Introduction

The BRICS nations—Brazil, Russia, India, China, and South Africa—have been critical in redefining the contours of the global economic landscape since the dawn of the twenty-first century. Coined by Jim O’neill of Goldman Sachs in 2001, the acronym BRIC emerged in his work, “Building Better Global Economic BRICs,” wherein he described the escalating influence and potential of these four nations within the global economic arena. O'neill (2001) claimed that the remarkable economic expansion and substantial population bases of these countries distinguished them as noteworthy entities in the realms of investment and economic growth. Notably, the remarkable economic expansion is marked by a staggering increase in GDP figures, placing these nations at the forefront of global economic prowess. According to Hawksworth et al. (2017), China is forecasted to become as the largest economy globally by 2050, boasting an anticipated GDP of $53.55 trillion. Similarly, India is expected to claim the position of the second-largest economy, with a projected GDP of $27.94 trillion. These projections solidify their roles as key players in the global economic landscape. Russia and Brazil are also expected to follow closely, ranking fifth and sixth, respectively, behind Japan (Pieterse, 2012; Siddiqui, 2016). These predictions highlight the BRICS countries’ integral role in the present configuration of the global economy and its future evolution.

The BRICs have been the subject of growing attention since the early years of the twenty-first century, fueled by their impressive rates of economic growth and their potential to significantly impact on global structures (Stuenkel, 2014). The significance of 2009 BRIC summit, held in Yekaterinburg, Russia, was important in this regard since it assembled the heads of state of these four emergent economies for the first time (Prashad, 2023). This summit, as well as its further developments, showed that BRIC countries had the potential to bind together not only for economic reasons but also for political and social matters. These meetings have been crucial milestones, allowing these nations to enhance their cooperative activities and coordinate major decisions that influence the global economic scene. In 2010, South Africa initiated its quest to become an affiliate of the BRIC consortium, starting in August and officially ending on December 24th, 2010, when it joined as a member state (Prashad, 2023; Rajan, 2023). Recent studies highlight how the inclusion of South Africa was driven by a strategic intent to enhance the geopolitical and economic influence of the group (Gouvea & Gutierrez, 2023).

The term “BRICS” not only captures the escalating economic competence of its participant countries but also reflects their ascending direction in political influence and collaborative endeavors. During the initial years of the twenty-first century, there was a significant rise in the economic reputation of these nations, resulting in an expansion of the BRICS concept well beyond its original economic framework. This era indicated a pronounced elevation in their roles within global commerce and international diplomacy, effectively establishing BRICS as a distinguished entity on the world stage. To comprehend the essence of BRICS and BRICS-plus, it is crucial to delve into the specific economic and political factors that have solidified the collaboration among these nations. The studies suggest a substantial transformation within the BRICS nations, characterized by a notable evolution in their economic growth and geopolitical power (Siddiqui, 2016; Wu et al., 2017).

In 2022, during the BRICS Leaders’ meeting, China’s President ** highlighted the importance of adding new members to the group, and Argentina and Iran expressed their interest in becoming part of the BRICS cohort. At its August 2023 summit, the BRICS alliance decided to expand to six countries (Argentina, Egypt, Ethiopia Iran, Saudi Arabia, and the United Arab Emirates) by January 2024.

As the global economy is constantly changing and evolving, the role and influence of BRICS and BRICS-plus countries have become increasingly important. The existing literature highlights the significant contributions of BRICS countries and identifies factors that encourage their expansion and enhance their influence (Hussain et al., 2023; İltaş, 2020; Khalfaoui et al., 2023; Nyakurukwa & Seetharam, 2023; Smolo et al., 2022). However, there is a growing need for more specific and targeted research that delves into the economic intricacies of the BRICS-plus countries, particularly in terms of non-linear relationships and short- and long-term dynamics within these markets (Chang et al., 2023a, 2023b; Sehgal et al., 2019).

To address these gaps, the present study employs a robust methodological framework that incorporates both regression models and empirical analysis. Our research methodology utilizes Quantile Vector Autoregressive and frequency analysis to explore the non-linear relationships and short- and long-term dynamics in the markets of BRICS-plus countries (Ahmad et al., 2018; Chang et al., 2023a, 2023b; Lai et al., 2023; Nasr et al., 2018; Sharma et al., 2019). In this study, the primary objective is to analyze the interdependencies and spillover effects on the major emerging economies belonging to the BRICS-plus countries. With this aim, Quantile Vector Autoregressive (QVAR) and frequency analysis are used to explore non-linear relationships and short- and long-term dynamics in these markets, aiming to delve deeper into the economic intricacies of the BRICS-plus countries. The study also proposes adaptive risk management strategies based on the observed dynamics, thereby contributing to the broader discourse on risk management in emerging markets. The study includes a novel quantile and frequency connectedness approach, along with a comprehensive examination of the impact of various crises on these indices, including the COVID-19 pandemic and the Russia-Ukraine conflict. To establish the scientific foundation of our research, the methodology and data section presented detailed information on the quantitative tools employed and the rationale behind their selection. This analysis is expected to play an important role in understanding market dynamics, risk management, investment strategies, and policy development in the context of global financial trends and the interconnectedness of emerging markets.

The decision to focus on BRICS-plus countries, encompassing some of the foremost emerging economies, is underpinned by a series of critical considerations. Analyzing the stock indices of BRICS-plus countries during this particular period provides an extensive overview of how emerging markets function in global crises. These countries, which collectively use extensive power in the global economy, exhibit a range of economic frameworks and a range of responses to both internal and external economic alarms. By examining stock indices over this period, a comparative analysis is conducted that provides insights into the strategies employed by these economies. Beyond risk assessment and opportunity identification in these countries, this analysis reveals their contribution to overall financial trends and the degree of interconnectedness among emerging markets, especially during periods of economic challenges.

The main objective of this article is to study the dynamic connectivity of BRICS-plus stock indices during global crises. Using a robust methodological framework that incorporates both regression models and empirical analysis, our goal is to provide a nuanced comprehension of how financial markets interact and respond to significant global events. This paper contributes to the existing literature by offering a comprehensive analysis of the both temporal and frequency domains, thus capturing the complex dynamics of market interactions across various quantiles and time periods. Our findings provide actionable insights for financial practitioners and policymakers, highlighting the importance of adaptive risk management strategies and informed policy formulation to navigate forthcoming financial turbulence.

The paper is organized as follows. Sect. "Literature" introduces the related literature, Sect. "Methodology and Data Description" describes the methodology and the data, Sect. "Results" presents the results, and Sect. "Conclusion" presents the concluding remarks. In conclusion, our study not only sheds light on the immediate dynamics of BRICS-plus economies but also provides a framework for understanding their role in sha** the future of the global economic landscape. The concluding remarks offer reflections on the broader implications of our findings and suggest potential avenues for further research in this critical area.

Literature

The purpose of the study is to analyze the interdependency and spillover effect on the major emerging economies belonging to the BRICS-plus countries. While the existing literature has been substantially confined to BRICS countries and focuses on stock indices, economic growth patterns, and financial market behavior, there is a significant gap concerning in the current literature regarding BRICS-plus countries. The existing literature has indeed focused extensively on the interconnectedness and dynamics within the BRICS countries, as evidenced by some studies (Ahmad et al., 2018; Khalfaoui et al., 2023; Panda et al., 2021; Rajput, 2022). However, there remains a relative scarcity of research that extends this analysis to include the broader BRICS-plus group. Our study aims to close this gap by providing an in-depth analysis of the dynamic connectivity between BRICS-plus stock indices during periods of global crises, thus contributing to the understanding of emerging market dynamics. This underscores the significance of our research. This points out the fact that the economic dynamics of BRICS-plus countries and their contributions to the global economy, which may not have been fully explored. This analysis tries to understand the way in which these countries interact both among themselves and with global financial markets, providing a more comprehensive understanding of the global economy. Therefore, it is considered that this study can address this literature gap and contribute meaningfully to the existing body of knowledge.

Studies on spillover effects and interdependency within the BRICS countries typically encompass five distinct areas: Spillover Effects in Commodity and Equity Markets, Cryptocurrency and Digital Asset Interconnectedness, Sectoral Analysis and Specific Market Dynamics, Risk Analysis and Management, Geopolitical Influences and Impact of Crash.

The analyses for Spillover Effects in Commodity and Equity Markets particularly focus on oil and gold. For instance, Li et al. (2021) utilize wavelet coherence and spillover index methodologies to unravel the intricate connections among oil, gold prices, and BRICS geopolitical risks. They find a significant short-term sensitivity of these markets to geopolitical events, highlighting their impact on investment and policy decisions. In a similar vein, Kang et al. (2021) investigate the hedging effectiveness of oil and gold for US sector ETFs, with their time–frequency analysis reveals that oil is a more effective hedge than gold in fluctuating market conditions. Further extending this analysis, Chang et al., (2023a, 2023b) employ a quantile connectedness approach to examine the interconnectedness between Brent oil prices and BRICS stock markets, discovering that the connectedness intensifies during periods of market turmoil, such as financial crises and pandemics. Moreover, Chang et al., (2023a, 2023b) examine the relationship between stock and oil markets in BRICS countries from 2001 to 2022. They find that China and India’s stock markets are major net receivers, while Brazil, Russia, South Africa’s stock markets, and the oil market are significant net transmitters of both returns and volatility.

In addition, Ahmad et al. (2018), using the Diebold-Yilmaz spillover index methodology, investigate the financial interlinkages between BRICS countries and other major economies. The study reveals significant insights into the dynamics of these linkages, with Russia and South Africa emerging as major transmitters of shocks within the BRICS group, and China and India displaying weaker connectedness. This variance in connectedness suggests not only potential diversification opportunities within BRICS but also highlights the role of global economic powers, particularly the strong interconnectedness observed between China and the US bond markets. McIver and Kang (2020), employing the multivariate DECO-GJR-GARCH model and spillover index method, investigate time variations in volatility and the significant dynamic spillovers between the US and BRICS stock markets. The study illuminates the increased spillover effects observed during the global financial crisis and European sovereign debt crisis. Interestingly, it points out the roles of the USA, Brazil, and China as major volatility transmitters, whereas Russia, India, and South Africa emerge as primary volatility recipients.

Liu et al. (2022) employ a high-dimensional conditional Value-at-Risk (CoVaR) connectedness approach, based on the LASSO-VAR model, to analyze the risk spillovers from oil markets to the G20 stock system. The findings of this study are significant, revealing substantial risk spillovers, which become particularly pronounced during crisis periods. The research highlights the critical influence that shifts in oil markets can have on global stock systems, underscoring the importance of monitoring these spillovers to prevent systemic risks. The study by Panda et al. (2021) use the Diebold and Yilmaz volatility spillover index; their analysis covers data from 2002 to 2017, providing a comprehensive view of market behavior over a substantial period. The study reveals that volatility spillovers notably increased during the financial crisis and then decreased significantly post-crisis. It also identifies Brazil, Hong Kong, Germany, and Japan as major receivers of market volatility, whereas South Africa, the UK, and the USA emerge as key transmitters. These findings are instrumental in enhancing our understanding of global market dynamics, particularly in times of financial uncertainty.

Hung (2022) provides a nuanced understanding of the interplay between commodity prices, specifically crude oil and gold, and the equity markets of BRICS nations. Utilizing advanced analytical techniques such as MGARCH-DCC and Wavelet Coherence, Hung discovers that return correlations between these commodities and BRICS financial markets are not static but vary over time, exhibiting negative and positive relationships. Particularly noteworthy is the finding that China, India, and Brazil’s currencies show higher correlations with the international commodities market. The study underscores the short-term influence of international commodities on BRICS financial markets, while in the long term, the BRICS stock and exchange markets impact crude oil and gold prices. Panda et al. (2023) use MGARCH-BEKK and the Diebold–Yilmaz (DY) volatility spillover index; their analysis sheds light on the nature of volatility spillovers within and across these emerging markets. The study reveals a critical insight: own-market volatility within each BRICS country tends to be higher than cross-market spillovers, with this trend intensifying during financial crises. Interestingly, the research notes a decrease in cross-market volatility spillovers post-crisis. Additionally, it identifies Brazil as the largest net transmitter of volatility and China as the largest net receiver, with significant volatility connectivity between China and India.

Nyakurukwa and Seetharam (2023), in their study, utilize quantile connectedness and asymmetric TVP-VAR methods; their research delves into the analysis of return spillovers, especially under extreme market conditions. The study uncovers significant return connectedness in the extreme tails of return distributions, indicating heightened interconnectivity during periods of market stress. Notably, South Africa emerges as a major net transmitter of these spillovers, while China is identified as a major net receiver.

The second segment, Cryptocurrency and Digital Asset Interconnectedness, scrutinizes the evolving relationship between digital and traditional financial markets. Dahir et al. (2020) explore the volatility connectedness between Bitcoin and BRICS equity markets using a TVP-VAR approach. Their findings indicate that Bitcoin’s volatility has a limited but growing impact on these equity markets. Complementing this, Bejaoui et al. (2023) examine the dynamic interconnectedness of emerging stock markets, gold, cryptocurrencies, DeFi, and NFTs in Gulf countries and BRICS. They reveal significant, time-varying connectedness, especially during major health and political events, suggesting potential diversification benefits of NFTs and DeFi in portfolio management.

The Sectoral Analysis and Specific Market Dynamics studies investigate specific market sectors and their unique dynamics within BRICS economies. Mensi et al. (2021) focus on the spillover effects and network connections among crude oil, gold, and Chinese sector stock markets. They find significant spillover effects, with industrial and consumer sectors being major contributors and recipients, particularly influenced by global crises. Similarly, Umar et al. (2021) investigate the interaction between components of the Chinese sovereign yield curve and sectorial equity indices, discovering that the level component of the yield curve is a major transmitter of return spillovers, especially during market events like stock market crashes and trade wars.

BenSaïda (2023) employs the regular vine copula method, alongside benchmark models like the multivariate t copula and the DCC-GARCH model, to dissect the relationship between Bitcoin and fiat currencies in both developed (G7) and emerging (BRICS) markets. The study is particularly focused on the effects of major Bitcoin crashes, including those during the COVID-19 pandemic and the 2022 Russia-Ukraine conflict. The findings reveal a nuanced increase in cross-market linkage between Bitcoin and traditional currencies during these periods of Bitcoin volatility, with significant levels observed during the 2021 and 2022 crises. This suggests a diminishing trend in Bitcoin’s market isolation, indicating its growing influence and interconnectedness with conventional financial systems. Khalfaoui et al. (2023) offer perspectives on the emerging financial landscape involving cryptocurrencies. Their analysis demonstrates significant interconnectedness between cryptocurrencies and BRICS stock markets, with the sensitivity to quantiles analysis indicating a switching behavior in net transfer spillovers.

The Risk Analysis and Management studies’ main focus is the strategies used to manage economic risks. Younis et al. (2023) explore the risk co-movements and portfolio strategies between energy, gold, and BRICS markets, finding significant risk connections, especially during the pandemic, suggesting strengthened market linkages in times of crisis. In a related study, Gao et al. (2021) analyze risk spillover and network connectedness in China’s financial markets, focusing on green bonds. They identify significant two-way risk spillovers between the green bond market and traditional bond markets, underscoring the importance of monitoring these dynamics for risk management. In addition, a study analyzing the impact of global economic and policy uncertainties on capital flows in financial markets was conducted by Çepni et al., 2021. In particular, this study reveals how bond and equity flows to Turkey interact with global and US policy uncertainty. The study highlights the dynamics of capital flows and the importance of risk management strategies during periods of uncertainty.

Building further on the theme of market dynamics and investor behavior, Fassas (2020) provides a detailed examination of investor sentiment and risk aversion. Focusing on variance premia spillovers among developed markets, emerging markets, and the US market, Fassas reveals a notable shift in investor sentiment and risk aversion connectedness across these markets during the pandemic. This highlights the dynamic nature of market interactions and investor behavior in response to global crises.

Apart from the investor behavior and risk aversion dynamics highlighted in Fassas (2020), the practical application of risk management strategies in financial markets are also important. In this perspective, Buyukkara et al. (2022) study the optimal hedging ratios and their effectiveness for different futures contracts in Borsa Istanbul. More specifically, they compare various methods of financial risk management with respect to the fixed and time-varying econometric models. Gouta and BenMabrouk (2023) employ the TVP-VAR model for analyzing spillovers and a modified CSAD measure for investigating herding behavior; their research provides crucial insights into the behavioral dimensions of financial markets. The study reveals the presence of herding behavior in the American market and certain BRICS markets, highlighting how investor psychology can significantly impact market movements. Notably, it finds that spillovers between G7 and BRICS increase during crises, suggesting that turbulent times exacerbate the tendency of investors to engage in herding behavior. This dynamic correlation between herding and spillovers, observable in both short-term and long-term perspectives, underscores the complex interplay between investor behavior and market volatility.

The concluding section of this review is dedicated to examining the Geopolitical Influences and Crisis Impact. Oyewole et al. (2023) state the interconnectedness of BRICS currency markets during the Russia-Ukraine war. Their Quantile VAR model reveals increased connectedness among BRICS currencies during the war, particularly during extreme market events. Complementing this perspective, Smolo et al. (2022) analyze the performance of Islamic and conventional equities during the COVID-19 pandemic in BRICS + T markets. Their findings indicate that Islamic equities were more resilient than conventional ones during the pandemic, offering valuable insights for diversification in turbulent times. The study by Tiwari et al. (2022) offer pivotal insights. Utilizing a quantile connectedness network methodology, their research assesses the vulnerability of emerging markets to shocks originating from the US market, oil prices, and the dollar index. The study reveals that emerging markets are significantly influenced by these global factors, with the magnitude and nature of the impact varying across different market conditions, such as bear, normal, and bull markets. This underscores the nuanced ways in which global economic shocks and geopolitical events shape the dynamics of emerging stock markets.

A critical study in this context by Qureshi (2022) delves into the interconnectedness between the dynamics of the COVID-19 pandemic and various economic indicators. Employing continuous wavelet transformation and DCC-GARCH models, Qureshi’s study uncovers significant coherence between the pandemic and long-term economic indicators, with a notable emphasis on the disparities observed between China and the US. The findings indicate that the pandemic has led to pronounced spillovers in stock markets, affecting domestic sectoral returns more significantly.

Su (2020) introduces a novel quantile variance decomposition framework to scrutinize extreme risk spillovers across international stock markets, specifically focusing on G7 and BRICS markets. This paper uncovers that extreme risk spillovers are of greater magnitude compared to traditional volatility spillovers, predominantly flowing from developed G7 markets to emerging BRICS markets. These findings are particularly illuminating as they highlight the heightened susceptibility of emerging markets to extreme risk conditions originating in developed markets.

Hussain et al. (2023) use the Diebold and Yilmaz method and GARCH models to investigate the intricacies of volatility connectedness and spillover among BRICS countries during pandemic-induced crises. The study uncovers significant volatility spillovers and connections in exchange rates and stock returns across these nations. Notably, it finds strong volatility connectedness between Russia and India and Brazil and South Africa, while China exhibits weaker volatility connections with other BRICS countries. These findings are pivotal in understanding the diverse impacts of the pandemic on different emerging economies. The research highlights the crucial implications of these volatility dynamics for financial market stability and the formulation of portfolio strategies in the face of unprecedented global crises.

Besides the volatility interconnectedness and spillover effects among BRICS countries by Hussain et al. (2023), Adekoya et al. (2022) analyze how this geopolitical and global health crisis influences financial markets in terms of comparing Islamic-conventional stock market performance during the pandemic. This research shows that Islamic stocks were relatively stable during the pandemic compared to conventional stocks, especially for BRICS + T markets. Thus, these outcomes underscore the importance of portfolio diversification and shifting toward resilient asset classes under pandemic-related ambiguities.

Our findings indicate significant fluctuations in the total connectivity index (TCI) across different periods, reflecting dynamic shifts in the interconnectivity of equity indices. The surge in TCI during the COVID-19 pandemic highlights heightened global market synchronization, a trend consistent with findings from studies by Panda et al. (2021) and Chang et al., (2023a, 2023b), which also observed increased market interconnectedness during times of crises. Conversely, the subsequent decrease in TCI during the war period suggests a reevaluation of risk exposures, amid geopolitical tensions, aligning with Lai et al. (2023) and Mensi et al. (2021).

Before the pandemic, indices such as MERVAL, EGX30, JTOPI, and RTSI were identified as net transmitters, echoing the findings of Ahmad et al. (2018) and McIver and Kang (2020), who identified key influencers within BRICS. However, during the pandemic, there was a shift in roles, with BVSP and TASI emerging as main transmitters. This observation supports the dynamic nature of market roles observed by Anyikwa and Phiri (2023) and İltaş (2020).

During the war period, significant changes were observed, notably with indices like MERVAL losing connections, while BSE and ADX emerged as new risk transmitters. This provides new empirical evidence on the impact of geopolitical events on financial market integration, which complements insights provided by Mensi et al. (2021) and Hussain et al. (2023).

The QVAR analysis in our study exhibited symmetrical connectivity, with time–frequency connectedness analysis highlighting the predominance of short-term interactions. This aligns with findings from Hung (2022) and Nyakurukwa and Seetharam (2023), who noted significant short-term interactions in financial markets during crises. The occasional occurrence of long-term interactions aligns with research by BenSaïda (2023) and Khalfaoui et al. (2023), indicating profound shifts in market dynamics associated with economic, political, or financial events.

One of the primary aims of this study is to address a notable gap in the literature by focusing on the BRICS-plus countries. Existing literature has tended to limit its scope to BRICS countries, predominantly exploring stock market indices, economic growth models, and financial market behaviors. However, there is a significant dearth of research on BRICS-plus nations, underscoring the importance of this investigation. This analysis strives to comprehend both the interactions among these countries and their relationships with global financial markets, offering a more comprehensive understanding of the global economy. Thus, this study is perceived as an attempt to fill a void in the literature and contribute to the existing body of knowledge by shedding light on the interactions and dynamics of these nations in the realm of global finance.

Methodology and Data Description

Methodology

To examine the quantile spillover mechanism across diverse financial markets, we employ the novel quantile and frequency connectedness approach that enables the investigation of propagation mechanisms by virtue of the quantile (q) and frequency (\(\omega\)). The quantile connectedness approach, as introduced by Ando et al. (2022), Bouri et al. (2021), and Chatziantoniou et al. (2021). Firstly, to capture the overall connectedness measure, we estimate a quantile vector autoregression (QVAR(p)). The model can be summarized in Eq. (1) as follows:

$${Y}_{t}= {\mu }_{t}\left(q\right)+ {\Phi }_{1}\left(q\right){Y}_{t-1}+ {\Phi }_{2}\left(q\right){Y}_{t-2}+\dots + {\Phi }_{p}\left(q\right){Y}_{t-p}+ {\varepsilon }_{t}\left(q\right)$$
(1)

where \({Y}_{t}\) and \({Y}_{t-j}\) are vectors representing endogenous variables with dimensions N × 1. The parameter \(q\) is a closed interval, which lies within the range [0, 1], while p represents the lag length of the QVAR model. \({\mu }_{t}\left(q\right)\) is an N × 1 dimensional vector representing the conditional mean, \({\Phi }_{j}\)(\(q\)) is an N × N dimensional matrix of QVAR coefficients, and \(\varepsilon \left(q\right)\) is an N × 1 dimensional error vector with an N × N dimensional error variance–covariance matrix, Σ \(\left(q\right)\).

Secondly, to compute the forward M-step Generalized Forecast Error Variance Decomposition (GFEVD), Eq. (1) needs to be transformed into the QVMA (∞) form by applying Wold’s theorem. The QVMA (∞) is expressed as Eq. (2):

$${Y}_{t}= \mu \left(q\right)+ \sum_{j=1}^{p}{\Phi }_{j}\left(q\right){Y}_{t-j}+ {\varepsilon }_{t}\left(q\right)= \mu \left(q\right)+ {\sum }_{i=0}^{\infty }{\Omega }_{i}\left(q\right){\varepsilon }_{t-i}$$
(2)

The next step involves calculating the generalized forecast error variance decomposition (GFEVD) with a forecast horizon of H, which is a crucial component of the connectedness approach (Koop et al., 1996; Pesaran & Shin, 1998). It could be interpreted as the impact that series j has on variable i in terms of its forecast error variances:

$$\phi_{ij}\left(H\right)=\frac{\left(\sum\left(q\right)\right)_{jj}^{-1}\sum_{h=0}^{H-1}\left({\left(\Omega_h\left(q\right)\boldsymbol\sum\left(q\right)\right)}_{ij}\right)^2}{\sum_{h=0}^H{\left(\Omega_h\left(q\right)\sum\left(q\right)\Omega'_h\left(q\right)\right)}_{ii}}$$
(3)
$${\widetilde{\phi }}_{ij}\left(H\right) = \frac{{\phi }_{ij}\left(H\right)}{{\sum }_{k=1}^{N}{\phi }_{ij}\left(H\right)}$$
(4)

In the Eq. (3), as the rows of \({\phi }_{ij}\left(H\right)\) do not sum up to one, we need to normalize them by the row sum, resulting in \({\widetilde{\phi }}_{ij}\) in Eq. (4). This normalization ensures that the row sum is equal to unity, representing how a shock in series i has influenced the series itself and all other series. Next, we get the following identities in Eq. (5):

$$\sum_{\text{i}=1}^{\text{N}}{\widetilde{\phi }}_{ij}\left(H\right)=1\text{and }{\sum }_{j=1}^{N}{\sum }_{i=1}^{N}{\widetilde{\phi }}_{ij}\left(H\right)=N$$
(5)

In a next phase, all connection measures may be computed. First, we start with the net pairwise directional connectivity (NPDC) in Eq. (6) as follows:

$${NPDC}_{ij}\left(H\right)= {\widetilde{\phi }}_{ij}\left(H\right)- {\widetilde{\phi }}_{ji}\left(H\right)$$
(6)

If \({NPDC}_{ij}\left(\text{H}\right)>0\) \(({NPDC}_{ij}\left(\text{H}\right)<0\)), it signifies that series j has a greater (lesser) influence on series I than the other way around.

In Eq. (7), the total directional connectedness towards others (TO) with respect to others assesses how much an impact in series i influences all other series j.

$${TO}_{i}\left(H\right)= \sum_{i=1, i \ne j}^{N}{\widetilde{\phi }}_{ji}\left(H\right)$$
(7)

In Eq. (8), the total directional connectedness from others (FROM) originating from others quantifies the level of impact on series i caused by shocks in all other series j.

$${FROM}_{i}\left(\text{H}\right)= \sum_{i=1, i \ne j}^{N}{\widetilde{\phi }}_{ji}\left(H\right)$$
(8)

The overall net total directional connectedness (NET) captures the difference between the total directional connectedness towards others and the total directional connectedness from others. This disparity can be interpreted in Eq. (9) as the net impact of series i on the predefined network.

$${NET}_{i}(H)= {TO}_{i}\left(\text{H}\right)- {FROM}_{i}\left(\text{H}\right)$$
(9)

When \({NET}_{i}\) > 0 (\({NET}_{i}\)< 0), it means that the series i has a greater (lesser) influence on all other series j compared to the amount of influence it receives from them. Therefore, it is categorized as a net transmitter (net receiver) of shocks.

The computation of the overall total connectedness index (TCI) evaluates the degree of interconnectedness within the network using Eq. (10). A higher value of TCI signifies increased market risk, while a lower value indicates the opposite.

$$TCI\left(H\right)= {N}^{-1}\sum_{i=1}^{N}{TO}_{i}\left(H\right)={N}^{-1}\sum_{i=1}^{N}{FROM}_{i}\left(H\right)$$
(10)

To investigate connectedness in the temporal domain, we assess connectivity within the frequency domain, utilizing Stiassny’s (1996) spectral decomposition method. Initially, we examine the frequency response function, represented as \(\Omega\) (\({e}^{-i\omega }\)) = \({\sum }_{h=0}^{\boldsymbol{\infty }}{e}^{-i\omega h}{\Omega }_{h}\),where i = \(\sqrt{-1}\) and \(\omega\) is the frequency. Subsequently, we proceed to analyze the spectral density of \({Y}_{t}\) at a specific frequency\(\omega\). This can be obtained by applying a Fourier transformation to the QVMA(∞) in Eq. (11):

$$s_x\left(\omega\right)=\sum_{h=-\circ}^\infty E\left(Y_tY'_{t-h}\right)e^{-i\omega h}=\Omega\left(e^{-i\omega h}\right){\textstyle\sum_t}\Omega'\left(e^{+i\omega h}\right)$$
(11)

Likewise, the frequency-based Generalized Forecast Error Variance Decomposition (GFEVD) is a fusion of the spectral density and the GFEVD. In the frequency domain, GFEVD should be normalized, similar to the requirement for normalization in the time domain. Its representation is articulated in Eq. (12) and Eq. (13) as follows:

$$\phi_{ij}\left(\omega\right)=\frac{{(\boldsymbol\sum\left(q\right))}_{jj}^{-1}\left|\sum_{h=0}^\infty{\left(\Omega\left(q\right){(e}^{-iwh})\sum\left(q\right)\right)}_{ij}\right|^2}{\sum_{h=0}^\infty{\left(\Omega{(e}^{-iwh})\sum\left(q\right)\Omega\left(q\right){(e}^{iwh})\right)}_{ii}}$$
(12)
$${\widetilde{\phi }}_{ij}\left(\omega \right) = \frac{{\phi }_{ij}\left(\omega \right)}{{\sum }_{k=1}^{N}{\phi }_{ij}\left(\omega \right)}$$
(13)

The expression \({\widetilde{\phi }}_{ij}\) (ω) refers to the fraction of the spectrum of the ith series at a given frequency ω that can be attributed to an impact on the jth series. This measurement is commonly referred to as an intra-frequency indicator. In Eq. (14), to evaluate connectedness across both short-term and long-term time frames, instead of focusing on a single frequency, we aggregate all frequencies within a specified range, denoted as: d = (a, b): a, b ∈ (− π, π), a < b:

$${\widetilde{\phi }}_{ij}(d)={\int }_{a}^{b} {\widetilde{\phi }}_{ij}(\omega ) d\omega$$
(14)

From this stage, we have the ability to compute similar connectedness measures as mentioned before; it can be evaluated using the same method. However, in this scenario, these measures are known as frequency-connectedness measures. They offer insights into the transmission of effects within specific frequency ranges (represented by d), which can be interpreted in a similar manner (between Eq. (15) and Eq. (19)):

$${NPDC}_{ij}\left(d\right)={\widetilde{\phi }}_{ij}\left(d\right)- {\widetilde{\phi }}_{ji}\left(d\right)$$
(15)
$${TO}_{i}\left(d\right)= \sum_{i=1, i \ne j}^{N}{\widetilde{\phi }}_{ji}\left(d\right)$$
(16)
$${FROM}_{i}\left(d\right)= \sum_{i=1, i \ne j}^{N}{\widetilde{\phi }}_{ij}\left(d\right)$$
(17)
$${NET}_{i}\left(d\right)= {TO}_{i}\left(d\right)- {FROM}_{i}\left(d\right)$$
(18)
$$TCI\left(d\right)= {N}^{-1}\sum_{i=1}^{N}{TO}_{i}\left(d\right)={N}^{-1}\sum_{i=1}^{N}{FROM}_{i}\left(d\right)$$
(19)

In our analysis, we define two frequency bands that capture short-term and long-term dynamics. The first band, d1 = (π∕5, π), covers a range of 1 to 5 days, while the second band, d2 = (0, π∕5], encompasses timeframes from 6 days to an infinite horizon. Consequently, NPDCij(d1), TOi(d1), FROMi(d1), NETi(d1), and TCI(d1) represent short-term total directional connectedness towards others, short-term total directional connectedness from others, short-term net total directional connectedness, and short-term total connectedness index, respectively. On the other hand, NPDCij(d2), TOi(d2), FROMi(d2), NETi(d2), and TCI(d2) depict long-term total directional connectedness towards others, long-term total directional connectedness from others, long-term net total directional connectedness, and long-term total connectedness index, respectively. Furthermore, we establish a relationship between the frequency-domain measures proposed by Baruník and Krehlik (2018) and the time-domain measures introduced by Diebold & Yilmaz, 2009, 2012, 2014) between Eq. (20) and Eq. (24):

$${NPDC}_{ij}\left(H\right)={\sum_{d} NPDC}_{ij}(d)$$
(20)
$${TO}_{i}\left(H\right)= {\sum_{d} \left(d\right)\bullet TO}_{i}(d)$$
(21)
$${FROM}_{i}\left(d\right)= {\sum_{d} \left(d\right)\bullet FROM}_{i}(d)$$
(22)
$${NET}_{i}\left(H\right)= \sum_{d} \left(d\right)\bullet {NET}_{i}\left(d\right)$$
(23)
$$TCI\left(H\right)= \sum_{d} \left(d\right)\bullet TCI\left(d\right)$$
(24)

To put it simply, the total connectedness measures can be derived by aggregating the frequency connectedness measures. It is crucial to highlight that all these measures are calculated using a specific quantile, denoted as q.2. This methodology not only provides a nuanced understanding of quantile spillover mechanisms but also offers a comprehensive analysis of frequency-based interconnectedness, contributing to the broader literature on financial market dynamics.

Data and Description

We analyzed an in-depth analysis of the interconnectedness among stock indices in several prominent economies, including China’s SSE Composite Index, Russia’s RTSI (MOEX Russia Index), India’s BSE Sensex 30, Brazil’s Bovespa (BVSP), South Africa’s FTSE/JSE Africa All Share Index (JTOPI), Saudi Arabia’s Tadawul All Share Index (TASI), Abu Dhabi’s (from United Arabic Emirates) ADX General Index (ADX), Egypt’s EGX 30 Index (EGX30), and Argentina’s Merval Index (MERVAL). This comprehensive analysis spanned various endogenous and exogenous crises, utilizing closing prices of stock indices from January 1, 2016, to October 10, 2023. Iran was excluded from the study due to specific constraints. The data were obtained from www.datastream.com, and we calculated returns using the equation Rt = ln (Pt /Pt-1), where Pt ​represents the price on a given day.

Our methodology involves the sequential application of Quantile Vector Autoregressive Analysis (QVAR), initially focusing on the median quantile (0.5) and subsequently extending the analysis across diverse quantiles. This method sheds light on the impact of structural shocks at different intensities on the interrelations and responses of variables, particularly in moments of extreme events. The investigation culminates with Time–Frequency Connectedness Analysis specifically, affording a thorough examination of dynamic relationships within the studied variables. The integration of these two analytical approaches yields a comprehensive understanding of the intricate dynamics within these financial markets, essential for effective risk management, informed investment strategies, and policy formulation.

The choice of BRICS-plus countries, composed of the most important emerging economies, is justified for several considerations. The study of the stock indices of BRICS-plus countries during this particular period offers a comprehensive insight into the intricate dynamics of emerging markets amidst crises. These nations, jointly influential in the global economy, present diverse economic structures and responses to both internal and external shockwaves. Examining their stock indices during this time allows for a comparative analysis, offering invaluable knowledge on how these economies navigate and rebound from adversity. This analysis not only helps in assessing investment risks and opportunities within these nations but also sheds light on their impact on global financial trends, policy responses, and the interconnectedness among these emerging markets during challenging times.

Table 1 outlines a descriptive overview of the returns on stock indices for the BRICS-plus countries. The sample covers the trajectory of these indices through two pivotal crises: the COVID-19 crisis and the conflict between Russia and Ukraine. The average and volatility of the observed variables throughout two distinct timeframes are displayed in the table. The primary drive of this analysis offers insights on the systemic nature of the relationship between these international stock indices of the most important emerging economies.

Table 1 Descriptive statistics
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When examining the descriptive statistics of BRICS union countries’ stock indices before the onset of COVID-19, distinct patterns emerge. Notably, only the indices of China and Egypt consistently display negative average returns, while others exhibit positive averages. Skewness statistics unveil a prevailing left-skewed distribution in return data except for India. Kurtosis statistics prove noteworthy across all indices, signifying deviations from a typical bell-shaped curve, highlighting the presence of outliers or heavier tails in return distributions. Symmetry is notably absent in return series, underscored by substantial Jarque Bera statistics, indicating a lack of normal distribution. Kendall’s Tau coefficients unveil significant correlations among most indices, except for specific pairs such as China with United Arabic Emirates (Abu Dhabi) and Argentina with Egypt.

During the pandemic, most indices display positive average returns, except for Egypt, which consistently showcases negative returns. The negative skewness common across indices suggests a higher frequency of extreme negative returns than extreme positive returns. This skewness could signify increased market volatility or a tendency for downturns to be more pronounced compared to upturns during this period across various markets. Interestingly, China deviates from the negative skewness trend, exhibiting a positively skewed distribution, depicting a right-skewed pattern. Persistent high kurtosis values indicated a distribution prone to extreme values, even pre-COVID. The overall lack of symmetrical distribution persisted, with significant correlations among most indices. Significant correlations exist among the majority of indices, with the absence of significant correlation between China’s with indices from Russia, Abu Dhabi, Egypt, and Argentina. Additionally, no significant correlation is observed between Russia and other BRICS-plus indices.

During the Russia-Ukraine conflict, noticeable positive returns are observed in specific indices like India’s BSE30, Abu Dhabi’s ADX, Egypt’s EGX30, and Argentina’s MERVAL, standing in contrast to negative returns in other indices. Skewness analysis shows positive skewness in select indices (India, BVSP, ADX, and MERVAL) and negative skewness in others. This analysis highlights differing market behaviors, portraying certain indices as more bullish with a propensity for stronger positive trends, while others exhibit a bearish inclination, showcasing more pronounced downturns compared to upturns during the analyzed period. Examining correlation structures via Kendall’s Tau statistics reveals generally substantial interconnections among the studied indices, except for specific instances where correlations are absent between certain indices. Lastly, throughout the entire observation period, the indices exhibit stationary behavior based on the ERS statistic, suggesting stable statistical properties without notable structural shifts during the observed period, pivotal for reliable financial analysis and forecasting.

Results

Our methodological approach starts by using the Quantile Vector Autoregressive (QVAR) connectivity approach to the median quantile. This first step establishes a solid foundation for assessing risk through an autoregressive vector framework. As we progress, our methodology systematically extends its focus to different quantiles, using QVAR to compare and contrast results at several points in the distribution. By deepening the quantile analysis, we improve our investigation by transitioning to the frequency domain. This strategic change allows us to understand the temporal characteristics of risk and interconnection in a specific quantile. This comprehensive approach allows us to assess the evolution of risk and interconnection across different quantiles and frequencies, thus achieving a complete understanding of the complex dynamics that govern market interactions.

Dynamic Connectedness Analysis at Median Quantile

The connectedness measures issued from the QVAR, particularly at the median quantile (0.5), allow us to examine the Total Connectedness Index (TCI), as demonstrated in Fig. 1. Before the onset of the pandemic, we observe that the Brazilian BVSP Index emerged as an important receptor, with 59.54% of transmissions from the other indices studied. At the same time, Argentina’s MERVAL Index proved to be a major issuer, transmitting about 61.22% of its influence to other indices. In analyzing net flows, Egypt’s EGX30 Index had the highest net contribution as an issuer, with a net percentage of 8.46%, indicating its ability to influence other markets. In contrast, the Abu Dhabi ADX Index ranked as the largest net receiver, with a net percentage of -6.67%, revealing a tendency to receive more influence from other markets studied. Moreover, we find that, on average, the variation of each variable within this network can be explained by 54.3% (that is, the value of the total connectivity index).

Fig. 1
figure 1

Dynamic total connectedness in the mean quantile

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During the pandemic period, our results reveal significant changes in index connectivity dynamics. The South African JTOPI emerged as the most important receptor, receiving about 61.35% of transmissions from the other indices examined. On the other hand, the Saudi Arabian TASI Index turned out to be the main issuer and net issuer, transmitting 66.87% and 10.78% of its influence to the other indices, respectively, in a net way. However, Egypt’s EGX30 Index ranked as the largest net receiver, posting a net percentage of -11.96%. In addition, the overall Total Connectivity Index (TCI) for this period was estimated at 58.19%, indicating a stronger interconnection between these indices, highlighting trends specific to the financial markets studied.

During the period of conflict between Russia and Ukraine, our observations reveal distinct changes in the connectivity patterns of the indices. Argentina emerged as the predominant receiver, receiving about 58.31% of transmissions from the other indices studied. In contrast, the South African JTOPI was identified as the main issuer and net issuer, transmitting 65.86% and 7.69% of its influence to the other indices, respectively. In net terms, China’s SSE Index ranked as the largest net receiver, posting a net percentage of -6.5%. The total connectivity index for this period was valued at 54.27%, demonstrating substantial interconnection between the indices, although slightly lower than during the pandemic. This value nevertheless reaches the level recorded before the emergence of the global health crisis.

Compared to periods before and during crisis periods, distinct trends in connectivity are shown. During COVID, the JTOPI, BVSP, TASI, and RTSI are more resilient to risk transmission, while during the war, RTSI and TASI continue to be resilient but with lower intensity side to side to BSE30, JTOPI, and ADX. Finally, it is interesting to note a higher total connectivity index compared to before COVID-19 period. These variations highlight the sensitivity of financial markets to specific geopolitical events and underscore the evolution of connectivity dynamics over different periods of global instability.

Examining the connectivity dynamics of the indices shown in Figs. 1 and 2, several key observations emerge. Figure 1 shows several notable peaks in late 2017, where challenges loom over the North American Free Trade Agreement (NAFTA), as uncertainties and potential changes threaten the stability of this trade agreement. In Brazil, a notable political risk has emerged, marked by uncertainties and challenges in the country’s political landscape. Simultaneously, there is heightened concern and panic surrounding the Argentine peso, reflecting widespread fears about its stability and value. Meanwhile, the Chinese economy is experiencing a gradual slowdown, possibly influenced by changing demographic trends, trade tensions, and evolving economic policies. Other peaks are depicted, during the pandemic period and during the war. Looking at Fig. 2, which illustrates the dynamic net connectivity of each index, specific characteristics emerge for different indices. The SSE has stability as a receiver, with a few short periods of net transmissions. Similarly, RTSI is positioned as an almost constant net issuer, although it has some exceptions with net receipts towards the end of 2018 and around 2021, in addition to a significant peak in net transmission at the beginning of the war. However, the EGX30 is experiencing a transition from net transmission to net reception from the beginning of 2018, with momentary periods of net transmission around in the beginning of 2020 and during the second half of the year. The other indices show varying trends between net reception and transmission.

Fig. 2
figure 2

Dynamic net connectedness in the mean quantile

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To better understand these dynamics, an additional analytical approach is undertaken, using net connectivity graphs per pair. This method aims to provide clearer information on the directional flows of influence and the relationships between the variables analyzed, thus illuminating the dominant patterns of connectivity and the influential pathways that influence the dynamics of the BRICS-plus indices by splitting the whole sample into three periods. While an ample research focused on the tail risk spillover among markets (Aboura & Chevallier, 2018; Dai & Harris, 2023; Salisu et al., 2022; Stoja et al., 2023; Wang et al., 2015), some focused on emerging markets, particularly as Prabheesh et al. (2024) and Shah et al. (2024). Particularly, Zhang et al. (2024) examine an uneven pattern of inherent tail dependence from three distinct viewpoints: the directional impact in reaction to external shocks at different quantiles, the magnitude and duration of this impact, and a change in the dependency structure during different market phases.

Figures 3, 4, and 5 below present a network of the assets returns using a graph considered a system of nodes. The nodes represent the variables, while the (vertices) directed arrows show the static pairwise directional connectedness. Blue nodes represent net transmitters, while the yellow nodes represent net recipients of shocks in the system. Vertices are weighted by averaged net pairwise directional connectedness measures. The thicker the node and vertices, the higher the influence the instrument has on the system. The size of nodes represents weighted average net total directional connectedness. The network plot results are based on a TVP-VAR model with lag length of 4 order one (BIC) and a 10-step-ahead generalized forecast error variance decomposition.

Fig. 3
figure 3

Network plot of net connectedness before COVID-19. Notes: Blue (yellow) nodes represent net transmitter (net recipient) of shocks. Vertices are weighted by averaged net pairwise directional connectedness measures. The size of nodes represents weighted average net total directional connectedness. The network plot results are based on a TVP-VAR model with lag length of order one (BIC) and a 10-step-ahead generalized forecast error variance decomposition

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Fig. 4
figure 4

Network plot of net connectedness during COVID-19. Notes: Blue (yellow) nodes represent net transmitter (net recipient) of shocks. Vertices are weighted by averaged net pairwise directional connectedness measures. The size of nodes represents weighted average net total directional connectedness. The network plot results are based on a TVP-VAR model with lag length of order one (BIC) and a 10-step-ahead generalized forecast error variance decomposition

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Fig. 5
figure 5

Network plot of net connectedness during the war. Notes: Blue (yellow) nodes represent net transmitter (net recipient) of shocks. Vertices are weighted by averaged net pairwise directional connectedness measures. The size of nodes represents weighted average net total directional connectedness. The network plot results are based on a TVP-VAR model with lag length of order one (BIC) and a 10-step-ahead generalized forecast error variance decomposition

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Before the pandemic, the results show that some indices like MERVAL, EGX30, JTOPI, and RTSI acted as “net transmitters” of risks. This means that they were significant contributors to the spread of financial disruptions in the system. In other words, fluctuations or shocks in these markets tended to spread more widely and influence other markets. Conversely, indices such as SSE, ADX, TASI, BVSP, and BSE30 were considered “net receptors” of these shocks. They were more likely to be impacted by external disruptions rather than passing them on to other markets. The particular observation of the strong shock transmission connection from TASI to RTSI highlights a significant link between these two specific markets, suggesting that fluctuations or events in the TASI market could have a significant impact on the RTSI market. These results provide crucial insights into how different markets interacted in terms of financial risk.

During the pandemic, the roles of different indices have evolved. The results show that, in descending order, EGX30, SSE, MERVAL, BSE30, and ADX became net risk receivers. These indices were more sensitive receiving shocks or disruptions rather than passing them on to other markets. On the other hand, TASI appeared as the main transmitter of shocks, followed in an equivalent way by RTSI, JTOPI, and BVSP. This means that they have had a major impact in spreading financial disruptions during this period. The shock transfer intensities have also changed, highlighting a strong shock transmission from TASI to EGX30. In addition, a less but intense connection was observed, indicating a shock transfer from BSE30 to EGX30, as well as from BVSP and JTOPI to SSE. These new dynamics during the pandemic indicate significant changes in the way different markets interact in terms of financial risk transmission. These shifts in transfer roles and intensities underscore the sensitivity of markets to external events and how these events can spread across different indices.

During the war period, radical changes in the connections between the indices were observed. In fact, there has been a noticeable loss of connection between some indices, mainly MERVAL which has lost all connection with other indices in the financial system. This suggests a significant break in MERVAL’s relationship with other markets during this period. This could offer an insight on the cause of its rejection to join the BRICS union. Only an intense connection was detected between SSE and EGX30, followed by a relatively weaker connection from TASI and JTOPI to BVSP. The other relationships identified are very weak or almost non-existent. These results indicate a breakdown of the usual links between the different markets during the war period. The loss of MERVAL’s connection with all other indices, as well as the scarcity of meaningful relationships between other markets, point to a period of volatility and disruption in the usual financial interactions between stock exchanges. Overall, EGX30, BVSP, and SSE are net risk transmitters while the other indices turn to be net chock receivers.

According to Table 2, the variations observed in the total connectivity index and the different roles assumed by the various national indices as net transmitters or risk receivers underline the importance of implementing prudent risk management strategies and global financial dynamics. Financial entities, especially those with interests in the nations concerned, should adjust their investment and risk mitigation strategies by considering this complexity of connectivity and the significant influence of global crises. This could involve strengthening financial reserves during periods of increased connectivity or directing investments towards indices demonstrating resilient and stable performance during unstable periods. In addition, policy formulation could have insight from the varying impacts of crises on different economies, in order to optimize frameworks to stabilize their respective financial markets in the face of future turbulence.

Table 2 Dynamic connectedness analysis results
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Quantile Dynamic Connectedness

A comprehensive understanding of market dynamics could be obtained through the analysis of total connectivity and net directional BRICS indices in time-quantile space. Indeed, the heat map presented in Fig. 6 was generated using a 100-day moving window and a 20-day forecast using the QVAR model. The x-axis represents the timeline, while the quantiles, ranging from 0.05 to 0.95 and iterated in 1% intervals, are represented by the y-axis. Warmer hues on the graph indicate higher levels of connectivity. Results show high connectivity for strongly negative returns (below 20% quantile) and very positive changes (above 80% quantile), suggesting symmetrical total connectivity. Furthermore, the average quantile represents the total average connectivity over the entire period. Distinct values at specific intervals are observed, and spillover effects intensified particularly during the pandemic, with less intensity during the war, reflecting the moderate resilience of these countries during the war compared to the pandemic.

Fig. 6
figure 6

Dynamic total connectedness for all markets

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As previously mentioned, Fig. 7 indicates the quantile net directional spillovers. Warmer red shades on these plots indicate a net-transmitting, while blue shades designate a net-receiving asset. Focusing on the two-crisis period, the global pandemic and the war between Russia and Ukraine, aims to understand how investors respond to various market conditions, encompassing bearish (low quantile), stable (middle quantile), and bullish (high quantile) scenarios. Our research reveals evolving attributes over time that play a crucial role in identifying numerous economic events sha** the dynamic transmission of impacts across various quantiles.

Fig. 7
figure 7

Dynamic total net connectedness for all markets

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Fig. 8
figure 8

Total connectedness analysis through frequencies

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Fig. 9
figure 9

Total net connectedness analysis through frequencies

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Fig. 10
figure 10

Total net pairwise connectedness analysis through frequencies

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During the pandemic, MERVAL showed a strong receptivity, but during the war, this receptivity decreased, unlike its usual role of transmission. It is crucial to emphasize that its position in the different levels of fluctuation is not symmetrical. EGX30 primarily acted as a strong shock transmitter in 2017, but it became a weak receiver until October 2023. What stands out is that around 2021, in the lowest fluctuation level, it moved to a role of shock transmitter. For ADX, there is a strong tendency to act as a transmitter of shocks from 2020 until early 2021, but this trend weakened during the war, even in the median and high fluctuation levels. In most cases, ADX appears to be a receptor, except in almost all fluctuation levels.

TASI tended to be a net transmitter during the pandemic and a net receiver during the war, especially in the lowest fluctuation level. Outside of these periods, it showed low receptivity or transmission. On the other hand, JTOPI has been a net transmitter during the health crisis and war, mainly in the median and high fluctuation levels. What is striking is that BVSP has been a net transmitter in almost all fluctuation levels until the end of 2021. However, in 2022, in the median fluctuation level, there was a loss of connection with the system, unlike extreme conditions. Specifically, it has become a net receiver in the lowest fluctuation level and a net transmitter in the highest fluctuation level. The analysis of the BSE30 index reveals fluctuations in its behavior in the face of economic shocks. Before 2020, it changes status between transmission and shock reception. During the spread of the pandemic, it functioned primarily as a receiver of these shocks, reacting strongly to external events. However, between 2021 and October 2023, it adopted a different role, becoming a transmitter of shocks, but this transition was not uniform. Its influence on other aspects of the financial system was more pronounced at low values, indicating a more powerful transmission in these situations. Finally, for the connectivity of the RTSI with the rest of the system, unexpected results were observed. There has been a noticeable loss of links in most cases, except at the lowest level. At this level, RTSI has become a major risk transmitter since the beginning of the war in 2022 until the beginning of 2023, before seeing its impact diminish until the end of the period studied. This unexpected outcome suggests a complex dynamic where RTSI has lost its usual connection to the financial system, except in circumstances where it has suddenly acted as a significant vector of risks to the system.

Time Frequency Dynamic Connectedness

Such an approach is significant as it unveils the intricate interplay between immediate impacts and enduring relationships within the network, providing a comprehensive understanding of its dynamics. The results show a greater importance of short-term frequency, suggesting an increased responsiveness of these markets to immediate events or temporary fluctuations. This implies an ability to react quickly to specific elements, creating significant short-term interactions between these indices. However, at specific times, the long-term frequency becomes more predominant (e.g., beginning and end 2018, beginning of 2020 and the end of 2021). This may reflect periods where prolonged events or structural trends further influence connectivity between these markets. These moments could represent prolonged phases of major economic impacts or significant geopolitical changes, creating more sustained long-term connectivity between indices.

To summarize, the temporal dynamics of the links between the BRICS-plus stock indices exhibit a predominance of short-term interactions over long-term interactions, except in specific periods. This suggests a marked responsiveness of these markets to immediate events or temporary fluctuations. It indicates that these markets react quickly to specific elements, generating significant short-term impacts between these various indices. However, there are specific times when the trend is reversed, where long-term interactions take over. These periods could be extended periods when structural events or underlying trends have a greater impact on the relationships between these markets. These phases could result from major economic changes or significant geopolitical transformations, thus creating lasting links between indices Figs 8, 9 and 10.

Conclusion

Our study employs a twofold approach, beginning with the Quantile Vector Autoregressive (QVAR) connectivity model at the median quantile and extending to several other quantiles. This framework is boosted by incorporating frequency domain characteristics to capture temporal dynamics. By balancing the precision of regression models with the empirical richness of quantile and frequency analyses, we aim to provide a comprehensive understanding of market interactions. This robust methodology reveals the critical importance of understanding dynamic connectedness in global financial markets, particularly during periods of crisis.

Our results underscore the varying degrees of sensitivity financial markets exhibit in response to different global events. For example, indices such as JTOPI, BVSP, TASI, and RTSI showed notable resilience during the COVID-19 pandemic, while indices like BSE30, JTOPI, and ADX displayed varied resilience during the Russia-Ukraine conflict. These findings align with and contribute to existing literature on interconnectedness and risk transmission among BRICS and other major equity markets.

The analysis validates significant spillover effects and heightened market synchronization during the COVID-19 pandemic and the war in Ukraine, indicating the vulnerability of emerging markets to global shocks. The dynamic nature of financial market integration and contagion is consistent with previous research, with significant return and volatility spillovers across BRICS stock markets being sustained by various studies, (Anyikwa & Phiri, 2023; Chang et al., 2023a, 2023b; Hussain et al., 2023; İltaş, 2020; Lai et al., 2023; Owusu Junior et al., 2021; Panda et al., 2021; Smolo et al., 2022). Additionally, shifts in the roles of BRICS-plus countries during the war period, such as MERVAL losing its connections and BSE and ADX becoming net transmitters, offer new empirical evidence on the impact of geopolitical events on financial market integration.

Our comprehensive analysis of both short-term and long-term market interactions offers valuable insights for optimizing investment strategies and policymaking. It highlights the need for financial entities to adjust their risk management strategies by bolstering financial reserves and diversifying investments during periods of heightened connectivity. Policymakers should also tailor their frameworks to alleviate systemic risks and enhance market stability, considering the differential impacts of global crises on various economies. Finally, our study provides a crucial understanding for better navigating future financial turbulence.

While our study provides valuable insights, it is critical to acknowledge certain limitations. The exclusion of Iran, due to specific constraints, introduces a potential gap in the representation of the whole BRICS-plus. Future research could explore the integration of Iran into the analysis for a more comprehensive understanding of financial dynamics in the broader geopolitical context.

Our findings are intricately tied to the dataset’s temporal scope, spanning from January 1, 2016, to October 10, 2023. Financial markets are inherently dynamic, subject to ever-evolving global events, policy changes, and economic shifts. It is more difficult to extrapolate our findings to align with the dynamics of both the current and future market situations because of the limits ingrained in our dataset.

In conclusion, our research offers valuable insights into the evolving dynamics of BRICS-plus stock indices, but these findings should be interpreted within the context of the mentioned limitations. Addressing these limitations in future research endeavors will strengthen the robustness and applicability of findings in navigating the complexities of emerging markets.