Exploring the Dynamic Link Between Crude Oil and Islamic Stock Returns: A BRIC Perspective During the GFC

Abstract

This study examines the relationship between crude oil returns (CRT) and Islamic stock returns (ISR) in BRIC countries during the Global Financial Crisis (GFC), employing wavelet-based comovement analysis and regression models that incorporate both contemporaneous and lagged CRT across 40 cases. The wavelet analysis reveals strong long-term comovement at low frequencies between ISR and CRT during the GFC. Contemporaneous regressions show that increases (decreases) in CRT align with corresponding movements in ISR. Lagged regressions indicate that CRT can predict ISR up to one week ahead for Brazil, Russia, and China, and up to two weeks for India, although the predictive strength weakens beyond this window. These findings challenge the perception that Islamic stocks were immune to the GFC, showing they were affected by global oil market dynamics, albeit with varying degrees of resilience across countries and time horizons.

1. Introduction

This research investigates the dynamic relationship between crude oil market movements and Islamic stock returns in BRIC countries during the Global Financial Crisis (GFC), aiming to uncover whether oil price dynamics serve as predictive signals for Islamic equities in emerging markets. This study is significant as it explores the vital connections among three key components: the global financial crisis that reshaped economic landscapes, the use of crude oil data to predict stock market returns, and Islamic stocks. However, forecasting stock returns during the GFC using crude oil returns necessitates a comprehensive understanding of the specific characteristics and dynamics of crude oil as a reliable indicator of impending financial downturns. While the existing literature addresses the linkage, such as volatility spillover between crude oil prices and stock returns, we specifically focus on the forecasting capacity of the crude oil market and its effectiveness in predicting returns in the context of the GFC and Islamic stocks.

The motivation for studying Islamic stocks stems from the ongoing debate regarding their purported immunity to financial crises. Numerous studies suggest that Islamic stocks, due to their adherence to Sharia law principles, exhibit a positive relationship with financial stability and act as a safe haven during crises. Islamic stocks are governed by the principles of Sharia law, which prohibit excessive risk-taking (gharar), interest-bearing transactions (riba), and investment in non-compliant sectors (e.g., alcohol, gambling, conventional financial services) (Hassan et al., 2023). As a result, firms included in Islamic indices tend to exhibit stronger balance sheets, lower leverage, and greater operational transparency, all of which are characteristics commonly associated with financial resilience.

Philosophically, Islamic finance is rooted in ethical investment, risk-sharing, and the real-economy linkage. These features promote a sustainable and socially responsible financial framework, which inherently resists speculative bubbles and systemic risk buildup. During financial crises such as the GFC, conventional markets, driven by leverage and derivative exposure, tend to collapse more sharply (Ahmed, 2010). In contrast, Islamic equities are somewhat insulated from such speculative exposures, leading to the hypothesis that they may act as safe havens or at least exhibit lower downside risk during global turmoil. This assertion is based on their historically superior performance and the lack of evidence showing their susceptibility to market contagion following the onset of the GFC (Rizvi et al., 2015; Kenourgios et al., 2016; Hkiri et al., 2017). However, the extent to which Islamic stocks truly offer protection or serve as insurance for investors during crises remains an open question. Given the intricate interdependencies within the global financial market, it is plausible that Islamic stocks might also be vulnerable to market contagion during financial upheavals (Hoque et al., 2024).

The inclusion of oil stock studies is crucial in assessing the claim of Islamic stocks’ immunity to the GFC. The oil industry has a significant influence on global financial markets, and analyzing the relationship between oil stocks and Islamic stocks provides valuable insights into the economic interdependence and market behavior during crises. This analysis is particularly pertinent for the BRIC countries, where Islamic stocks often have substantial exposure to the energy sector (Mensi et al., 2018). BRIC countries are major players in global energy and financial systems, making them highly relevant in an oil-Islamic finance dynamic. Russia and Brazil are among the world’s largest oil producers (Hamilton, 2019). China and India are the top two crude oil consumers, making them highly sensitive to oil price volatility (BP, 2022). This dual role as oil exporters and importers within BRIC offers a balanced testing ground for oil–shariah equity interactions under differing economic exposures. Researchers like Hassan et al. (2020) and Kenourgios et al. (2016) have examined the role of BRIC (Brazil, Russia, India, China) countries concerning Islamic stocks. Hassan et al. (2020) observed that, while the relationship between Islamic stocks and developed economies has been well-documented, there is a scarcity of research focusing on emerging markets like the BRIC nations.

Although BRIC countries are not predominantly Muslim-majority nations, their inclusion in the analysis of crude oil and Islamic stock returns is both empirically sound and strategically meaningful for several compelling reasons. Islamic equity indices, while grounded in Shariah principles, are increasingly recognized by both Muslim and non-Muslim investors as effective tools for risk management and ethical investing. Their rising popularity in Europe underscores this broader appeal (Bellalah & Chayeh, 2015). Prominent European exchanges such as the London Stock Exchange and the Luxembourg Stock Exchange have launched Islamic ETFs and sukuk offerings tailored to institutional investors beyond religious boundaries. Supporting this trend, Fitch Ratings (Fitchratings.com, 2024) reports that by the end of the third quarter of 2024, the Irish Stock Exchange (Euronext Dublin) was the leading global venue for sukuk listings denominated in hard currencies, accounting for 38% of global sukuk issuance, with the London Stock Exchange and Nasdaq Dubai following closely.

Islamic finance has also seen notable growth in non-OIC nations, including those in the BRIC bloc. India and Russia, with substantial Muslim populations of approximately 200 million (Maizland, 2024) and 25 million (Islamic Bridge, 2022) respectively, have witnessed increasing domestic interest in Shariah-compliant financial products. In India, the Bombay Stock Exchange has introduced the BSE TASIS Shariah 50 index, and various non-banking institutions offer Islamic microfinance and sukuk instruments. Russia has shown policy-level support for Islamic finance, with the Bank of Russia initiating pilot programs for Islamic banking since 2021 (Bifolchi, 2024). China, while not a Muslim-majority country, has explored Islamic finance through its trade relations with the Middle East and experimental projects in regions such as Xinjiang (Reeves, 2025). All four BRIC countries are represented by Islamic or Shariah-compliant equity indices, including Dow Jones, S&P, and MSCI Islamic indices. These indices adhere to established Shariah screening standards, such as those set by Accounting and Auditing Organization for Islamic Financial Institutions (AAOIFI), ensuring consistency with research conducted in Islamic-majority economies and enabling comparative analysis of Islamic equity performance in major emerging markets.

Since Shariah-compliant funds are investing in emerging market equities, including BRIC stocks, understanding oil shocks in BRIC Islamic indices equips investors with insights for cross-border portfolio hedging and risk management. Most Islamic finance research has focused on GCC and Southeast Asian markets, often excluding non-Muslim-majority emerging economies. The BRIC focus addresses a clear literature gap, especially considering that Islamic indices in these markets behave differently under GFC due to structural and policy differences. It offers insights into the spillover effects of oil shocks in less-studied Islamic stock environments. By studying the resilience and response of Islamic indices in BRIC, the research contributes to the globalization of Islamic financial practices and their applicability in broader economic systems.

With the rising interest of international investors in emerging markets and the notable growth potential of BRIC countries, this study aims to analyze the Islamic stock market within these nations. By investigating these linkages, researchers can determine whether Islamic stocks demonstrate resilience compared to conventional markets, thereby supporting diversification and risk management strategies for investors. Additionally, the findings can inform policymakers in developing strategies for future crises and validate whether the principles of Islamic finance offer a buffer against global financial shocks. Ultimately, this research provides additional empirical evidence that is useful in analyzing the immunity of Islamic stocks during the GFC, addressing a critical gap in the literature.

Although numerous studies have investigated the volatility spillover mechanism from oil prices to stock prices (Singh et al., 2019; D. Zhang, 2017; Feng et al., 2017; Khalfaoui et al., 2019), there is a lack of research examining the forecasting capacity of crude oil market to predict stock returns in the context of the GFC, Islamic stocks, and BRIC nations. Understanding the volatility spillover from the crude oil market to the stock market aids in risk management and portfolio diversification. Still, it does not necessarily facilitate the prediction of future market movements. Investors and policymakers need tools to anticipate future trends and prepare accordingly.

While prior research (e.g., Trabelsi, 2019; Arshad, 2017; Chang et al., 2020; Boubaker & Rezgui, 2020) has examined the oil–Islamic stock nexus, this study uniquely focuses on the predictive power of crude oil returns beyond correlation or volatility spillover, specifically during the GFC and within the underexplored BRIC context using wavelet-based comovement and lagged regression analysis. Understanding correlation or volatility spillover is crucial, but they do not necessarily imply that CRT can forecast ISR. Non-causal relationships identified using correlation and linkage studies do not establish that changes in crude oil prices can reliably predict stock prices. Additionally, financial markets are dynamic, and static analyses may fail to account for changing conditions and structural breaks over time. While volatility spillover analysis provides valuable insights into interconnected risks, it does not offer the directional or magnitude information needed for accurate forecasting. To address these limitations, our study goes beyond merely examining the linkage. We conducted a comprehensive analysis that includes studying the comovement first, then the regression with contemporaneous effect of CRT on ISR, and finally the lagged CRT IN predicting ISR. The comovement analysis was performed to identify the strong comovement between ISR and CRT during GFC. The wavelet method was employed in studying the comovement as wavelet has the capability to capture the comovement at varying frequencies (short term and long term). The finding of strong long-term comovement between CRT and ISR further encouraged us to investigate the relationship between ISR and CRT by incorporating a linear regression model. The regression with contemporaneous CRT allowed us to evaluate the model’s performance using historical data, ensuring it accurately captures the relationship and adjusts for any noise or anomalies. Finally, the regression with lagged CRT test then validated the model’s predictive power. By rigorously testing our model using these methodologies, we ensure its robustness and predictive accuracy. This comprehensive approach makes our study unique, providing valuable insights into the predictive capacity of crude oil prices for Islamic stock returns, particularly in the context of the GFC. This rigorous testing framework not only enhances our understanding of market dynamics but also provides a reliable tool for investors and policymakers to anticipate future trends and prepare accordingly.

The research yielded several noteworthy findings. By applying a wavelet-based comovement analysis, the study first ensured that both Islamic stocks in BRIC nations and the crude oil market exhibit strong comovement at the long term during the turbulent period of the GFC. Secondly, the contemporaneous regression framework for the GFC period (2007–2009) confirmed that the crude oil market contains significant information content about Islamic stock returns of each of the BRIC countries. Finally, the lagged CRT test substantiated the predictive power of the crude oil market in forecasting Islamic stock returns for Brazil, Russia, and India within a one-week forecast horizon during the GFC period.

This study contributes to the existing literature in several novel ways. First., unlike most existing research which focuses on Islamic-majority or oil-exporting countries, this study uniquely targets BRIC countries, i.e., emerging economies with growing Islamic financial instruments but diverse oil market roles, thus offering new empirical evidence from underexplored regions. This geographic diversification broadens the applicability of Islamic finance research beyond traditional OIC markets.

Second, the study provides insights that are relevant not only to faith-based investors but also to mainstream investors seeking risk mitigation tools, by highlighting the behavior of Islamic stocks, often perceived as conservative, ethical assets in response to global commodity shocks. These contributions are timely and relevant given the evolving landscape of ethical investing and the volatility of global oil markets.

Third, and importantly, this study captures the time evolution of the relationship between CRT and ISR, with specific attention to the GFC period. By studying comovement over an extended time frame, we uncover how the oil–stock linkage intensifies or weakens during periods of systemic stress. This temporal dimension enhances our understanding of Islamic equities’ behavior not only in normal times but also under extreme market conditions, adding depth to both asset pricing and financial stability debates in the Islamic finance domain.

This paper is structured as follows: The subsequent section presents the literature review and outlines the research objectives of the study. Section 3 details the research methodology and data utilized. The empirical analysis is conducted in Section 4. Section 5 discusses the findings of empirical research and provides the conclusion.

2. Literature Review and Research Objectives

2.1. Empirical Insights on Oil–Stock Interactions in China

Our literature review concentrates on oil–stock studies in the context of BRIC countries and Islamic stocks. Among the BRIC countries, China has recorded the highest GDP growth rate over the last couple of decades. Due to its impressive growth performance, China has been extensively studied in comparison to other BRIC markets, although with mixed findings. Cong et al. (2008) reported no significant impact of oil price shocks on Chinese real stock returns, while Broadstock et al. (2012) found that energy-related stocks became highly correlated with world oil prices after the 2008 financial crisis. Li et al. (2012) indicated that oil prices and sectoral stocks are cointegrated, with oil prices having a positive impact on sectoral stocks. Q. Chen and Lv (2015) evidenced a positive extreme dependence between the Chinese stock market and the world oil market, which increased significantly during the GFC, indicating contagion. Zhu et al. (2016) concluded that there is a positive dependence between Chinese industrial stock returns and crude oil price changes. Zheng and Su (2017) found that liquidity in the Chinese stock market increases (decreases) when positive oil price shocks are caused by oil-related demand (supply). Ding et al. (2016) used a nonlinear quantile causality test to demonstrate bidirectional causality between oil price returns and stock price returns in China at lower quantiles. You et al. (2017) applied quantile regression to show that higher oil prices exert a negative impact on stock returns at extreme higher quantiles before the financial crisis. C. Chen et al. (2017) documented the significant predictive power of oil return volatility over momentum payoffs of China’s industrial sector stocks. Wei and Guo (2017) found that oil shocks have a greater impact on stock returns than on volatility.

2.2. Oil–Stock Price Nexus Across BRIC Economies: Broader Evidence Beyond China

Several studies have examined the oil–stock price nexus in other BRIC member countries. For India and Russia, Fang and You (2014) demonstrated a negative impact of oil price shocks on stock prices, while there was no significant response in China. Reboredo et al. (2017) found weak evidence of dependence between oil and stock prices before the GFC in BRIC countries, the UK, the USA, and the European Monetary Union (EMU) region; however, they documented strong evidence of dependence during the financial crisis of 2008–09. B. Zhang and Li (2016) noted that the hike in oil–equity correlation in 2008 in the UK, the USA, Germany, South Africa, and the four BRIC countries was a long-run, not a transitory, phenomenon. Ghosh and Kanjilal (2016) found no cointegrating relationship between oil and stock prices in India before the financial crisis; however, they observed evidence of cointegration post-crisis. Silvapulle et al. (2017) reported a long-run equilibrium relationship between crude oil and stock prices in a panel of net oil-importing countries, including China. Recently, Boubaker and Raza (2017) documented volatility spillover between oil and BRIC and South African stock markets. Finally, Mensi et al. (2018) studied the comovement between oil and stocks in BRICS.

2.3. Oil–Islamic Stock Market Linkages: A Review of Key Studies

Despite extensive research on the interplay between crude oil and conventional stock markets, scholarly attention toward the relationship between crude oil and Islamic stock markets remains relatively limited. Arshad (2017) analyzed Islamic stock markets in major oil-importing countries using EGARCH and MF-DFA, finding that oil price volatility closely influences Islamic market volatility due to their real-economy linkages. Emerging markets showed higher volatility and lower efficiency than developed ones, reflecting their rapid economic transitions. Shahzad et al. (2018) conducted a study, analyzing the global relationship between oil and Islamic stock indices and concluding that there is a notable volatility spillover between them. The study by Badeeb and Lean (2018) revealed a nonlinear long-term relationship between oil and Islamic stock indices and observed that Islamic stock indices exhibit a weak response to changes in oil prices.

These findings align with core Islamic finance principles, which emphasize risk-sharing, asset-backing, and prohibition of speculative activities (gharar). Such principles often lead Islamic equities to be more grounded in the real economy, potentially reducing their responsiveness to short-term speculative shocks while still remaining sensitive to broader macroeconomic changes like oil price movements. This explains the mixed, often delayed, transmission observed in empirical studies.

Building upon these foundations, recent studies have further advanced this discourse with fresh empirical and methodological perspectives. Mokni and Youssef (2019) applied a time-varying copula approach to assess comovements between oil prices and Islamic stocks during crisis periods. They found that dependence structures vary over time and are intensified during market stress. Trabelsi (2019) examined the spillover effects and connectedness among Islamic equities, Sukuk (Islamic bonds), crude oil, and gold across different time frequencies (short, medium, and long term). It aimed to understand how shocks in one asset class transmit to others, particularly in the context of Islamic finance. It found that crude oil is a major transmitter of shocks, especially to Islamic equities, due to its economic significance in Muslim-majority (especially GCC) markets.

These studies underscore how Islamic equities, due to their structural filters (e.g., low leverage, exclusion of speculative sectors), can respond differently to shocks than conventional stocks. During financial crises, Islamic indices often reflect a more stable or lagged reaction, as seen in crisis-period studies, making them attractive to investors seeking ethical or lower-risk diversification.

Hassan et al. (2019) studied the total volatility spillover from oil price to Islamic stocks in BRIC countries. Finally, Hassan et al. (2020) studied the directional volatility spillover from crude oil to Islamic stocks in BRICS. Chang et al. (2020) investigated the impact of oil price fluctuations on the Dow Jones Islamic Index and its sectoral components using advanced quantile-based methods. Their quantile-on-quantile analysis reveals asymmetric effects: lower oil price quantiles negatively influence upper quantiles of the Islamic index and vice versa. Lin and Su (2020) explored the relationship between oil market uncertainty, measured by the Oil Volatility Index (OVX), and Islamic stock markets across four representative countries. Using the quantile-on-quantile (QQ) approach, they identified an overall negative association between oil market uncertainty and Islamic stock returns. Their findings also highlighted significant heterogeneity and asymmetry in this relationship, indicating that the impact of oil uncertainty varies across different market conditions and quantile levels. Boubaker and Rezgui (2020) examined the comovement between oil, gas, gold, and the Dow Jones Islamic Market Index (DJIM) from 2006 to 2019 using wavelet analysis. They found a long-term link between oil and DJIM, weaker ties with gas, and minimal influence from gold. The study concludes that Islamic stock investors are generally not driven by commodity price movements. Mensi et al. (2022) explored asymmetric spillovers between oil and Islamic equity sectors using BEKK-GARCH models, emphasizing that Islamic sectors such as energy and industrials are more vulnerable than financials.

This enriched body of research demonstrates that the relationship between oil and Islamic stock markets is complex, time-varying, and significantly influenced by crises and methodological nuances. The inclusion of BRIC nations in this context contributes an underexplored geographic angle, particularly when considering the growth of Islamic financial instruments in emerging economies.

2.4. Research Objective and Hypotheses

While prior studies have examined the volatility transmission and comovement between crude oil and Islamic stock markets, the specific question of whether crude oil returns can predict Islamic stock returns in emerging markets remains underexplored. This study addresses this research gap by evaluating the predictive role of crude oil in Islamic equity performance, particularly during periods of systemic financial stress like the GFC.

Following the approach of (Endri et al., 2024), this study is grounded in the principles of modern portfolio theory (MPT) and its extensions into international asset pricing, specifically the international capital asset pricing model (ICAPM) and the international arbitrage pricing theory (IAPT). According to MPT, investors seek to diversify their portfolios internationally to maximize returns and minimize risk. This diversification is only effective when returns across markets are not perfectly correlated. In the context of this study, if ISR in BRIC markets exhibit low or time-varying correlation with CRT, investors may benefit from diversification. However, if oil shocks influence all markets simultaneously or strongly, it signals market integration or synchronization, reducing the benefits of diversification. The ICAPM, pioneered by Solnik (1974) and later refined by Black (1974) and Adler and Dumas (1984), posits that in a fully integrated global financial market, expected returns on assets are determined solely by global risk factors. Crude oil prices, due to their macroeconomic influence, can be considered one such global factor. In contrast, in segmented markets, local risks dominate return variation. This duality is especially relevant for emerging markets, such as BRIC nations, where partial segmentation often exists. Studies like Bekaert and Harvey (1995) and Arouri et al. (2012) further show that market integration is not static but evolves over time, particularly in response to financial liberalization, trade openness, and crisis episodes such as the GFC.

In parallel, IAPT, developed from arbitrage pricing theory (APT), extends asset pricing to international settings and focuses on the role of multiple macroeconomic factors, including oil, as sources of systematic risk. Together, these frameworks support the core objective of this study: to examine whether CRT systematically influence ISR in BRIC countries and determine how this relationship may vary over time and across economic conditions (e.g., during the GFC).

Based on these theoretical underpinnings and guided by empirical findings such as those of Arouri and Rault (2011), who examined the short- and long-run comovements between oil prices and stock indices, and Naifar and Al Dohaiman (2013), who analyzed risk transmission between oil and Islamic equities, we propose the following testable hypotheses:

Hypothesis 1 (H1).

Islamic stock returns in BRIC countries exhibit significant comovement with crude oil returns during the GFC period.

This hypothesis tests the contemporaneous relationship between the two asset classes, suggesting that systemic shocks in oil markets are transmitted to Islamic equities.

Hypothesis 2 (H2).

There exists a statistically significant relationship between crude oil returns and Islamic stock returns in BRIC countries during the GFC period.

If H1 is supported, H2 explores the strength and direction of the linkage, moving beyond comovement to assess whether oil returns contribute to Islamic equity performance during periods of financial stress.

Hypothesis 3 (H3).

Crude oil returns possess predictive power in forecasting Islamic stock returns in BRIC countries during the GFC period.

Building on H1 and H2, this hypothesis examines the forward-looking informational content of oil returns for Islamic equities to determine their relevance for market timing and portfolio allocation.

This three-stage inferential framework is designed to progressively assess the degree, nature, and directionality of the relationship between crude oil and Islamic stock returns. It avoids assumptions of causality or determinism and instead relies on empirical validation to substantiate theoretical expectations.

3. Data and Research Methodology

3.1. Data and Sample

Daily WTI crude oil prices were sourced from the Energy Information Administration (EIA), and MSCI Islamic Indices for the BRIC countries were obtained from Datastream, covering the period from 3 June 2002, to 28 March 2017. All MSCI Islamic Index data for BRIC countries and WTI crude oil prices were collected and analyzed in USD terms to maintain consistency and eliminate exchange rate noise. This approach allows us to assess the transmission of oil shocks from a global investor’s perspective. We acknowledge, however, that analyzing returns in local currencies could offer complementary insights, particularly regarding domestic market dynamics, and we highlight this as a potential area for future research. To establish a meaningful benchmark for comparing the comovement between Islamic stock returns (ISR) and crude oil returns (CRT), we selected a sufficiently long sample period that spans both pre-GFC and post-GFC phases. This design enables a comparative analysis of comovement patterns before, during, and after the GFC. While the GFC period is broadly defined as 1 March 2007, to 31 August 2012 (Hassan et al., 2017), we conducted our regression analyses specifically for the span from 2007 to 2009, following Bhuiyan et al. (2023), who identified this period as the core phase of stock market disruption during the crisis.

3.2. Methodology

The methodology of this study was developed in three key stages. First, to test H1, a wavelet-based comovement analysis was conducted to examine the dynamic relationship between ISR and crude oil returns CRT. Second, H2 was tested using regression analysis with contemporaneous CRT to assess their informational relevance to ISR during the GFC. Finally, to test H3, regression analysis with lagged CRT was performed to evaluate their predictive relationship with ISR over the same period.

3.2.1. Wavelet Coherence

To investigate H1, wavelet coherence analysis was conducted using R Studio 2023.06.0. Wavelet coherence allows for the examination of interactions between two time series. The concept derives from the cross wavelet transform. According to Torrence and Compo (1998), the cross-wavelet spectrum of two time series x(t) and y(t) is defined as follows:

$$W_{xy}(u,s)=W_x(u,s)W_y^{*}(u,s)$$

(1)

where W_x (u, s) and W_y (u, s) are continuous wavelet transforms of x(t) and y(t), respectively. Here u represents a position index, s indicates the scale, and the symbol * indicates a complex conjugate. The absolute value of the cross wavelet transform, ∣Wxy(u,s)∣, signifies the cross wavelet power, which measures the local covariance between the time series at the respective scale. Wavelet coherence reveals the degree and range of comovement between two time series in the time-frequency plane.

Torrence and Webster (1999) define the wavelet-squared coherence as follows:

$$R^2(u,s)={\displaystyle \frac{|S(s^{-1}{W}_{xy}(u,s)){|}^2}{S(s^{-1}|W_x(u,s){|}^2\left)S\right(s^{-1}|W_y(u,s\left){|}^2\right)}}$$

(2)

where SS is a time-scale smoothing operator. Without this operator, the squared coherency would always be one (Priestley, 1982). The squared wavelet coherence coefficient ranges from 0 to 1, where a value of 0 indicates no correlation and a value of 1 indicates strong correlation between the two series. Squared wavelet coherence measures the local linear correlation between two stationary time series at each scale. For statistical inference, Monte Carlo simulation is used since the theoretical distribution of $R^2(u,s)$ is unknown.

The lead-lag and in-phase/anti-phase relationships between two time series are measured by the phase difference, which indicates delays in oscillation between the series. Torrence and Webster (1999) define the wavelet coherence phase difference as follows:

$${\varphi }_{xy}\left(u,s\right)={\tan }^{-1}\left({\displaystyle \frac{\mathfrak{I}\left\{S\left(s^{-1}{W}_{xy}\left(u,s\right)\right)\right\}}{\mathfrak{R}\left\{S\left(s^{-1}{W}_{xy}\left(u,s\right)\right)\right\}}}\right)$$

(3)

In this study, we applied the maximal overlap discrete wavelet transform (MODWT) using the wavelets package in R to examine the time-scale decomposition of the relationship between CRT and ISR. MODWT is preferred over discrete wavelet transform (DWT) as it is translation invariant and better suited for analyzing financial time series with non-stationary structures. MODWT allows for non-dyadic sample sizes and does not downsample, retaining alignment with original time series. We employed the Daubechies least-asymmetric wavelet (LA8), which provides smoothness and time-frequency localization suitable for financial data. The series were decomposed into 11 scales, corresponding to a total data length of 2¹¹ = 2048 capturing short- to long-term horizons.

3.2.2. Regression Analysis

We have conducted the regression analysis where the ISR is regressed by CRT and lagged CRT (L.CRT) as in Equations (4) and (5).

$${\mathrm{I}\mathrm{S}\mathrm{R}}_{t,i}={\alpha }_0+{\alpha }_1{\mathrm{C}\mathrm{R}\mathrm{T}}_t+{\epsilon }_{t,i,j}$$

(4)

$${\mathrm{I}\mathrm{S}\mathrm{R}}_{t,i}={\alpha }_0+{\alpha }_1\mathrm{L}.{\mathrm{C}\mathrm{R}\mathrm{T}}_t+{\epsilon }_{t,i,j}$$

(5)

Here,

${\alpha }_0=interceptcoefficient$

${\alpha }_1=slopecoefficient$

${\forall }_i=$ Brazil, Russia, India, China

Equation (4) examined H2, i.e., whether CRT contains significant information content in relation to ISR. If statistically α₀ = 0 and α₁ > 0 in Equation (4), we conclude that crude oil return impacts the ISR positively, i.e., if crude oil price increases Islamic stock return increases and vice versa.

Equation (5) tested H3 by evaluating the predictive power of CRT for ISR during the GFC period. Specifically, it examined the relationship between ISR and 1- to 10-day lagged values of CRT (i.e., ISR_t−1). If statistically α₀ = 0 and $\left|{\mathsf{\alpha }}_1\right|>0$ in Equation (5), we can conclude that CRT can predict ISR during the GFC.

In our regression analysis, we employed an ARMA-GARCH framework that accounts for both return dependencies and time-varying volatility. The ARMA component captures autocorrelation in returns through a combination of autoregressive (AR) terms, which model the persistence of returns, and moving average (MA) terms, which account for the impact of past shocks. This allows us to control for short-term momentum or reversal effects in the data. The GARCH component then models the conditional variance of the residuals, addressing volatility clustering by incorporating both recent shocks (ARCH effects) and persistent volatility (GARCH effects). Using standardized residuals from this model in subsequent analyses, we ensure that our results are not biased by heteroskedasticity or autocorrelation, providing more reliable estimates of the oil–equity relationship.

4. Empirical Analysis

4.1. Descriptive Statistics

Table 1. Descriptive statistics of crude oil Islamic index returns.

	Brazil	China	India	Russia	Crude Oil
Mean	0.020801	0.00987	0.01369	−0.03357	0.047322
Std. Dev.	0.785461	0.818228	0.692237	1.09156	1.01834
Skewness	−0.30243	−0.15544	−0.32264	−0.40367	0.329142
Kurtosis	5.602389	5.78025	7.795374	13.61283	7.739847
Jarque–Bera	233.1841 ***	255.6634 ***	764.7921 ***	3700.606 ***	748.0499 ***
ADF Unit Root Test (t-statistics)	−8.1644 ***	−8.2490 ***	−8.5706 ***	−6.6570 ***	−11.5388 ***

Note: *** indicates 1% level of significance.

provides the descriptive statistics and unit root test results for the daily returns of crude oil and Islamic stock indices for BRIC countries. This preliminary analysis offers foundational insights into the characteristics of the return series, which is crucial for testing the study’s three core hypotheses, especially the comovement (H1), informational content (H2), and predictive capacity (H3) of CRT with respect to ISR. The return series for Brazil, China, India, and crude oil all exhibit positive mean returns, while Russia shows a slightly negative mean return, reflecting regional heterogeneity in market behavior during the study period. The relatively high standard deviations, particularly for Russia and crude oil, suggest greater return volatility, an important consideration when examining comovement and spillover effects under H1. All return distributions deviate from normality, as indicated by the statistically significant Jarque–Bera test statistics (p < 0.01). This non-normality reinforces the need for robust econometric techniques (like wavelet analysis) capable of handling non-Gaussian data structures, particularly relevant when assessing time-frequency comovement and information asymmetries between CRT and ISR. Importantly, the augmented Dickey–Fuller (ADF) test confirms that all series are stationary at levels. This ensures the validity of the wavelet-based comovement analysis and regression models used to test H2 and H3, as it mitigates the risk of spurious relationships arising from non-stationary data. However, given the highly volatile nature of financial markets during the GFC, we recognize the potential for structural breaks in the data series. Future iterations of this analysis should capture nonlinear regime shifts over time through the application of Markov regime-switching models providing a more flexible framework for modeling the dynamic behavior of crude oil and Islamic stock returns, especially under varying volatility regimes.

4.2. Wavelet Coherence

Wavelet coherence measures the extent to which two time series co-vary in both the time and frequency domains. When the coherence value approaches one, the respective time series exhibit very similar behavior. Conversely, when the coherence value is close to zero, the time series are not considered coherent. In our wavelet coherence plots, depicted in Figure 1, Figure 2, Figure 3 and Figure 4, the color scale represents the coherence value, with blue indicating the lowest level of coherence and red indicating the highest level. The semi-transparent area in the plots, known as the cone of influence, highlights regions affected by edge effects. The white contours denote the 10% significance level.

In our wavelet coherence plots, the y-axis (scale axis) can be classified into short-term, mid-term, and long-term fluctuations. Short- and mid-term fluctuations are represented by scale 1 (2 to 4 days), scale 2 (4 to 8 days), and scale 3 (8 to 16 days). The remaining scales correspond to long-term fluctuations. Along the x-axis (time plane), the period from day 1239 to day 2675 corresponds to the crisis period (1 March 2007, to 31 August 2012). The wavelet coherence plots clearly show an increase in the comovement between all stock and oil markets over increasing scales.

4.3. Testing Informational Content of CRT

Since the wavelet coherence plots exhibit strong comovement between the ISR and CRT series, this study further investigated whether the CRT series contains information regarding ISR series. First, regression analysis was conducted for H2 using Equation (4). Next, the slope coefficient of regression Equation (4) during GFC was assessed for the following information:

• A statistically significant slope coefficient suggests a relationship between ISR and CTR during the GFC period.
• The positive sign of the slope coefficient indicates the that increases in crude oil returns are associated with increases in Islamic stock returns during the GFC period. Conversely, decreases in crude oil returns are associated with decreases in Islamic stock returns during the GFC period.

The results have been documented in

Table 2. Testing information content of CRT regarding ISR during GFC (Hypothesis 2).

BRIC Countries	Intercept α0		Slope α1		R2	Accommodating Serial Correlation		Accommodating Heteroskedasticity		Is There a Linear Relationship Between Crude Oil Returns and Islamic Returns
	Coefficient	p-Value	Coefficient	p-Value		ARMA	DW	GARCH	F-Stat
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
Brazil	0.0249	0.36	0.3242 ***	0.00	0.56	(1, 1)	1.97	(1, 1)	0.70	Yes
Russia	−0.0094	0.76	0.2672 ***	0.00	0.59	(1, 1)	1.84	(1, 1)	0.89	Yes
India	0.0437	0.13	0.1337 ***	0.00	0.54	(1, 1)	1.86	(1, 1)	0.00	Yes
China	0.0393	0.24	0.1573 ***	0.00	0.53	(1, 1)	2.01	(1, 0)	2.30	Yes

Note: *** indicates 1% level of significance.

. The final column (column 11) of Table 2 reports the conclusions on whether there is a linear relationship between ISR and CRT based on the positive slope coefficient, indicated as “Yes” or “No.” In this regression analysis, considerations for serial correlation and heteroskedasticity were made to ensure the credibility and objectivity of the results. Serial correlation was addressed using the ARMA(p, q) model, as detailed in column (7) of Table 2, where p represents the order of the autoregressive component and q represents the order of the moving average component. The ARMA(p, q) model was iterated until the Durbin Watson (DW) statistic approached two, as shown in column (8), to adequately address serial correlation. Additionally, the F-statistics (F-stat) reported in column (10) addressed heteroskedasticity by employing the GARCH(p, q) model, as indicated in column (9), with p and q representing the order of the GARCH and ARCH terms, respectively. The GARCH(1, 1) specification addresses conditional heteroscedasticity, characterized by time-varying volatility and periods of volatility clustering by modeling the conditional variance of returns as a function of past squared errors and past variances. The findings from the MODWT wavelet analysis revealed that the comovement between CRT and ISR is concentrated at low-frequency bands, corresponding to longer-term horizons. This indicates that the relationship between these markets is more likely driven by macroeconomic and structural factors, such as oil revenue cycles, inflation expectations, or policy transmission, rather than short-term trading dynamics. Conversely, the short-term (high frequency) wavelet components were dominated by noise, suggesting limited or unstable comovement in daily fluctuations. This insight supports the use of ARMA-GARCH models: the ARMA component helps account for short-term autocorrelation and momentum effects in ISR, while the GARCH component effectively models volatility clustering, aligned with the slower, more persistent interdependencies identified in the wavelet analysis. Given that our model includes ARMA components and the Durbin–Watson test is only appropriate for AR (1) models with strict exogeneity, we further employed the Ljung–Box Q-test on the residuals of each ARMA-GARCH model, using up to 10 lags. In most cases, the null hypothesis of no autocorrelation could not be rejected (p-values > 0.05), suggesting that the residuals behave as white noise and that the model is properly specified.

4.4. Predictive Power of Lagged CRT on ISR During the GFC

Table 3. Prediction of ISR by lagged CRT during the GFC (Hypothesis 3).

BRIC Countries	Forecast Horizon		Intercept α0		Slope α1		R2	Accommodating Serial Correlation		Accommodating Heteroskedasticity		Can Crude Oil Predict Islamic Stock Return?
			Coefficient	p-Value	Coefficient	p-Value		ARMA	DW	GARCH	F-Stat
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
Brazil	1 Week	1-day	0.0127	0.70	−0.0024	0.90	0.47	(1, 1)	1.86	(1, 0)	1.07	Case 1: No
		2-day	0.0131	0.69	0.0179	0.39	0.48	(1, 1)	1.93	(1, 0)	1.19	Case 2: No
		3-day	0.0150	0.65	0.0304	0.18	0.47	(1, 1)	1.85	(1, 0)	1.19	Case 3: No
		4-day	0.0151	0.64	0.0640 ***	0.00	0.48	(1, 1)	1.83	(1, 0)	1.55	Case 4: Yes
		5-day	0.0030	0.92	−0.0073	0.70	0.48	(1, 1)	1.86	(1, 0)	1.13	Case 5: No
	2 Weeks	6-day	0.0202	0.54	0.0139	0.54	0.48	(1, 1)	1.86	(1, 0)	1.19	Case 6: No
		7-day	0.0052	0.87	−0.0378	0.06	0.47	(1, 1)	1.84	(1, 0)	1.10	Case 7: No
		8-day	0.0553	0.07	−0.0392	0.16	0.48	(1, 1)	1.93	(1, 1)	2.07	Case 8: No
		9-day	0.0165	0.63	0.0689	0.08	0.47	(1, 1)	1.88	(1, 0)	0.88	Case 9: No
		10-day	0.0532	0.08	−0.0381	0.11	0.48	(1, 1)	1.93	(1, 1)	2.27	Case 10: No
Russia	1 Week	1-day	0.0135	0.68	0.0528	0.11	0.54	(1, 1)	1.86	(1, 1)	1.57	Case 11: No
		2-day	0.0229	0.51	−0.0163	0.61	0.54	(1, 1)	1.86	(1, 1)	1.56	Case 12: No
		3-day	0.0180	0.59	0.0181	0.54	0.54	(1, 1)	1.86	(1, 1)	1.68	Case 13: No
		4-day	0.0097	0.77	0.0756 ***	0.01	0.55	(1, 1)	1.87	(1, 1)	1.98	Case 14: Yes
		5-day	0.0203	0.54	−0.0414	0.16	0.55	(1, 1)	1.86	(1, 1)	1.45	Case 15: No
	2 Weeks	6-day	0.0257	0.44	−0.0017	0.95	0.55	(1, 1)	1.85	(1, 1)	1.32	Case 16: No
		7-day	0.0287	0.39	−0.0321	0.28	0.55	(1, 1)	1.86	(1, 1)	1.39	Case 17: No
		8-day	0.0216	0.53	0.0180	0.51	0.54	(1, 1)	1.85	(1, 1)	1.48	Case 18: No
		9-day	0.0248	0.46	0.0019	0.94	0.54	(1, 1)	1.85	(1, 1)	1.43	Case 19: No
		10-day	0.0207	0.54	−0.0003	0.99	0.54	(1, 1)	1.85	(1, 1)	1.46	Case 20: No
India	1 Week	1-day	0.0500	0.09	−0.0604	0.90	0.51	(1, 1)	1.99	(1, 1)	0.04	Case 21: No
		2-day	0.0463	0.12	0.0002	0.98	0.51	(1, 1)	2.01	(1, 1)	0.04	Case 22: No
		3-day	0.0499	0.08	−0.0236	0.19	0.51	(1, 1)	2.02	(1, 1)	0.05	Case 23: No
		4-day	0.0469	0.12	0.0074	0.70	0.51	(1, 1)	2.01	(1, 1)	0.04	Case 24: No
		5-day	0.0532	0.08	−0.0569	0.60	0.51	(1, 1)	2.02	(1, 1)	0.00	Case 25: No
	2 Weeks	6-day	0.0481	0.11	0.0244	0.30	0.51	(1, 1)	2.02	(1, 1)	0.06	Case 26: No
		7-day	0.0579	0.05	−0.0778	0.47	0.51	(1, 1)	2.01	(1, 1)	0.13	Case 27: No
		8-day	0.0498	0.09	0.0421 ***	0.02	0.51	(1, 1)	2.03	(1, 1)	0.05	Case 28: Yes
		9-day	0.0478	0.10	0.0005	0.97	0.51	(1, 1)	2.01	(1, 1)	0.04	Case 29: No
		10-day	0.0415	0.16	−0.0178	0.37	0.51	(1, 1)	2.02	(1, 1)	0.02	Case 30: No
China	1 Week	1-day	0.0469	0.17	0.0786 ***	0.00	0.50	(1, 1)	2.00	(1, 1)	2.72	Case 31: Yes
		2-day	0.0502	0.14	−0.0094	0.21	0.50	(1, 1)	2.00	(1, 1)	3.25	Case 32: No
		3-day	0.0530	0.12	−0.0044	0.86	0.50	(1, 1)	2.02	(1, 1)	3.44	Case 33: No
		4-day	0.0910	0.12	0.0259	0.35	0.51	(1, 1)	2.04	(1, 1)	2.94	Case 34: No
		5-day	0.0528	0.13	0.0218	0.38	0.50	(1, 1)	1.99	(1, 1)	3.24	Case 35: No
	2 Weeks	6-day	0.0542	0.12	0.0142	0.58	0.50	(1, 1)	2.01	(1, 1)	3.47	Case 36: No
		7-day	0.0577	0.10	0.0080	0.74	0.50	(1, 1)	2.01	(1, 1)	3.39	Case 37: No
		8-day	0.0610	0.08	−0.0293	0.26	0.50	(1, 1)	2.01	(1, 1)	2.98	Case 38: No
		9-day	0.0601	0.08	−0.0224	0.40	0.50	(1, 1)	2.00	(1, 1)	3.33	Case 39: No
		10-day	0.0565	0.10	−0.0233	0.32	0.50	(1, 1)	2.00	(1, 1)	3.53	Case 40: No

Notes: *** indicates 1% level of significance.

presents the results of testing H3 using regression Equation (5) to assess whether lagged crude oil returns (CRT) can predict Islamic stock returns (ISR) in BRIC countries during the GFC. Ten lags of CRT were tested (from 1-day to 10-day lags) across 40 cases. We employed a lag length of 10 based on both economic reasoning and model selection criteria. Specifically, the choice reflects a two-week trading window (assuming 5 trading days per week), which is commonly used in short- to medium-term forecasting models in financial econometrics Moreover, the Ljung–Box Q-test conducted during the testing of H2 revealed that extending the lag length beyond 10 resulted in significant autocorrelation in the residuals, indicating potential model misspecification. Hence, a 10-lag structure was both theoretically justified and empirically optimal. A statistically significant slope coefficient suggests a relationship between lagged CRT and 1 to 10 days ahead of ISR.

• Statistically significant nonzero slope coefficient indicates that lagged CRT can predict ISR for the forecast horizon period. Positive (negative) slope coefficient indicates that increases (decreases) in crude oil returns are associated with increases (decreases) in Islamic stock returns during the GFC period.

The final column (Column 13) reports the conclusion for each case indicating “Yes” if lagged CRT significantly predicts ISR, and “No” otherwise. In the regression analysis, the possibility of serial correlation and heteroskedasticity was considered and accommodated by employing the ARMA(p, q) model, as described in Section 4.2 and presented in column (9) of Table 3. The ARMA(p, q) component models the autocorrelation structure in the return series, capturing the persistence and mean-reversion patterns often present in financial time series. The GARCH(1, 1) specification addresses volatility clustering where periods of high volatility tend to follow one another by modeling the conditional variance of returns. This dual approach allows us to generate more reliable residuals and avoid inflated standard errors in the regression coefficients. The DW was approximately two, as reported in column (10) of the table to ensure that serial correlation was accommodated. Since the Durbin–Watson test is unsuitable for ARMA models, we applied the Ljung–Box Q-test (up to 10 lags). The results showed no significant autocorrelation (p > 0.05), indicating well-specified models with white noise residuals. In addition, F-stat was given in column (12) to accommodate the underlying issue of heteroskedasticity by employing the GARCH(p, q) model, as mentioned in column (11), where p and q represent the order of the GARCH and ARCH terms, respectively.

5. Robustness of Analysis

To examine the predictive relationship between crude oil prices and Islamic stock market indices, we employed two complementary econometric techniques: Granger causality tests and impulse response analysis. First, we conducted pairwise Granger causality tests reported in

Table 4. Granger causality test: CRT vs. ISR.

BRIC Countries	Does CRT Cause ISR?	Does ISR Cause CRT?
Brazil	Yes (2.45 ***)	No (1.25)
Russia	Yes (3.33 ***)	No (1.13)
India	Yes (2.72 ***)	Yes (2.31 ***)
China	Yes (43.03 ***)	No (1.15)

Note: *** indicates 1% level of significance.

, within a vector autoregression (VAR) framework to determine whether lagged values of crude oil returns exhibit statistically significant causal relationship for stock market returns (and vice versa). Optimal lag length criteria of 10 was selected according to the Akaike Information Criterion (AIC). For each country (Brazil, Russia, India, and China), we tested the null hypothesis that oil prices do not Granger-cause stock returns, reporting F-statistics and corresponding p-values in the parenthesis to assess significance as follows. The results reveal that CRT Granger-cause ISR in Brazil, Russia, India, and China, with all tests statistically significant at the 1% level. In case of India, we find evidence bidirectional causality. The results provide strong evidence that lagged oil price movements contain predictive information regarding the future behavior of Islamic stock market returns in these emerging economies.

Figure 5, Figure 6, Figure 7 and Figure 8 illustrate the impulse response functions (IRFs) of BRIC equity markets to a Cholesky one standard deviation structural shock in crude oil prices, based on a 10-lag VAR system. In each case, crude oil is ordered first in the Cholesky decomposition, implying it is contemporaneously exogenous to the equity markets. The solid lines represent the response magnitudes, while the dashed lines indicate the ±2 standard error confidence bands.

Figure 5 (Brazil) shows a strong and statistically significant positive response to crude oil shocks in the first period, with the impact nearing 0.4. This response quickly decays and becomes insignificant after the second period, although some mild oscillations remain. The initial spike highlights Brazil’s economic sensitivity to oil prices, reflecting its role as a major oil exporter.

Figure 6 (Russia) displays a similar pattern: a large, immediate, and statistically significant positive response to oil shocks, peaking near 0.4. The effect diminishes over time and becomes statistically indistinguishable from zero after the third period. This reinforces Russia’s dependence on oil revenue and the high responsiveness of its stock market to oil price changes.

In contrast, Figure 7 (India) presents a more moderate and short-lived response. The initial impact is positive (~0.17) but quickly becomes statistically insignificant as the confidence bands widen. The fluctuating response and lack of sustained significance are consistent with India’s position as a net oil importer with weaker oil-market linkages.

Figure 8 (China) shows a positive but short-lived response, with an initial value around 0.22. The response sharply declines and converges to zero by the third period, remaining statistically insignificant thereafter. This suggests that while China is affected by oil shocks, structural buffers such as state control, subsidies, and diversified energy strategies reduce its stock market’s exposure.

Overall, the IRFs demonstrate an asymmetric response across BRIC nations: Brazil and Russia, as oil exporters, exhibit stronger and more immediate reactions to oil shocks, while India and China, as importers, show weaker and more transient effects. These results align with the Granger causality findings and emphasize the short-run, oil-driven volatility in emerging equity markets.

6. Discussion

6.1. Theoretical Implications

The results of the wavelet coherence and lagged regression analyses provide meaningful insights into the dynamic relationship between crude oil returns and Islamic stock returns across BRIC countries during the GFC. The significant comovement and predictive patterns observed at medium- and low-frequency bands align with the financial contagion hypothesis, which suggests that systemic shocks in one asset class (e.g., crude oil) can spill over to others (e.g., Islamic equities) during periods of crisis. This pattern supports the notion of increased cross-asset correlation under stress conditions, consistent with ICAPM, where global risk factors such as oil drive asset returns across countries.

The time-varying correlation structure supports the decoupling hypothesis, which holds that Islamic financial markets may behave differently from conventional markets due to structural and governance differences. However, our results suggest only partial decoupling, particularly in the case of India and Russia, where Islamic stock markets show moderate but delayed responses to oil shocks. This implies a degree of interdependence, but also a potential for diversification, especially at different investment horizons. The partial decoupling observed resonates with the market segmentation theory embedded in the ICAPM and IAPT frameworks. While oil-exporting nations like Russia show stronger linkages due to macroeconomic dependency on oil, India’s weaker but delayed responsiveness suggests that local market structures and partial segmentation still play a role. This is consistent with the concept of mild segmentation (Errunza & Losq, 1985), where both global and domestic factors influence returns. The findings also support aspects of the resource-dependence theory, where the economic exposure of countries to crude oil (as importers or exporters) influences the extent of oil–equity market linkages.

Although we observe some statistically significant coefficients in the predictive regressions, especially at medium-term horizons, the economic significance of these results appears limited. The magnitude of the coefficients, coupled with low R-squared values, suggests that while CRT may contain informational value for ISR under specific conditions (e.g., during the GFC in oil-sensitive economies), its overall predictive power is weak. This implies that other unobserved factors, such GFC, sectoral composition of Islamic indices, or domestic monetary policies likely play a more dominant role in explaining ISR fluctuations.

6.2. Comparison with Existing Literature

Our findings are broadly consistent with, but extend, earlier work in this field. For instance, Shahzad et al. (2018) and Mensi et al. (2022) documented significant volatility spillovers between oil and Islamic equity markets. Our study confirms this comovement using wavelet coherence, but adds value by providing a multi-scale and time-specific lens, highlighting how these dynamics intensified during the peak of the GFC.

Unlike Trabelsi (2019) and Badeeb and Lean (2018), who focused on linear relationships, our regression results account for time-varying predictability, demonstrating that crude oil returns can forecast Islamic stock returns in BRIC countries during crisis periods, particularly in low-frequency bands. This echoes the findings of Hassan et al. (2020), who observed directional volatility spillovers from oil to Islamic equities in BRICS, but our model extends their framework by incorporating both lead–lag relationships and frequency decomposition.

In comparing our findings with the existing literature, we observe both alignment and divergence. For instance, the significant predictive relationship between crude oil returns (CRT) and Islamic stock returns (ISR) in India and Russia aligns with the volatility spillover effects reported by Shahzad et al. (2018) and Hassan et al. (2020). However, the absence of significant predictive power in Brazil and China under certain time scales deviates from the findings of Trabelsi (2019) and Naifar and Al Dohaiman (2013), who reported more generalized effects across regions. These variations likely reflect differences in oil dependency, Islamic finance penetration, and macroeconomic exposure across BRIC nations.

Overall, the combination of methodological novelty and the specific BRIC context allows us to validate and deepen the empirical understanding of the crude oil–Islamic equity nexus during crisis environments.

6.3. Islamic Finance Perspective

From an Islamic finance viewpoint, the results carry important implications. Shariah-compliant equities, by design, avoid excessive leverage and speculative activity and are typically overexposed to tangible sectors such as energy, industrials, and basic materials, all of which are influenced by commodity price movements. This structural composition inherently ties Islamic stocks more closely to crude oil dynamics, particularly during periods of economic instability.

Our findings suggest that while Islamic stock markets are not fully insulated from oil price shocks, they demonstrate distinct responsiveness patterns, particularly in the medium- and low-frequency domains. This confirms earlier assertions by Naifar and Al Dohaiman (2013) that Islamic equities offer risk-sharing and reduced speculative volatility but remain susceptible to fundamental macroeconomic shifts such as oil price fluctuations.

The results are also significant for faith-based and ethical investors, as they highlight that Islamic stocks can serve both ethical and strategic diversification purposes in portfolios exposed to commodity risks. These findings further support the growing view that Islamic finance instruments can play a stabilizing role in global financial markets when crises disrupt conventional asset classes.

7. Conclusions

7.1. Comovement Between ISR and CRT

The wavelet plots support H1 as they provide evidence of strong comovement between all the stock and oil markets during the crisis period, as indicated by the large red zone in the middle of all coherence plots. No significant comovement is observed between the oil and stock markets during the pre-crisis and post-crisis periods. Notably, red zones, indicating strong comovement, become visible from scale 3 in the Brazil–Oil, China–Oil, and India–Oil coherence plots. In the Russia–Oil plot, the red zone appears at scale 2. In all plots, distinct red zones are visible at higher scales, indicating that comovement is weak in the short and medium term but stronger in the long term.

Focusing on the red zone during the crisis period, we observe that for Brazil, Russia, and India, at a scale of approximately 512 days (around 2 years), the arrows predominantly point to the right, indicating an in-phase comovement between Islamic stock returns (ISR) and crude oil returns (CRT) with no evident lead-lag relationship. However, at other time scales, the phase arrows display both in-phase and anti-phase dynamics, reflecting varying correlation patterns and shifting lead–lag relationships between the two markets across different investment horizons. The observed significant comovement challenges the proponents who claim that Islamic stocks serve as a safe haven. The strong comovement during the crisis period underscores the interconnectedness of oil and stock markets in times of economic stress, prompting further investigation into the predictive capacity of crude oil returns on Islamic stock returns.

7.2. Relationship Between ISR and CRT

The regression analysis results support H2, indicating a significant positive linear relationship between crude oil returns and Islamic stock returns for Brazil, Russia, India, and China during the study period. The positive slope coefficients and high significance levels suggest that increases in crude oil returns are associated with increases in Islamic stock returns for these countries.

7.3. Predictive Capacity of Lagged CRT

The research findings support H3, as lagged CRT exhibits predictive power in relation to ISR for specific forecast horizons in Brazil (4 days), Russia (4 days), India (8 days), and China (1 day) during the GFC period. However, the ability of crude oil returns to predict Islamic stock returns is limited to a few days and is not consistent across all forecast horizons. For Brazil, Russia, and China, crude oil returns can forecast Islamic stock returns within a one-week horizon. In contrast, for India, this predictive relationship extends up to a two-week horizon. However, it is observed that the forecasting power diminishes with increasing forecast periods and does not extend beyond a two-week horizon.

7.4. Research Significance

7.4.1. Energy Market Signals and Islamic Stock Behavior During Financial Distress

The empirical evidence supports the view that CRT plays an influential role in shaping Islamic stock returns (ISR), particularly during times of systemic distress, such as the GFC. The strong long-term comovement identified using wavelet coherence reinforces the notion that these markets are interdependent at the macroeconomic level. The direction and intensity of this comovement, particularly at higher time scales, highlight that oil price movements can serve as a signal of market-wide risk sentiment, especially in energy-sensitive economies like BRIC.

7.4.2. Immunity of Islamic Stocks During the GFC

The findings challenge the notion that Islamic stocks were immune to the GFC. The significant comovement between crude oil and Islamic stocks during the crisis period suggests that Islamic stocks were not entirely insulated from global financial shocks. While Islamic stocks demonstrated some resilience, particularly in their predictive relationship with crude oil returns, the relationship was not uniformly strong across all forecast horizons and varied by country and specific forecast period. This research underscores the complex interplay between crude oil returns and Islamic stock returns, highlighting the need for considering different time scales and forecast horizons when analyzing their predictive capacity. The study contributes to a better understanding of market dynamics during economic crises. It provides valuable insights for investors and policymakers in managing and forecasting market behavior in similar future scenarios.

7.4.3. Investors and Policymakers

The findings of this study carry several important policy and practical implications, particularly for policymakers, portfolio managers, and Shariah-compliant investment institutions operating in emerging markets.

Firstly, the evidence that crude oil returns predict Islamic stock returns in specific BRIC markets during crisis periods suggests a tangible macroeconomic transmission channel. In oil-dependent economies, fluctuations in oil prices affect trade balances, exchange rates, inflation, and fiscal revenues. These macroeconomic shifts in turn influence corporate profitability and investor sentiment, i.e., factors that are directly reflected in stock performance, including Islamic indices. For instance, during periods of rising oil prices, improved fiscal conditions in oil-exporting countries may stimulate investor confidence, leading to upward movements in Islamic equities, which are often heavily weighted in tangible asset sectors like energy, materials, and industrials.

Second, the predictive relationship varies by country, reflecting differences in oil reliance, domestic Islamic finance development, and exposure to global risk sentiment. This heterogeneity indicates that policy coordination between energy market regulators and financial supervisory bodies can enhance financial stability, particularly in countries with growing Islamic finance sectors like India and Russia. Authorities could integrate oil price forecasts into stress testing models or develop financial instruments (e.g., Shariah-compliant oil-linked bonds) to help Islamic investors hedge against commodity shocks.

The implications extend to investment strategy, risk hedging, and policymaking. Short-term predictive relationships can help traders develop tactical asset allocation strategies that capitalize on the oil–stock information link during crises. Policymakers can also use oil market movements as a barometer for financial stress in emerging Islamic capital markets. Meanwhile, the diminishing predictive power beyond two weeks suggests that oil price signals are more suited for short-term forecasting rather than long-horizon portfolio planning.

7.4.4. Future Research

While this study provides novel insights, several avenues for future research are worth exploring. First, extending the analysis to include other oil benchmarks, such as Brent crude, could help validate whether the findings are consistent across global oil markets. Second, incorporating conventional BRIC stock indices could reveal whether the observed relationships are specific to Islamic stocks or part of broader market dynamics. Third, exploring non-linear models or machine learning approaches (e.g., LSTM or random forests) could enhance predictive accuracy, remove reverse causality bias, and capture more complex relationships. Lastly, while this study centers on the GFC period using data up to 2017, future research should extend the analysis to include recent crises such as COVID-19 and post-pandemic oil shocks. This will validate the robustness of our findings under evolving market dynamics.