1 Introduction

Many recent studies indicate diverse facets of global economic phenomena, encompassing financial market interdependencies, sustainability practices, resource-driven growth dynamics, and trade determinants Kakran et al. (2023) underscore the interconnectedness of Asia-Pacific Economic Cooperation (APEC) stock markets, highlighting the dominant influence of major economies such as the US, Canada, and Mexico on volatility spillovers. This interplay between global financial hubs resonates with the findings of Urom et al. (2023), which elucidate the intricate relationships between oil price shocks and interest rates across diverse economies, underscoring the role of external exposure and stability factors in driving integration dynamics.

Concurrently, the inquiries into environmental, social, and governance (ESG) practices by Rao et al. (2023) and the exploration of oil market shocks by Dagher and Hasanov (2023) both intersect at the nexus of sustainable economic development. Rao et al. (2023) delineate the nuanced impact of ESG metrics on financial performance among Indian companies, while Dagher and Hasanov (2023) disentangle the differential effects of oil supply and demand shocks on financial stability in Asian markets. These analyses collectively underscore the imperative for policy frameworks that integrate sustainability imperatives with financial resilience objectives.

Furthermore, the investigations into the resource curse phenomenon by Belaid et al. (2021) and the implications of dollarization rates on financial stress by Mansour Ishrakieh et al. (2020) converge on the broader theme of resource-driven economic dynamics. Belaid et al. (2021) unpack the nuanced relationship between oil revenues and economic growth in the Middle East and North Africa (MENA) region, while Mansour Ishrakieh et al. (2020) illuminate the pivotal role of dollarization rates in shaping financial stress indices, particularly in heavily dollarized economies.

Complementing these macroeconomic analyses, Piwowar-Sulej et al. (2023) delve into organizational resilience and sustainable human resource development practices, emphasizing the imperative of adapting to disruptive events such as the COVID-19 pandemic. Lastly, Dagar and Malik (2023) offer insights into the determinants of trade exports, shedding light on the interplay between oil prices, macroeconomic uncertainty, and export dynamics in Pakistan. These inquiries collectively underscore the multifaceted interdependencies within global economic systems and offer nuanced insights for policymakers, investors, and corporate practitioners alike.

Following the global financial crisis in 2008, economic uncertainty has prompted investors to seek alternative investment assets that offer risk diversification and hedging capabilities (Huynh et al., 2020a). Understanding the relationship between EGS, BRT, GLB, CRY, and ISM is crucial for asset allocation in portfolios, risk assessment, and risk management. Investor behavior varies in periods of bullish and bearish markets, leading them to allocate investments towards a combination of stocks that offer significant diversification benefits to their portfolios (Taghizadeh-Hesary et al., 2019).

Numerous studies have examined the link between different assets, particularly the interaction between Brent and global markets, as well as more recent assets such as cryptocurrencies and green investments, in order to identify the optimal markets for hedging. Green investments have emerged as a viable option for risk diversification and hedging, gaining international prominence. Green bonds, in particular, have gained popularity among investors due to their ability to address both financial and environmental sustainability concerns (Su et al., 2023; K.-H. Wang et al., 2023).

On the other hand, GLB has traditionally been viewed as a safe haven for investors seeking stability. Unlike certain markets, such as BRT, which are particularly sensitive to political pressures and global crises, GLB has shown resilience during challenging times. Its dependability makes it an appealing choice for risk-averse investors seeking consistent returns on their investments (Ji et al., 2020; Tiwari et al., 2019).

Recently, CRY has emerged as a new channel for investment and hedging strategies. Its decentralized structure and extreme volatility have attracted a significant number of investors seeking high returns. The ability to trade CRY 24/7 and the potential for rapid price swings make it an enticing option for investors looking to capitalize on market movements (Ahmed, 2021a, b; Aliu et al., 2021).

From a different perspective, ISM, from different perspective, has gained appeal among Sharia-compliant investors. These markets operate in accordance with Islamic finance principles, which prohibit interest-based transactions and promote ethical investment practices. By investing in Sharia-compliant assets, individuals can align their financial actions with their religious convictions, contributing to the growth of these specialized markets (Akinlaso et al., 2023; Chang et al., 2020; Sensoy, 2016).

Based on the foregoing, Understanding the lead-lag relationship and tail dependencies among different financial markets is crucial for investors, policymakers, and market participants. This academic paper aims to explore the lead-lag relationship and tail dependency of oil with respect to green investment, cryptocurrency, equity markets, and Islamic equity.

This research significantly advances the intersection of investment portfolio construction theory and environmental sustainability by examining the interdependencies among markets, including BRT, GLB, EGS, CRY, and ISM, within the context of climate change impact and sustainability considerations. Through advanced statistical techniques, nuanced patterns of market interactions are uncovered, introducing implications for portfolio diversification strategies. The study also plays a crucial role in bridging the gap between financial analysis and environmental concerns by providing insights into how sustainable investments can be effectively integrated into portfolios. Furthermore, solutions to the challenge of constructing resilient portfolios amidst environmental instability are presented, offering practical guidance for investors seeking to incorporate sustainability principles into their investment decision-making processes.

The purpose of this study is to analyze the dependency between a network of financial markets, including BRT, EGS, GLB, ISM, and CRY. Additionally, the study aims to determine the bivariate lead-lag relationship between these financial markets based on the relationships identified in the dependency analysis.

Various techniques were utilized in the existing literature to examine the interdependence of regional exchange rates. In this particular research, we utilize two approaches: (1) the Regular Vine copula approach, which involves the application of multivariate copula functions. This approach offers advantages over conventional correlation analysis by incorporating tail dependence coefficients to evaluate the interdependence between variables, encompassing both extreme positive and negative cases (Loaiza Maya et al., 2015). The Regular Vine copula represents a recent and reliable advancement in Copula types, as it allows for flexible dependency modeling and the measurement of both linear and nonlinear correlations. To establish the Multivariate Copula among the variables, we follow the methodology proposed by (Dissmann et al., 2013), while the marginal distribution is modeled using GARCH (1,1) with t-student innovation. (2) The wavelet transform and phase difference.Wavelet analysis is considered the most commonly employed technique for association analysis. It offers a significant advantage by allowing the simultaneous extraction and analysis of information in both the time and frequency domains. This functionality is crucial since relevant data is often available only in the frequency domain (Mar’i & Tursoy, 2022).

This study contributes significantly to investment portfolio construction theory by addressing the intricate relationships among specific markets—BRT, GLB, EGS, CRY, and ISM—which impact portfolio performance. Existing literature recognizes the importance of diversification across asset classes but lacks insight into these market interdependencies. Through advanced statistical techniques like copula and wavelet analyses, the study unveil nuanced patterns of market interactions during both bullish and bearish phases. Furthermore, this research contributes new insights by revealing the dynamic nature of intermarket dependencies.

The importance of the study stems from its discussion of the multiple relationships and interactions between the financial markets with each other in the bullish and bearish markets, identifying the dominant markets and the influence of other markets on their movement. Investors look for suitable markets to hedge and avoid investment risks.

2 Literature Review

2.1 The Relationship Between Oil and Financial Markets

Several studies have investigated the interaction between BRT and other financial markets from various perspectives, including EGS, CRY, GLB, and ISM, providing valuable insights into the relationship, effects, and spillovers between BRT and these markets.

In the context of green investment, Su et al. (2023) conducted a quantile-based analysis and found that in the short run, BRT has a positive effect on the growth of EGS. However, in the medium and long term, BRT overstock and increased earnings in the EGS industry have a negative impact. Similarly, (K.-H. Wang et al., 2023) employed a Granger-causality test and identified both positive and negative effects of BRT on EGS. While high BRT enhances the profitability of the EGS market, the high profitability of the industry and the abundance of oil supply can lead to a negative impact between BRT and EGS. Additionally, Rehman et al. (2023) highlighted the forecasting potential of BRT shocks for EGS markets, indicating that BRT shocks can serve as reliable predictors of EGS indices.

In the realm of cryptocurrency, studies have examined the relationship between CRY and BRT. Musialkowska et al. (2020) investigated the safe haven properties of assets such as gold, BRT, and CRY in crisis-ridden Venezuela. The findings suggest that gold is a more reliable safe haven compared to BRT, while CRY is considered a weaker safe haven. Attarzadeh and Balcilar (2022) empirically analyzed the association between CRY, GLB, and BRT, finding that return shocks are transmitted from GLB to both CRY and BRT, while volatility shocks are received from CRY and BRT by GLB. Additionally, Salisu et al. (2023) explored the impact of BRT prices on the realized volatility of CRY returns, indicating that higher BRT prices have a dampening effect on the profitability and volatility of CRY.

Regarding equity markets, researchers have examined the association between BRT and GLB. Tiwari et al. (2019) discovered a significant long-term dependent coherency between GLB and BRT, with most BRICS stock markets exhibiting immediate dependency in both directions on BRT. Liao et al. (2019) highlighted a positive dependency on BRT returns for both G7 and BRICS nations, with the G7 countries exhibiting an even greater dependence on GLB. Furthermore, Ji et al. (2020) analyzed the dynamic reliance and risk spillover between GLB and various BRT shocks, indicating significant risk spillover from BRT-specific demand shocks to GLB returns across all sample nations.

In the context of Islamic equity, Chang et al. (2020) explored the influence of oil prices, specifically BRT, on the ISM, revealing a negative impact of lower and higher quantiles of BRT prices on the upper and lower quantiles of the ISM. Khan et al. (2022) examined the relationship between BRT pricing and the performance of ISM and traditional market indices, highlighting a strong reaction of both indices to BRT prices, initially detrimental in the short and medium run but becoming beneficial in the long term. Additionally, Khan et al. (2023) investigated the dynamic connections among ISM, BRT, gold prices, and global policy uncertainty, revealing positive connections between gold prices and ISM, negative coherence during times of turmoil, and positive connections between BRT and ISM.

The studies reveal mixed effects of BRT on EGS, with short-term positive effects but negative impacts in the medium and long term. The relationship between BRT, CRY, and GLB also exhibits mixed effects, with both positive and negative associations observed. BRT prices have a dampening effect on the profitability and volatility of cryptocurrencies. The association between BRT and ISM indicates a negative impact on certain quantiles of the ISM but becomes beneficial in the long term. Additionally, BRT shocks have forecasting potential for EGS markets and result in significant risk spillovers to GLB returns.

2.2 The Relationship Between EGS and Financial Markets

Several studies have explored the relationship between EGS, CRY, GLB, and ISM in the context of volatility spillovers and causal linkages, as well as complex asset connections. In this subsection, we present the most recent studies that have examined the relationship between EGS and these markets.

Huynh et al. (2020b) found greater volatility transmission in the short run between robotics stocks, EGS, CRY, and gold, indicating that short-term shocks contribute more to volatility. (Yadav et al., 2023) examined the volatility spillover effects of EGS on renewable energy and the CRY market, revealing evidence of volatility spillovers from EGS to both sectors, with spillovers being more prominent in the medium and long runs. Additionally, Lee et al. (2023) explored the causal linkages between CRY and EGS, discovering a significant tail connection and two-way Granger-causality between these variables.

The relationship between EGS and GLB has also been investigated. Laborda and Sánchez-Guerra (2021) studied the impact of EGS offerings on company share prices in GLB markets, finding that the announcement of an EGS issuance generates a positive market effect. Park et al. (2020) examined the volatility dynamics and spillovers between EGS and GLB, uncovering asymmetric volatility in the EGS market and volatility spillover effects between the two sectors.

In the context of ISM, the relationship between EGS and ISM has been explored. Ejaz et al. (2022) investigated the market risk, dependency structure, and portfolio diversification advantages of EGS in comparison to ISM and GLB, finding symmetric upper and lower tail dependency between EGS and ISM. Umar et al. (2023) examined the effects of BRT shocks on various fixed income asset classes, including ISM and EGS, and identified a strong link between BRT shocks and these asset classes. Furthermore, Billah et al. (2023) investigated the return association between ISM and EGS, observing fluctuations in the return relationship over time, with a significant influence detected during the COVID-19 pandemic.

Regarding EGS and financial markets, there are volatility spillovers from EGS to renewable energy sectors and CRY, particularly in the medium and long runs. Causal linkages are identified between CRY and EGS. EGS also influences GLB, and ISM markets, with positive effects observed upon the announcement of EGS issuance and volatility spillovers between the two sectors.

2.3 The Relationship Between CRY and Financial Markets

Several studies have investigated the relationship between CRY and GLB, as well as ISM, in terms of risk sensitivity, diversification potential, and spillover effects. These studies contribute to our understanding of the relationships between CRY, GLB, and ISM, providing insights into risk sensitivity, diversification potential, and spillover effects in these markets.

Regarding the relationship between GLB and CRY, Aliu et al. (2021) examined the diversification risk of a CRY portfolio compared to a GLB portfolio and found that CRY has a larger positive connection and is more volatile than GLB. Bouri et al. (2020) studied the capacity of prominent cryptocurrencies to diversify against GLB and found evidence that CRY can be used as a hedge against GLB, particularly in Asian Pacific and Japanese equities. The study also highlighted the time-variability in the diversification potential of CRY, suggesting that their effectiveness as hedges may change over time. Hanif et al. (2022) investigated the spillovers between CRY and GLB, discovering risk spillovers from CRY to GLB.

In the context of ISM, Rehman et al. (2020) examined the risk sensitivity of the CRY and ISM markets, finding substantial long memory capabilities and a time-varying correlation between ISM and CRY. Ahmed (2021a) explored the reactivity of ISM stocks to realized volatility in CRY and observed that CRY’s upside volatility has immediate and delayed negative effects on ISM in developed markets, particularly during down market situations. The study also found that the correlation patterns between CRY volatility and ISM are asymmetric and have strengthened in recent years. Akinlaso et al. (2023) investigated whether ISM can provide portfolio diversification benefits for CRY investors and concluded that ISM can offer diversification alternatives for CRY investors, although ISM may be inefficient and prone to short-term speculative behaviors.

The relationship between CRY and financial markets reveals their larger positive connection and higher volatility compared to global equity markets. CRY offer diversification potential against GLB, although the effectiveness of this diversification may change over time. Risk spillovers are detected from CRY to GLB. In the context of ISM, CRY offer diversification alternatives but may exhibit inefficiency and short-term speculative behaviors.

2.4 The Relationship Between GLB and ISM

There have been numerous studies contributing to our understanding of the relationship between GLB and ISM markets from various perspectives, including systematic risk, interdependence, dynamics, and efficiency. These studies have shed light on the presence of interaction and asymmetric spillovers between the two markets, particularly during times of global crises. One notable study in this area is conducted by Sensoy (2016), who utilized dynamic risk indicators to compare the systematic risk levels of GLB and ISM markets. The analysis revealed that, for the majority of the sample period, GLB markets exhibited slightly higher levels of systematic risk compared to ISM markets. However, this difference in systematic risk was substantial in less than 3% of the sample period, indicating that ISM shares may not offer lower market risk than their GLB counterparts during financial turmoil.

Hammoudeh et al. (2014) examined the interdependence and dynamics between ISM and key GLB indexes. Their study found that the ISM market index demonstrated significant dependence on GLB and global parameters that are crucial to the global financial system, particularly during periods of economic turmoil. The relationship between ISM and GLB was shown to change over time, with certain circumstances leading to an unbalanced relationship between the two markets, especially in bear and bull market conditions.

Similarly, El Khamlichi et al. (2014) investigated the efficiency and diversification potential of ISM compared to GLB. Their findings indicated that ISM and GLB exhibited similar levels of efficiency or inefficiency. Furthermore, the analysis of cointegration revealed that ISM from the GLB did not have cointegrating relationships with their respective benchmarks, suggesting that the two markets may operate independently of each other.

The relationship between GLB, particularly ISM, and financial markets is examined in terms of systematic risk, interdependence, dynamics, and efficiency. GLB generally exhibit slightly higher systematic risk levels compared to ISM. The interdependence between Islamic equity markets and global equity markets is evident, especially during economic turmoil, with changing relationships over time. Efficiency and diversification potential show similar levels between ISM and GLB. Figure 1 encapsulates the interconnections among the study variables as discussed in prior research.

Fig. 1
figure 1

The interconnections among the study variables

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3 Data and Methodology

This study followed specific procedures for analysis, beginning with data collection and processing and concluding with the derivation of results, ensuring the attainment of reliable findings. Figure 2 illustrates these procedural steps graphically.

Fig. 2
figure 2

Study procedures

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3.1 The Data

To examine the dependency relationship between different financial assets and Brent oil, this study selected an index of green financial assets represented by EGS. The EGS index measures the performance of financial assets that prioritize sustainability. Additionally, a representative index of cryptocurrencies, CRY, was included. This index tracks the performance of the most valuable digital currencies in the market. Furthermore, an index for Islamic assets, ISM, was chosen to track the performance of financial assets that comply with Islamic sharia. Finally, the GLB indicator, representing 70% of the global market capitalization, was incorporated.

Diversifying an investment portfolio across distinct asset classes or sectors is crucial for managing risk and optimizing returns. The selected markets—BRT, GLB, EGS, CRY, and ISM—represent unique segments within the financial landscape, each offering specific characteristics and performance drivers. Brent serves as a global crude oil benchmark, influenced by geopolitical events and supply-demand dynamics. Global markets encompass major stock indices worldwide, reflecting diverse economies and industries. The green market focuses on sustainable investments, driven by regulatory trends and technological advancements. Cryptocurrencies in the crypto market offer high volatility and growth potential, independent of traditional markets. The Islamic market adheres to Sharia principles, providing Sharia-compliant investment opportunities. Incorporating these markets diversifies risk by spreading it across uncorrelated or negatively correlated assets, enhancing portfolio resilience. Investors benefit from exposure to various market dynamics and risk-return profiles, underscoring the importance of comprehensive portfolio diversification strategies.

The data covers the period from January 1, 2014, to December 30, 2022. The data was obtained from S&P Global Market Intelligence (2023). Financial data is influenced by a range of economic and political factors, which can introduce noise. To mitigate this noise, the data has been transformed into continuous returns, as illustrated in Eq. (1).

$${R}_{t}=100*{ln}\left({P}_{t}/{P}_{t}-1\right)$$
(1)

where \({R}_{t}\)represents the continuous returns, \({P}_{t}\) indicates the price at time t, and \({P}_{t}-1\) represents the previous price (Brooks, 2019).

The operational schedules of financial markets vary across different markets. While the digital currency market operates continuously throughout the week, other markets function for five days only, resulting in gaps in the study data. To address this issue, the operational schedules of all financial markets were standardized to five days, resulting in a total of 11,330 observations for each variable.

Figure 3 displays the study’s data in the form of continuous returns. The figure clearly illustrates the volatility within the study data. CRY exhibits the highest intensity, fluctuating between 20 and − 30. BRT follows with volatility ranging approximately from 10 to -20. It appears that EGS is the least volatile.

Fig. 3
figure 3

Assets behaviour

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4 The Methodology

4.1 GARCH (1, 1)

Financial data is well-known for its reliance on past values, which gives rise to a statistical concern known as autocorrelation when analyzing the data (Brooks, 2019). To address this issue, the GARCH (1,1) model is commonly employed, particularly when utilizing the copula approach ((Liu, 2011).

The study employs a two-step estimation procedure. In the first step, the conditional variance for the marginal distributions is estimated by applying the GARCH (1,1) model, and the standardized residuals are obtained. In the second step, copula data is defined based on the standardized residuals derived from the GARCH model (Mar’i & Tursoy, 2021). The initial step involves modeling with GARCH (1,1). However, it is recognized that the original assumption of GARCH assumes normality in the disturbance term, which does not align with financial data exhibiting fat tails (Czado, 2019). Therefore, in this domain, the Student’s t-distribution is typically utilized as follows:

$${Y}_{t}={\sigma }_{t}{Z}_{t}$$
(2)
$${\sigma }_{t}=\omega +\alpha {{Y}^{2}}_{t-1}+\beta {{\sigma }^{2}}_{t-1}$$
(3)

Where\({\sigma }_{t}=var\left({Y}_{t}\right|{Y}_{1},\dots ,{Y}_{t-1})\), the innovation \({Z}_{t}\) is assumed to follow student t-distribution.

4.2 The R-vine Copula

The copula method is commonly used in finance and economics research, particularly in studies exploring the dependence between financial markets, economic contagion, and the transfer of financial risks between markets (Mar’i & Tursoy, 2021). For example, Hammoudeh et al. (2014) employed the copula approach to investigate the dynamic dependence between ISM and GLB. Similarly, Rehman et al. (2020) utilized time-varying copulas to examine the risk spillover between CRY assets and ISM. Huynh et al., (2020) employed copula to study the interaction between EGS and CRY. Ejaz et al. (2022) utilized copula to investigate the risk spillover, dependency, and diversification benefits of EGS in relation to ISM and GLB. Furthermore, Hanif et al. (2022) explored the interaction between CRY’s assets and GLB using copula.

In the subsequent step, the copula data is established utilizing the standardized residual obtained from the preceding GARCH(1,1) model. This process generates pseudo-observations, which are subsequently employed for estimating the copula. The generation of pseudo-observations is accomplished through the following equation:

$${u}_{it}=F(\frac{{y}_{it}}{{\widehat{\sigma }}_{it}};{\widehat{v}}_{i})$$
(4)

Where \(\hat {{\sigma }}_{it}^{2}\) is estimated conditional variance for market \(i\)= 1,2,.,6, \(\hat {{\nu }}_{i}\) is degree of freedom, and \(t\) refers to time 1,2,…,T.

According toSklar’s (1959) theorem, the copula refers to a specific joint distribution formed by given marginals.Sklar (1959) states in his theorem that for an n-dimensional random vector \(X=({X}_{1},\dots ,{X}_{n})\) with each \({X}_{i}\) having a univariate marginal continuous distribution function \({F}_{i}\) defined on the interval [0,1], the joint distribution function can be expressed as:

$$F\left({X}_{1}, \dots ,{X}_{d}\right)=C({F}_{1}\left({X}_{1}\right),\dots ,{F}_{n}\left({X}_{n}\right)$$
(5)

Where, C represents the copula function, which combines the individual marginal distribution functions \({F}_{1}\left({X}_{1}\right)\), \({F}_{2}\left({X}_{2}\right)\), …, \({F}_{n}\left({X}_{n}\right)\) to determine the joint distribution \({F}_{1}({\text{X}}_{1}, \dots , {\text{X}}_{n})\).

By generating an initial pair of copulas to construct a multivariate copula in terms of distribution functions, (Joe, 1997) proposed conditioning as the optimal method for building multivariate distributions using bivariate structures alone. Additionally, (Bedford & Cooke, 2001) and (Bedford & Cooke, 2002) developed new copula designs that were more representative and introduced a comprehensive framework for defining all possible structures.

The density function \(f({x}_{1},\dots ,{ x}_{n})\), which represents the Pair-Copula Decomposition (PCCs), can be factored as follows:

$$f\left({x}_{n}\right).f\left({x}_{n-1}|{x}_{n}\right).f\left({x}_{1}|{x}_{2},\dots {x}_{n}\right)$$
(6)

The marginal distribution in the preceding equation can now be expressed as follows:

$$f\left({x}_{i}|k\right)={c}_{{x}_{i}{v}_{l}|v-l}(f\left({x}_{i}|{k}_{-l}\right),F\left({k}_{j}|{k}_{-l})\right).f\left({x}_{i}|{k}_{-l}\right)$$
(7)

Where, \(k={x}_{i+1},\dots , {x}_{n}\) represents the marginal distribution of xi, and k1 is a variable in the set k. The term \(f\left({x}_{i}|k\right)\) represents the bivariate density copula and the product of the marginal density function of \({x}_{i}\). \({k}_{l-1}\) represents the remaining variable(s) still present in k after removing \({k}_{l}\). The index i refers to {1,….,(n-1)}, and the density function c is defined as:

$$\frac{\partial C({u}_{1},{u}_{2})}{\partial {u}_{1}\partial {u}_{2}}$$
(8)

The normal vine copula is one among several types of the PCCs, which calculates c as the product of bivariate copulas (n(n-1)/2. This approach is valuable for modeling dependencies as it accommodates asymmetry and variable reliance on upper and lower tails (Loaiza-Maya et al., 2015).

The R-vine copula was initially introduced by Bedford and Cooke (2001, 2002) and is described as follows:

$$\eqalign{& f\left( x \right) = \prod\limits_{k = 1}^n {{f_k}} \left( {{x_k}} \right)\prod\limits_{i = 1}^{n - 1} {\prod\limits_{j = 1}^{n - i} {{c_{mi,i,mj,i|{m_j} + 1,i, \ldots ,{m_n},i}}} } \cr & \left( {{f_{mi,i|mj + 1,i, \ldots {m_{n,i}}}}} \right),{F_{mj,i|mj + 1,i, \ldots ,{m_{n,i}}}}\left( {{x_{mj,i|mj + 1,i, \ldots ,{m_{n,i}}}}} \right) \cr}$$
(9)

Where \({m}_{n,i}\) represents the R-vine matrix element in the m matrix. Tail dependency indicates the extent to which bivariate variables depend on each other in extreme situations. In other words, tail dependency illustrates the probability that a particular variable will exceed a given threshold if the other variable does. The study estimates the upper and lower dependency tails using Joe’s (1997) definition:

$${\lambda }_{u}=\underset{u\to {1}^{-}}{{lim}}p\left({X}_{1}>{F}_{1}^{-1}\left(u\right)|{X}_{2}>{F}_{2}^{-1}\left(u\right)\right)=\underset{u\to {1}^{-1}}{{lim}}\frac{1-2u+C(u,u)}{1-u}$$
(10)
$${\lambda }_{m}=\underset{u\to {0}^{-}}{{lim}}p\left({X}_{1}<{F}_{1}^{-1}\left(u\right)|{X}_{2}>{F}_{2}^{-1}\left(u\right)\right)=\underset{u\to {0}^{+1}}{{lim}}\frac{1-2u+C(u,u)}{1-u}$$
(11)

4.3 Cross-Wavelet Transform

Financial time series data encompass several unresolved issues regarding their behavior across different frequencies. Consequently, researchers have employed various techniques to gain a better understanding of this behavior. Currently, wavelet analysis is the most frequently utilized tool for this purpose. Its primary advantage lies in its ability to simultaneously capture time-domain and frequency-domain data (Tursoy & Mar’i, 2020; Tursoy & Mar’i, 2022).

Wavelet transforms utilize a fundamental function called the mother wavelet, which is stretched and shifted to capture local characteristics in both time and frequency domains. By combining various permutations of shifting and stretching the original wavelet, the wavelet transform captures all information in a time series and associates it with specific time horizons and positions in time (Gençay et al., 2001).

Cross-wavelet analysis is considered an effective tool for evaluating potential connections between two time series. The continuous wavelet transform can be extended to incorporate time series and construct cross-wavelet transforms, which identify regions of significant joint influence and provide additional information on phase relationships (Grinsted et al., 2004). When two wavelet transforms are applied to the same mother wavelet, the cross-wavelet transform displays the degree of similarity between the initial wavelet transforms or signals. The magnitude of the cross-wavelet transform can be used to infer the presence of mutual signals or to determine the source of these shared signals. Similarity can arise due to various reasons, and different approaches may provide distinct explanations for this similarity. The magnitude of the cross-wavelet transform will exhibit a peak that indicates this similarity (Young, 1993).

The cross-wavelet transform provides valuable information for the interaction between two time series, x and y, in the time and frequency domain, through bivariate analysis. It can be defined as follows:

$$wxy \left(t,s\right)=wx\left(t,s\right).\overline{w}y\left(t,s\right)$$
(12)

Where \(wx\) and \(wy\) represent the wavelet transformations of x and y, respectively. The cross-wavelet power is determined by \(\left|wx,y\left(t,s\right)\right|\)and can be defined as an indicator of the local variance of a time series. The cross-wavelet power of two time series indicates the local co-variance between the two series at each time and frequency. In this study, we follow the approach of (Veleda et al., 2012), who utilize the cross-wavelet transform to avoid introducing any inaccuracies by giving equal importance to large-scale connecting phenomena and small-scale phenomena.

To examine the lead-lag relationship between the variables, the study utilizes the phase difference approach proposed by Torrence and Compo (1998), following the methodology Rösch & Schmidbauer (2016a)). The phase difference is determined as follows:

$$Angle(\mathcal{T},\mathcal{S})=Arg(Wave.xy(\mathcal{T},\mathcal{S}\left)\right)$$
(13)

The x-over-y phase difference at each time and scale can be interpreted as the difference between individual local phase angles when translated into an interval angle \(\left[-\pi ,\pi \right]\). If the absolute value of the phase difference at a specific scale is less than or greater than π/2, the two series are considered to be in phase (anti-phase). For further details and interpretation of phase differences, see Appendix 1.

The study methodology, which serves to elucidate the intricate web of interdependence among financial markets, bears significant implications for a spectrum of societal stakeholders, including policymakers, investors, financial institutions, and regulatory bodies. This study offers several notable societal benefits:

  1. 1.

    Risk Management Implications: In the context of an increasingly interconnected global economy, the comprehension and effective management of financial risks are paramount. Our research contributes insights into the dependencies among diverse markets, enabling stakeholders to comprehend and mitigate systemic risks more effectively.

  2. 2.

    Portfolio Diversification Optimization**: The construction of diversified portfolios to minimize risk and optimize returns is foundational to investment strategy. Through the identification of dependencies between distinct financial markets, our study facilitates the construction of more resilient portfolios capable of navigating market volatility with greater efficacy. This, in turn, promotes long-term financial security and wealth preservation for both individual and institutional investors.

  3. 3.

    Sustainable Finance Implications: With the burgeoning interest in EGS factors, understanding the interplay between green investments and conventional financial markets assumes paramount importance. Our research sheds light on these dynamics, offering insights into how different markets influence one another within both bullish and bearish contexts. Such insights are instrumental in informing sustainable investment strategies, facilitating the allocation of capital towards environmentally and socially responsible projects.

In summary, the societal benefits of this study extend beyond academic discourse, offering practical implications for risk management, investment decision-making, regulatory oversight, and the advancement of sustainable finance. By fostering a deeper understanding of financial market interdependencies, this research contributes to the broader goal of promoting stability, resilience, and sustainability in the global financial system.

4.4 Results and Discussions

4.4.1 Descriptive Statistics

Table 1 presents the descriptive statistics of the study sample. The table displays the means of the variables. It is evident that GLB has the highest mean value of 0.135, while ISM has the lowest mean value, which is negative, at -0.014. This may indicate negative returns. However, the median values reveal that ISM has the highest median of 0.107, whereas CRY has the lowest median of 0.047. The significance of the median lies in its resilience against extreme values.

The standard deviation values indicate that GLB is the most volatile, with a value of 4.420, followed by ISM with a value of 2.487. On the other hand, BRT exhibits the least volatility, with a value of 0.986.

Regarding the deviation and distributional asymmetry of the data, Table 1 indicates that all variables exhibit a left-skewed distribution, as evidenced by their longer left tails compared to the right tails. Specifically, ISM and BRT display the greatest leftward deviation, with values of -0.840 and − 0.801, respectively. Similar patterns are observed for kurtosis, where ISM and BRT exhibit heavy tails with values of 17.167 and 15.591, respectively. Additionally, EGS exhibits the most pronounced heavy tails, with a value of 18.933, while GLB exhibits the least significant heavy tails, with a value of 7.086.

Table 1 Descriptive statistics
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With regard to normality, the data does not conform to a normal distribution, as indicated by the Jarque-Bera test. Additionally, the Arch test suggests that the data’s variance is not constant, indicating the presence of heteroscedasticity. To address this issue, the GARCH (1, 1) model was employed, as explained in the methodology section. The augmented Dickey-Fuller test (ADF)unit root test proposed by Dickey and Fuller (1979) indicates that the variables are statistically significant, thereby accepting the alternative hypothesis that the data does not contain a unit root.

4.5 Copula Analysis

The analysis of the R-Vine copula begins by examining the pairwise relationships among the research variables, as shown in Fig. 4. The contour shapes suggest the presence of bivariate dependencies between the variable pairs.

Fig. 4
figure 4

The dependence between the variables

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The right side of the plots displays the copula dependence values between the variables, with the diagonal histogram depicting the copula margins. On the left side, normalized contour plots represent the variables.

Overall, it is evident that the dependencies among variables are predominantly positive, except for the dependence between ISM and EGS, as well as between ISM and CRY. According to Kendall’s correlation coefficient, the range of dependence values varies between − 0.014 and 0.40.

Table 2; Fig. 5 present the results of multivariate copula dependency using R-vine copula. Tree 1 in Fig. 5 indicates dependencies between BRT and EGS, with values of 0.38 in the upper tail and 0.07 in the lower tail. There is also a dependency between CRY and EGS, with a value of 0.19 in both the upper and lower tails. Furthermore, the first tree also reveals a dependency between EGS and GLB, with a value of 0.25 in both the upper and lower tails. And finally in tree 1, there is a dependency between ISM and GLB in the lower tail, with a value of 0.12, while no dependency (independence) is observed in the upper tail.

Fig. 5
figure 5

Copula analysis

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Tree 3 reveals no dependence between GLB and crypto with BRT and EGS. Additionally, it indicates no dependence between BRT and ISM with EGS and GLB. Similarly, Tree 4 demonstrates no dependence between CRY and ISM with BRT, GLB, and EGS.

Table 2 R-vine copula’s results
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Tree 2 demonstrates dependencies between BRT and CRY with EGS in both the upper and lower tails, with a value of 0.05 for each. However, the dependency between BRT and GLB with EGS is zero. Similarly, there is no dependency observed between ISM and EGS with GLB.

4.6 Cross-Wavelet Transform

After analyzing the dependency relationships among different markets, the study further examined the interaction and lead-lag relationship between the markets in a bivariate form, using the results obtained from copula analysis.

Figure 6 shows the cross-wavelet transform between BRT and other financial markets, along with the phase difference. In terms of the bivariate relationship between EGS and CRY, an interaction between the two variables is observed over time and at different frequencies. Specifically, at low frequencies (2–32) around 2016, CRY lags behind EGS. However, the relationship switches, and EGS becomes the leading variable while CRY lags around 2018. In 2020, EGS continues to lead, but there is no clear pattern in 2022 at low frequencies. At medium frequencies (32–128) and high frequencies (> 120), EGS consistently leads while CRY lags, except for the year 2022.

Regarding the bivariate relationship between BRT and EGS, it is observed that BRT leads at medium and high frequencies, while EGS lags, except for the year 2016. At low frequencies, EGS leads while BRT lags, except for the year 2020.

Fig. 6
figure 6

Wavelet analysis

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Figure 6 presents the cross-wavelet transform of BRT and financial indexes. The contour lines represent the 5% significance threshold against red noise, with lighter shades indicating the cone of effect. The cone of effect is determined through Monte Carlo simulations using phase randomized surrogate series. The color code for power ranges from blue (low power) to red (high power). Additionally, arrows are used to indicate phase shifts.

With respect to the bivariate relationship between EGS and GLB, it is observed that EGS has a dominant role, with GLB lagging and EGS leading at all different frequencies (low, medium, and high).

Finally, regarding the relationship between GLB and ISM, there is a changeable role between the variables at low frequencies. However, there is no lead-lag relationship at medium and high frequencies until 2020. After that, it is observed that GLB leads while ISM lags at all frequency horizons.

4.7 Discussion the Results

The results of the study indicate that the dependency between the two financial markets does not extend to other markets. This means that the interaction between the two markets, whether during bullish or bearish times, does not have an impact on or interact with the performance of other markets. The influence of the interaction between these markets remains bilateral. However, there is an exception in the case of the dependency between BRT and CRY, where the effect may be transmitted to EGS during both bullish and bearish periods.

Regarding the bivariate dependency, the results confirm the existence of a dependency between BRT and EGS. This finding is consistent with previous research (Azhgaliyeva et al., 2022; Rehman et al., 2023; Su et al., 2023) that confirms a positive relationship between BRT and EGS. However, it is not fully aligned with the study by (Wang et al., 2022), which indicated a negative relationship between BRT and EGS.

Overall, this result demonstrates that the relationship between BRT and EGS strengthens during bearish market conditions, while it weakens during bullish periods. This can be attributed to the differential response of the two variables to market shocks and news, whether positive or negative, as concluded by Lee et al. (2021) and indicated by Das et al. (2019). The reason for this may be related to theories concerning investor psychology, which suggest that investors react more strongly to negative shocks compared to positive shocks, as noted by (Gupta et al., 2019).

The cross-wavelet transform analysis shows that BRT tends to lead EGS at medium and high frequencies, except for certain time periods, while EGS tends to lead BRT at low frequencies. The lack of a specific pattern in the lead-lag relationship confirms the bidirectional causality concluded Lee et al. (2021) and can be justified by the complexity of the nature of the BRT market and the way the market reacts to economic turmoil, as indicated by (K.-H. Wang et al., 2023).

The tail dependence between EGS and CRY, and EGS and GLB remains equivalent regardless of market movements, indicating that the bivariate relationship between these variables is not influenced by bullish or bearish market conditions since they have a sizeable effect in the lower and upper tails.

The results regarding EGS and CRY confirm the existing dependency between these markets in bullish and bearish cycles. This indicates that their movements can interact endogenously (Huynh et al., 2020b). This interaction can be attributed to the fact that they are volatile markets and are simultaneously affected by economic turbulence (Yadav et al., 2023). The wavelet analysis shows that EGS and CRY switch their roles in leading and lagging at different times and different frequency horizons. This confirms the bidirectional relationship between these variables, as noted byLee et al., (2023) and Syed et al. (2022)

Regarding EGS and GLB, the results confirm the dependency between the lower and upper tails and a positive relationship. The wavelet analysis shows that EGS leads at all frequencies and at all times. This could be the result of recent global trends towards environmentally friendly projects, thus increasing the impact of EGS volatility on the GLB. These results are consistent with (Laborda & Sánchez-Guerra, 2021), (Park et al., 2020), and (Verma & Bansal, 2023).

Finally, regarding GLB and ISM, the copula analysis confirms the existing dependency in the lower tails, while the upper tail shows independence. This is further supported by the wavelet analysis, which shows that the lead-lag relationship exists only at lower frequencies until 2020. This may be attributed to the increased interaction of investors and their reactions in the financial markets during negative circumstances in bearish periods, while this interaction decreases during bullish periods, as previously indicated. These results are consistent with (Rahman et al., 2021), who found independence between GLB and ISM in bullish markets. Figure 7 summarizes the results of the study obtained using copula analysis.

Fig. 7
figure 7

Direction of dependence between financial markets. Note: The arrows indicate the existence and direction of dependence between financial markets

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The results highlight the intricate web of interdependencies among financial markets, addressing the identified research problems and offering solutions grounded in empirical analysis through:

Firstly, the study investigates the dependency between two financial markets and its extension to other markets. This exploration stems from the recognized need to comprehend the interconnectedness of financial markets, particularly in light of economic and political fluctuations. The research problem centers on discerning whether the interaction between two markets, such as BRT and CRY, significantly influences the performance of other markets during both bullish and bearish periods. The solution involves employing rigorous statistical analyses, including copula and wavelet techniques, on comprehensive datasets spanning several years.

Theoretical contributions of the study emerge as the results unveil distinctive patterns of dependency and interaction among the examined financial markets. The findings reveal that while the dependency between specific markets does not uniformly extend to all markets, there are exceptions, such as the transmission of effects from BRT and CRY to EGS. This underscores the nuanced nature of market interdependencies and challenges simplistic notions of systemic influence.

Moreover, the study contributes theoretically by confirming the existence of a dependency between BRT and EGS, aligning with previous research findings. However, it also presents a nuanced perspective by demonstrating that this relationship varies across market conditions, strengthening during bearish periods and weakening during bullish periods. This nuanced understanding challenges conventional wisdom and enriches existing theoretical frameworks concerning market dynamics and investor behavior.

Furthermore, the research problem extends to exploring lead-lag relationships between financial markets. Theoretical contributions in this domain emerge as the study confirms bidirectional causality between BRT and EGS, as indicated by previous research. However, the study adds depth by elucidating the complexity of this relationship, particularly regarding the differential responses of the two variables to market shocks and news. This contributes to a deeper understanding of investor psychology and market dynamics, enriching theoretical discussions on market efficiency and information transmission mechanisms.

Additionally, the study examines the tail dependence between various financial markets, offering insights into the robustness of bivariate relationships across different market movements. Theoretical contributions arise as the findings demonstrate that certain relationships, such as EGS and CRY, exhibit consistent dependency across bullish and bearish cycles, reflecting the endogenous interaction between volatile markets. This adds nuance to theoretical discussions on market contagion and systemic risk, highlighting the importance of understanding market dynamics beyond linear correlations.

5 Conclusion

In this study, we analyze the network of dependence between financial markets, specifically Brent, global, green, crypto, and Islamic, in order to verify the existence of tails dependence between these financial markets in bullish and bearish markets. In addition to determining the lead-lag relationship between these markets, depending on the dependency results. This study covers data from January 1, 2014 to December 30, 2022. copula and wavelet analysis was used to obtain the results.

The results of this study provide interesting results about the dependency and interaction between various financial markets. The findings indicate that the dependency between two specific markets does not extend to other markets, suggesting that the influence of their interaction remains bilateral and does not impact the performance of other markets. However, an exception is observed in the case of the dependency between BRT and CRY, where the effect may be transmitted to EGS during both bullish and bearish periods.

Regarding the bivariate dependency, the results confirm the existence of a positive relationship between BRT and EGS, consistent with previous research. However, this relationship is found to strengthen during bearish market conditions and weaken during bullish periods, potentially due to the differential response of the variables to market shocks and news. This pattern aligns with theories of investor psychology that highlight stronger reactions to negative shocks. The lead-lag analysis reveals that BRT tends to lead EGS at medium and high frequencies, while EGS leads BRT at low frequencies, indicating a bidirectional causality between the two variables.

The tail dependence analysis indicates that the bivariate relationship between EGS and CRY, as well as EGS and GLB, remains consistent regardless of market movements. The dependency between EGS and CRY is observed in both bullish and bearish cycles, suggesting an endogenous interaction between these volatile markets. The relationship between EGS and GLB is also confirmed, with EGS leading at all frequencies and times, potentially due to global trends favoring environmentally friendly projects.

Regarding GLB and ISM, the copula and wavelet analyses reveal a dependency in the lower tails but independence in the upper tail. The lead-lag relationship is found to exist only at lower frequencies until 2020, indicating increased interaction and reactions of investors during negative circumstances in bearish periods. These results are consistent with previous research that found independence between GLB and ISM in bullish markets.

This study delved into the intricate network of interdependence among financial markets, encompassing Brent, global, green, crypto, and Islamic markets, employing copula and wavelet analysis methodologies. The research aimed to unveil the nuanced relationships between these markets during both bullish and bearish market phases.

Through rigorous analysis, this study contributes to the existing body of literature by providing insights into the complex interactions between financial markets. By examining the dependency structures without explicitly presenting the results in this conclusion, the study adds depth to our understanding of market dynamics.

The findings underscore the importance of comprehensively assessing the interplay between markets, particularly in times of market volatility. Such insights are invaluable for investors, policymakers, and financial institutions in devising robust strategies for risk management, portfolio diversification, and market regulation.

Moreover, the study sheds light on the evolving nature of market interactions, hinting at potential implications for investment decisions and policy formulations. By identifying patterns of dependency and lead-lag relationships, this research offers a foundation for further exploration into market interdependencies and their implications for financial stability and economic resilience.

Policy Implications:

  • Diversification Strategies: Investors should consider diversifying their portfolios across various markets to mitigate risks associated with interdependence. Understanding the dynamics between markets during different market conditions can inform more effective diversification strategies.

  • Risk Management: Policymakers and financial institutions should incorporate the findings into risk management frameworks. Recognizing the varying degrees of interdependence between markets can help in better assessing and managing systemic risks.

  • Environmental Investments: The observed lead-lag relationship between Brent and Green Investments, particularly during bearish periods, suggests potential opportunities for policymakers and investors to promote environmentally friendly projects during market downturns.

  • Market Regulations: Regulators should stay vigilant of the interconnectedness between different financial markets, particularly during volatile market conditions. Regulatory measures may need to be adjusted to address emerging risks arising from market interdependencies.

Limitations:

  • Data Limitations: The study covers data from January 1, 2014, to December 30, 2022. Future studies could benefit from including more recent data to capture evolving market dynamics.

  • Methodological Constraints: While copula and wavelet analyses provide valuable insights into market interdependence, they are not without limitations. Alternative methodologies or complementary analyses could offer further insights into market relationships.

  • Market Context: The study’s findings may be influenced by specific market conditions during the analyzed period. External factors such as geopolitical events or regulatory changes could impact market dynamics differently in future periods.

  • Generalizability: The findings of this study may not be directly applicable to all financial markets or regions. Consideration of market-specific factors is essential when extrapolating the results to different contexts.

6 Appendix 1

figure a

Based on Rösch & Schmidbauer (2016b).