indeed, the commodity factor distribution, which summarizes the volatility of the energy market, falls in the extreme right tail of its empirical distribution compared with the baseline indicator. Similarly, an important spike in the novel composite indicator is observed in 2022, in correspondence with the Russian invasion of Ukraine. Ukraine is indeed an important transit country for natural gas pipelines that transport Russian gas to Europe. The invasion created concerns about the stability of gas supplies, leading to uncertainty and speculation in the energy markets, thus causing a considerable price increase. Furthermore, geopolitical tensions and the threat of further escalation in the region have increased market uncertainty and risk perception. All these
<figure><img src="image_8.png" /><figcaption>Fig. 5. Temporal evolution of the composite indices (adj-CISS).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Temporal evolution of the European adj-CISS against the baseline CISS. Grey bars: recession dates. Blue line: adj-CISS. Black line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

events are not well captured by the baseline index, which fluctuates around relatively low levels. Note that the economic sanctions imposed on Russia after the invasion had an impact on its financial stability, especially considering the restricted access to international financial markets for Russian investors.

Thus, in-sample analysis shows the good performance of the proposed indicator to track financial stability. Therefore, policymakers can adopt the proposed indicator, for example, for out-of-sample forecasting of crisis periods. Figs. 9 and 10 show an exercise of this kind for the period from December 2019 to August 2022. We estimate Logit and Probit models with the dependent variable being 0 when the economy is not under a recession and 1 when it is, and the independent variable being the adj-CISS index. The training data set that runs from October 2006 to November 2019. Figs. 9 and 10 show the probabilities assigned by the index for the period outside the sample, that is, until August 2022.

The index correctly assigns maximum probabilities of recession during the COVID-19 lockdown in April and May 2020. Similarly, it assigns very high probabilities of recession for the EU and UK since the

<table><caption>Table 12
Performance statistics of the out of sample Logit forecasts for the period [09-2020, 08-2022].</caption><thead><tr><td>Statistic</td><td>EU</td><td>USA</td><td>UK</td></tr></thead><tbody><tr><td>Mean Error (ME)</td><td>-0.1756</td><td>-0.0109</td><td>0.0693</td></tr><tr><td>Mean Squared Error (MSE)</td><td>0.4152</td><td>0.2416</td><td>0.3608</td></tr><tr><td>Absolute Mean Error (AME)</td><td>0.3812</td><td>0.0869</td><td>0.1903</td></tr><tr><td>Bias proportion</td><td>0.1787</td><td>0.0020</td><td>0.0368</td></tr><tr><td>Regression proportion</td><td>0.0140</td><td>0.1776</td><td>0.0129</td></tr><tr><td>Random proportion</td><td>0.8072</td><td>0.8203</td><td>0.9501</td></tr></tbody></table>

start of the Russian-Ukraine armed conflict in February 2022. Tables 12 and 13 show the performance of the forecasts, with most of the errors being due to randomness and not because of biases, a highly desired property to ask to a forecasting model.

Eventually, the importance of the adj-CISS index to track recessions is further corroborated by the econometric models estimated for the full sample period, reported in Tables 14 and 15. The coefficients are
<figure><img src="image_10.png" /><figcaption>Fig. 7. Temporal evolution of the United States adj-CISS against the baseline CISS. Grey bars: recession dates. Red line: adj-CISS. Black line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Temporal evolution of the United Kingdom adj-CISS against the baseline CISS. Grey bars: recession dates. Green line: adj-CISS. Black line: CISS. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 13**
Performance statistics of the out of sample Probit forecasts for the period [09-2020, 08-2022].</caption><thead><tr><th>Statistic</th><th>EU</th><th>USA</th><th>UK</th></tr></thead><tbody><tr><td>Mean Error (ME)</td><td>-0.1764</td><td>-0.0090</td><td>0.0663</td></tr><tr><td>Mean Squared Error (MSE)</td><td>0.4159</td><td>0.2421</td><td>0.3615</td></tr><tr><td>Absolute Mean Error (AME)</td><td>0.3816</td><td>0.0853</td><td>0.1939</td></tr><tr><td>Bias proportion</td><td>0.1800</td><td>0.0014</td><td>0.0336</td></tr><tr><td>Regression proportion</td><td>0.0150</td><td>0.1802</td><td>0.0134</td></tr><tr><td>Random proportion</td><td>0.8048</td><td>0.8183</td><td>0.9529</td></tr></tbody></table>

positive and statistically significant as expected, with high marginal effects for all countries (specially for the EU and the UK) in both, the Logit and Probit models. Furthermore, the Mc-Fadden $R^2$ and adjusted $R^2$ statistics show values that go from 8% to 50%, which can be reasonably considered as high for only one independent variable, specially when taking into account that they rarely reach values beyond 0.5 (Smith and McKenna, 2013). The adj-CISS index correctly predicts

recessions with an accuracy that goes from 70% to 93.5% in both, Logit and Probit models.

## 6. Final remarks

This paper investigates the link between financial stability and energy commodities. With the COVID-19 pandemic and the Ukranian war causing significant disruptions in energy supply and demand, it has become evident that energy commodity shocks have important implications for financial stability. Despite the wide evidence supporting this relationship, current approaches to measuring financial stability overlook the influence of energy commodities.

To address this gap, we have first provided empirical evidence showing that a significant relationship between energy-related commodities and financial stability in key economies, namely the EU, UK, and US, exists. Building on this evidence, we proposed a new composite indicator of financial stability that is country-specific and incorporates relevant information from the commodity market. The construction of these composite indicators has been guided by a two-step methodology based on Dynamic Factor Models. After constructing
<figure><img src="image_12.png" /><figcaption>Fig. 9. Out of sample forecasts for the period [09-2020, 08-2022] of the Logit models with recession dates as dependent variables and the adj-CISS indices as independent variables. The models were trained with data from October 2006 to November 2019. The out of sample forecasting period goes from the beginning of December 2019 to the end of August 2022.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Out of sample forecasts for the period [09-2020, 08-2022] of the Probit models with recession dates as dependent variables and the adj-CISS indices as independent variables. The models were trained with data from October 2006 to November 2019. The out of sample forecasting period goes from the beginning of December 2019 to the end of August 2022.</figcaption></figure>

an energy-related commodity factor, we proposed an adjustment of the baseline indicator of financial stability. It can be highlighted an economic interpretation in light of portfolio theory of the resulting adjusted indicator, as in Hollo et al. (2012).

Our evaluation of the newly developed composite index has shown its effectiveness in tracking financial crises, including those associated with energy-related events such as the COVID-19 pandemic and the war in Ukraine. In contrast to conventional benchmarks, our composite index offers a more nuanced understanding of crises related to the commodity markets, particularly those influenced by energy dynamics. This perspective underscores the ability of the newly defined indicator to track impacts of energy-related shocks on financial stability. The practical implications of our findings can be relevant for policymakers. By furnishing policymakers with a refined tool for monitoring and analysing energy market risks, the proposed composite index facilitates informed decision-making in times of economic uncertainty. Furthermore, our research indicates the robustness of our

approach across different crisis definitions, further solidifying its reliability and applicability in real-world scenarios. Thus, the adoption of our composite index holds significant promise for enhancing risk management practices and fortifying financial resilience amidst energy market disruptions.

## 6.1. Future research

Importantly, some future research lines can be highlighted.

The first relates to the replication and amplification of our assessment to developing countries. Indeed, these are economies that are frequently specialized in exporting commodities and, therefore, exposed to fluctuations in their prices. Added to high levels of indebtedness, high volatility in the price of commodities can lead to a balance of trade imbalance, which, at the same time, can translate into debt repayment and refinancing difficulties. Additionally, this will decrease investor confidence in the country, leading to funding problems, which further exacerbate the financial difficulties of the country. Eventually,
<table><caption>**Table 14**
Results of the Logit model with adj-CISS as independent variables and recession phases as independent variables.</caption><thead><tr><th>Statistic</th><th>EU</th><th>USA</th><th>UK</th></tr></thead><tbody><tr><td>Constant</td><td>-1.3043***</td><td>-4.6989***</td><td>-3.7418***</td></tr><tr><td>Standard Error</td><td>(0.0506)</td><td>(0.1439)</td><td>(0.1032)</td></tr><tr><td>adj-CISS β̂</td><td>3.0771***</td><td>10.0788***</td><td>6.9292***</td></tr><tr><td>Standard Ereror</td><td>(0.1588)</td><td>(0.4099)</td><td>(0.2488)</td></tr><tr><td>Marginal effect (∂P(Y = 1)/∂X)</td><td>0.6978</td><td>0.3505</td><td>0.5037</td></tr><tr><td>Mc-Fadden R<sup>2</sup></td><td>0.0815</td><td>0.5107</td><td>0.3573</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.0807</td><td>0.5093</td><td>0.3561</td></tr><tr><td>Akaike Crit.</td><td>4901.92</td><td>1341.74</td><td>2199.12</td></tr><tr><td>Schwarz Crit.</td><td>4914.55</td><td>1354.38</td><td>2211.76</td></tr><tr><td>Hannan-Quin Crit.</td><td>4906.39</td><td>1346.21</td><td>2203.59</td></tr><tr><td>Correctly predicted</td><td>70%</td><td>93.5%</td><td>90.5%</td></tr><tr><td>f(β̂'X) for X̄</td><td>0.227</td><td>0.035</td><td>0.073</td></tr><tr><td>χ<sup>2</sup> likelihood ratio</td><td>434.651</td><td>1396.46</td><td>1220.56</td></tr><tr><td>p-value (χ<sup>2</sup>)</td><td>(0.0000)</td><td>(0.0000)</td><td>(0.0000)</td></tr></tbody></table>

<table><caption>**Table 15**
Results of the Probit model with adj-CISS as independent variables and recession phases as independent variables.</caption><thead><tr><th>Statistic</th><th>EU</th><th>USA</th><th>UK</th></tr></thead><tbody><tr><td>Constant</td><td>-0.8003***</td><td>-2.5640***</td><td>-2.0273***</td></tr><tr><td>Standard Error</td><td>(0.0298)</td><td>(0.0661)</td><td>(0.0460)</td></tr><tr><td>adj-CISS β̂</td><td>1.9078***</td><td>5.4409***</td><td>3.7408***</td></tr><tr><td>Standard Ereror</td><td>(0.0964)</td><td>(0.1969)</td><td>(0.1251)</td></tr><tr><td>Marginal effect (∂P(Y = 1)/∂X)</td><td>0.7076</td><td>0.4288</td><td>0.6131</td></tr><tr><td>Mc-Fadden R<sup>2</sup></td><td>0.0817</td><td>0.5198</td><td>0.3476</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.0809</td><td>0.5183</td><td>0.3464</td></tr><tr><td>Akaike Crit.</td><td>4900.99</td><td>1316.96</td><td>2232.35</td></tr><tr><td>Schwarz Crit.</td><td>4913.62</td><td>1329.59</td><td>2244.98</td></tr><tr><td>Hannan-Quin Crit.</td><td>4905.46</td><td>1321.43</td><td>2236.82</td></tr><tr><td>Correctly predicted</td><td>70%</td><td>93.5%</td><td>90.5%</td></tr><tr><td>f(β̂'X) for X̄</td><td>0.371</td><td>0.079</td><td>0.164</td></tr><tr><td>χ<sup>2</sup> likelihood ratio</td><td>435.589</td><td>1421.24</td><td>1187.33</td></tr><tr><td>p-value (χ<sup>2</sup>)</td><td>(0.0000)</td><td>(0.0000)</td><td>(0.0000)</td></tr></tbody></table>

if the country is of relevant magnitude for the financial system, with many other countries having open positions on it, it can result in a systemic crisis. This dependence on commodity prices of developing countries makes us expect a larger gap between traditional financial stress measures and our proposed amplification of the CISS index. The study of developing countries poses however additional challenges, such as the selection of relevant commodities to consider while constructing the adjusted indicator. Indeed, different commodities may be relevant for the financial stability of developing countries, depending on the particular structure of the economy (Bodart et al., 2015).

The second research line relates to the construction of the composite index and its adjustment mechanism. In this paper, we remain agnostic about the type of correlation structure that exists between CISS and CM. However, it would be possible to choose the degree of adjustment using a correlation-based approach. For example, we intend to explore the use of copula functions. In this respect, it would be interesting to understand whether more accuracy in tracking financial stability could be achieved by using a different approach to calculating the adjustment.

Finally, we notice that (8) assumes the existence of some correlation between CISS and CM, which can be due to variables affecting commodity prices that are factored in the CISS (such as the foreign exchange market, e.g., see Ayres et al., 2020). However, we are agnostic about the type of correlation structure existing between CISS and CM since the adjustment in (8) depends on marginal distributions, which can come out from different types of joint distributions.

It would be possible to select $δ_t$ by following a correlation-based approach. However, this procedure leads to a restriction of our perspective, in that we should exploit a copula function and apply Sklar's theorem (Sklar, 1959) to identify the joint distribution from the marginals.

However, the selection of the appropriate copula presents sources of arbitrariness, and it can also happen that two different subperiods are associated with different best copulas describing the (tail, more likely) dependence structure. Therefore, we would lose the generality of the proposed approach, which admits any choice of dependence structure while being simple and appropriately driven by empirical data.

In sum, we think that a copula approach is without doubt interesting, and deserves a devoted study. We plan to exploit the powerfulness of copulas for dealing with financial stability in presence of energy shocks in future research.

### CRediT authorship contribution statement

**Javier Sánchez-García:** Writing – review & editing, Writing – original draft, Validation, Software, Project administration, Methodology, Investigation, Data curation, Conceptualization. **Raffaele Matera:** Writing – review & editing, Writing – original draft, Software, Project administration, Methodology, Investigation, Data curation, Conceptualization. **Salvador Cruz-Rambaud:** Writing – review & editing, Validation, Supervision, Project administration, Formal analysis. **Roy Cerqueti:** Validation, Supervision, Project administration, Methodology, Formal analysis.

### References

Abaidoo, R., Agyapong, E.K., 2022. Commodity price volatility, inflation uncertainty and political stability. Int. Rev. Econ. 69 (3), 351–381.

Abaidoo, R., Agyapong, E.K., Boateng, K.F., 2023. Stability in the banking industry and commodity price volatility: perspective from developing economies. J. Econ. Adm. Sci. 39 (4), 988–1012.

Abbas, S.K., Lan, H., 2020. Commodity price pass-through and inflation regimes. Energy Econ. 92, 104977.

Ahmed, A.D., Huo, R., 2021. Volatility transmissions across international oil market, commodity futures and stock markets: Empirical evidence from China. Energy Econ. 93, 104741.

Akram, Q.F., 2009. Commodity prices, interest rates and the dollar. Energy Econ. 31 (6), 838–851.

Algieri, B., Leccadito, A., 2017. Assessing contagion risk from energy and non-energy commodity markets. Energy Econ. 62, 312–322.

Allen, F., Babus, A., Carletti, E., 2012. Asset commonality, debt maturity and systemic risk. J. Financ. Econ. 104 (3), 519–534.

Amar, A.B., Belaid, F., Youssef, A.B., Chiao, B., Guesmi, K., 2021. The unprecedented reaction of equity and commodity markets to COVID-19. Finance Res. Lett. 38, 101853.

Ayadi, A., Gana, M., Goutte, S., Guesmi, K., 2021. Equity-commodity contagion during four recent crises: Evidence from the USA, Europe and the BRICS. Int. Rev. Econ. Finance 76, 376–423.

Ayres, J., Hevia, C., Nicolini, J.P., 2020. Real exchange rates and primary commodity prices. J. Int. Econ. 122, 103261.

Baele, L., 2005. Volatility spillover effects in European equity markets. J. Financ. Quant. Anal. 40 (2), 373–401.

Bargigli, L., Di Iasio, G., Infante, L., Lillo, F., Pierobon, F., 2015. The multiplex structure of interbank networks. Quant. Finance 15 (4), 673–691.

Battiston, S., Dafermos, Y., Monasterolo, I., 2021. Climate risks and financial stability. J. Financ. Stab. 54 (100867).

Battiston, S., Gatti, D.D., Gallegati, M., Greenwald, B., Stiglitz, J.E., 2012. Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk. J. Econ. Dyn. Control 36 (8), 1121–1141.

Beker, V.A., 2014. The European debt crisis: Causes and consequences. J. Stock Forex Trading 3 (2), 1–9.

Ben Ameur, H., Ftitzi, Z., Louhichi, W., 2024. Interconnectedness of cryptocurrency markets: an intraday analysis of volatility spillovers based on realized volatility decomposition. Ann. Oper. Res. 1–23.

Berndsen, R.J., León, C., Renneboog, L., 2018. Financial stability in networks of financial institutions and market infrastructures. J. Financ. Stab. 35, 120–135.

Billio, M., Getmansky, M., Lo, A.W., Pelizzon, L., 2012. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. J. Financ. Econ. 104 (3), 535–559.

Bodart, V., Candelon, B., Carpentier, J.-F., 2015. Real exchanges rates, commodity prices and structural factors in developing countries. J. Int. Money Finance 51, 264–284.

Bouteska, A., Sharif, T., Abedin, M.Z., 2023. Volatility spillovers and other dynamics between cryptocurrencies and the energy and bond markets. Q. Rev. Econ. Finance 92, 1–13.

Brillinger, D.R., 2001. Time Series: Data Analysis and Theory. SIAM.

<footnote>*** indicates statistical significance at the 1%, ** at the 5%, and ** at the 1%.</footnote>

<footnote>*** indicates statistical significance at the 1%, ** at the 5%, and ** at the 1%.</footnote>
Caccioli, F., Ferrara, G., Ramadiah, A., 2024. Modelling fire sale contagion across banks and non-banks. J. Financ. Stab. 101231.

Capponi, A., Weber, M., 2024. Systemic portfolio diversification. Oper. Res. 72 (1), 110-131.

Chang, Y., Jiang, B., Park, J.Y., 2005. Nonstationary logistic regression. In: Meeograph. Department of Economics, Rice University.

Charles, A., Darné, O., Tripier, F., 2018. Uncertainty and the macroeconomy: evidence from an uncertainty composite indicator. Appl. Econ. 50 (10), 1093-1107.

Chinn, M.D., Coibion, O., 2014. The predictive content of commodity futures. J. Futures Mark. 34 (7), 607-636.

Christiansen, C., 2007. Volatility-spillover effects in European bond markets. Eur. Financial Manag. 13 (5), 923-948.

Constancio, V., et al., 2012. Contagion and the European debt crisis. Financ. Stab. Rev. 16, 109-121.

Cont, R., Moussa, A., et al., 2010. Network structure and systemic risk in banking systems. In: Edson Bastos e, Network Structure and Systemic Risk in Banking Systems (December 1, 2010).

Creti, A., Joëts, M., Mignon, V., 2013. On the links between stock and commodity markets' volatility. Energy Econ. 37, 16-28.

Dafermos, Y., Nikolaides, M., Galanis, G., 2018. Climate change, financial stability and monetary policy. Ecol. Econom. 152, 219-234.

De Bruykere, V., Gerhardt, M., Schepens, G., Vander Vennet, R., 2013. Bank/sovereign risk spillovers in the European debt crisis. J. Bank. Financ. 37 (12), 4793-4809.

Demirer, M., Diebold, F.X., Liu, L., Yilmaz, K., 2018. Estimating global bank network connectedness. J. Appl. Econometrics 33 (1), 1-15.

Diebold, F.X., Yilmaz, K., 2012. Better to give than to receive: Predictive directional measurement of volatility spillovers. Int. J. Forecast. 28 (1), 57-66.

Donath, L.E., Cismas, L.M., et al., 2008. Determinants of financial stability. Rom. Econ. J. 3, 27-44.

Doz, C., Giannone, D., Reichlin, L., 2011. A two-step estimator for large approximate dynamic factor models based on Kalman filtering. J. Econometrics 164 (1), 188-205.

Doz, C., Giannone, D., Reichlin, L., 2012. A quasi-maximum likelihood approach for large, approximate dynamic factor models. Rev. Econ. Stat. 94 (4), 1014-1024.

Dunsby, A., Nelson, K., 2010. A brief history of commodities indexes. J. Indexes 13 (3), 36-39.

Duprey, T., Klaus, B., Peltonen, T., 2017. Dating systemic financial stress episodes in the EU countries. J. Financ. Stab. 32, 30-56.

Eberhardt, M., Presbitero, A.F., 2021. Commodity prices and banking crises. J. Int. Econ. 131, 103474.

Eholi, M., 2004. Systemic Risk in Financial Networks: A Graph Theoretic Approach. Universita di Chieti Pescara.

Feng, H., Zhang, J., Guo, N., 2023. Time-varying linkages between energy and stock markets: Dynamic spillovers and driving factors. Int. Rev. Financ. Anal. 102714.

Flori, A., Pammolli, F., Spelta, A., 2021. Commodity prices co-movements and financial stability: A multidimensional visibility nexus with climate conditions. J. Financ. Stab. 54, 100876.

Forni, M., Hallin, M., Lippi, M., Reichlin, L., 2005. The generalized dynamic factor model: one-sided estimation and forecasting. J. Am. Stat. Assoc. 100 (471), 830-840.

Fukker, G., Kok, C., 2024. On the optimal control of interbank contagion in the euro area banking system. J. Financ. Stab. 101225.

García, C.J., Mejía, J., 2018. Macroeconomic stabilization of primary commodities price cycles in developing economies. J. Policy Model. 40 (5), 1050-1066.

Gelper, S., Croux, C., 2010. On the construction of the European economic sentiment indicator. Oxf. Bull. Econ. Stat. 72 (1), 47-62.

Geman, H., 2009. Risk Management in Commodity Markets: From Shipping to Agriculturals and Energy. John Wiley & Sons.

Gil-Alana, L.A., Monge, M., 2020. Crude oil prices and COVID-19: Persistence of the shock. Energy Res. Lett. 1 (1).

Gofman, M., 2017. Efficiency and stability of a financial architecture with too-interconnected-to-fail institutions. J. Financ. Econ. 124 (1), 113-146.

Greco, S., Ishizaka, A., Tasiou, M., Torrisi, G., 2019. On the methodological framework of composite indices: A review of the issues of weighting, aggregation, and robustness. Soc. Indic. Res. 141, 61-94.

Guan, B., Mazouz, K., Xu, Y., 2024. Asymmetric volatility spillover between crude oil and other asset markets. Energy Econ. 130, 107305.

Hanif, W., Mensi, W., Gubareva, M., Teplova, T., 2023a. Impacts of COVID-19 on dynamic return and volatility spillovers between rare earth metals and renewable energy stock markets. Resour. Policy 80, 103196.

Hanif, W., Teplova, T., Rodina, V., Alomari, M., Mensi, W., 2023b. Volatility spillovers and frequency dependence between oil price shocks and green stock markets. Resour. Policy 85, 103860.

Hautsch, N., Schaumburg, J., Schienle, M., 2015. Financial network systemic risk contributions. Rev. Financ. 19 (2), 685-738.

Hollo, D., Kremer, M., Lo Duca, M., 2012. CISS-A Composite Indicator of Systemic Stress in the Financial System. ECB Working Paper, http://dx.doi.org/10.2139/ssrn.2018792.

Hu, Z., Borjigin, S., 2024. The amplifying role of geopolitical risks, economic policy uncertainty, and climate risks on Energy-Stock market volatility spillover across economic cycles. N. Am. J. Econ. Financ. 102114.

Iqbal, N., Bouri, E., Liu, G., Kumar, A., 2024. Volatility spillovers during normal and high volatility states and their driving factors: A cross-country and cross-asset analysis. Int. J. Finance Econ. 29 (1), 975-995.

Jia, Z., Wen, S., Lin, B., 2021. The effects and reacts of COVID-19 pandemic and international oil price on energy, economy, and environment in China. Appl. Energy 302, 117612.

Karali, B., Ramirez, O.A., 2014. Macro determinants of volatility and volatility spillover in energy markets. Energy Econ. 46, 413-421.

Katsiampa, P., Corbet, S., Lucey, B., 2019. Volatility spillover effects in leading cryptocurrencies: A BEKK-MGARCH analysis. Finance Res. Lett. 29, 68-74.

Kilian, L., Lütkepohl, H., 2017. Structural Vector Autoregressive Analysis. Cambridge University Press.

Koch, N., 2014. Tail events: A new approach to understanding extreme energy commodity prices. Energy Econ. 43, 195-205.

Lautier, D., Raynaud, F., 2012. Systemic risk in energy derivative markets: A graph-theory analysis. Energy J. 33 (3), 215-240.

Lee, C.-C., Lee, C.-C., Li, Y.-Y., 2021. Oil price shocks, geopolitical risks, and green bond market dynamics. N. Am. J. Econ. Financ. 55, 101309.

Li, J., Umar, M., Huo, J., 2023a. The spillover effect between Chinese crude oil futures market and Chinese green energy stock market. Energy Econ. 119, 106568.

Li, S., Zhang, W., Zhang, W., 2023b. Dynamic time-frequency connectedness and risk spillover between geopolitical risks and natural resources. Resour. Policy 82, 103554.

Louzis, D.P., Vouldis, A.T., 2012. A methodology for constructing a financial systemic stress index: An application to Greece. Econ. Model. 29 (4), 1228-1241.

Mattera, R., Di Sciorio, F., Trinidad-Segovia, J.E., 2022a. A composite index for measuring stock market inefficiency. Complexity 2022, 1-13.

Mattera, R., Misuraca, M., Spano, M., Scepi, G., 2022b. Mixed frequency composite indicators for measuring public sentiment in the EU. Qual. Quant. 1-26.

Morales, M.A., Estrada, D., 2010. A financial stability index for Colombia. Ann. Financ. 6 (4), 555-581.

Mupunga, N., Ngundu, T., 2020. Commodity price shocks and financial sector stability in commodity dependent countries in southern Africa. Stud. Econ. Econometrics 44 (3), 109-137.

Naeem, M.A., Karim, S., Yarovaya, L., Lucey, B.M., 2023. COVID-induced sentiment and the intraday volatility spillovers between energy and other ETFs. Energy Econ. 122, 106677.

Nazlioglu, S., Soytas, U., Gupta, R., 2015. Oil prices and financial stress: A volatility spillover analysis. Energy Policy 82, 278-288.

Ng, A., 2000. Volatility spillover effects from Japan and the US to the Pacific-Basin. J. Int. Money Financ. 19 (2), 207-233.

Oet, M.V., Dooley, J.M., Ong, S.J., 2015. The financial stress index: Identification of systemic risk conditions. Risks 3 (3), 420-444.

Olson, E., Vivian, A.J., Wohar, M.E., 2014. The relationship between energy and equity markets: Evidence from volatility impulse response functions. Energy Econ. 43, 297-305.

Park, J.Y., Phillips, P.C., 2000. Nonstationary binary choice. Econometrica 68 (5), 1249-1280.

Qiao, T., Han, L., 2023. COVID-19 and tail risk contagion across commodity futures markets. J. Futures Mark. 43 (2), 242-272.

Ribeledo, J.C., Ugolini, A., 2018. The impact of energy prices on clean energy stock prices. A multivariate quantile dependence approach. Energy Econ. 76, 136-152.

Sánchez-García, J., Cruz-Rambaud, S., 2023a. Inflation and systemic risk: A network econometric model. Finance Res. Lett. 104104.

Sánchez-García, J., Cruz-Rambaud, S., 2023b. Macrofinancial determinants of volatility transmission in a network of European sovereign debt markets. Finance Res. Lett. 53, 103635.

Sánchez-García, J., Cruz-Rambaud, S., 2023c. The network econometrics of financial concentration. Rev. Manage. Sci. 1-39.

Sánchez-García, J., Cruz-Rambaud, S., 2023d. Volatility spillovers between oil and financial markets during economic and financial crises: A dynamic approach. J. Econ. Financ. 47 (4), 1018-1040.

Sanders, D.R., Irwin, S.H., 2014. Energy futures prices and commodity index investment: New evidence from firm-level position data. Energy Econ. 46, S57-S68.

Sklar, M., 1959. Fonctions de répartition à n dimensions et leurs marges. In: Annales de l'ISUP. Vol. 8, pp. 229-231.

Smith, T.J., McKenna, C.M., 2013. A comparison of logistic regression pseudo R2 indices. Mult. Linear Regres. Viewp. 39 (2), 17-26.

Sokhanvar, A., Bouri, E., 2023. Commodity price shocks related to the war in Ukraine and exchange rates of commodity exporters and importers. Borsa Istanbul Rev. 23 (1), 44-54.

Sorić, P., Lolić, I., Čižmešija, M., 2016. European economic sentiment indicator: an empirical reappraisal. Qual. Quant. 50, 2025-2054.

Stock, J.H., Watson, M.W., 2002. Forecasting using principal components from a large number of predictors. J. Am. Stat. Assoc. 97 (460), 1167-1179.

Tang, W., Wu, L., Zhang, Z., 2010. Oil price shocks and their short-and long-term effects on the Chinese economy. Energy Econ. 32, S3-S14.

Uddin, G.S., Luo, T., Yahya, M., Jayasekera, R., Rahman, M.L., Okhrin, Y., 2023. Risk network of global energy markets. Energy Econ. 125, 106882.
Umar, Z., Hadhri, S., Abakah, E.J.A., Usman, M., Umar, M., 2024. Return and volatility spillovers among oil price shocks and international green bond markets. Res. Int. Bus. Finance 102254.

Wang, K.-H., Liu, L., Li, X., Oana-Ramona, L., 2022. Do oil price shocks drive unemployment? Evidence from Russia and Canada. Energy 253, 124107.

Wang, K., Wen, F., Gong, X., 2024. Oil prices and systemic financial risk: A complex network analysis. Energy 130672.

Yadav, M.P., Sharif, T., Ashok, S., Dhingra, D., Abedin, M.Z., 2023. Investigating volatility spillover of energy commodities in the context of the Chinese and European stock markets. Res. Int. Bus. Finance 65, 101948.

Zhao, J., Cui, L., Liu, W., Zhang, Q., 2023. Extreme risk spillover effects of international oil prices on the Chinese stock market: A GARCH-EVT-Copula-CoVaR approach. Resour. Policy 86, 104142.