Exploring weak-form efficiency in global Islamic stock markets: evidence from machine learning and wavelet analysis

Capital markets are institutional arrangements that facilitate matching between borrowers and lenders, thereby helping to convert savings into investment (Khan et al., 2011; Trang, 2022). When functioning efficiently, they play important roles in financial markets: they support growth, enhance transparency, increase investor confidence, and help reduce transaction costs (Emenike and Joseph, 2018; Ülev and Selçuk, 2022). Due to this central role, market efficiency remains one of the most debated topics in finance (Awan and Subayyal, 2016; Dias et al., 2020).

This idea is examined in the literature in the context of the Efficient Market Hypothesis (EMH). Based on Bachelier's random walk theory and later developed by Samuelson (1965) and Fama (1965, 1970), this theory defines an efficient market as a structure where all available information is fully reflected in prices (Yavrumyan, 2015; Dubey, 2023). Weak-form efficiency, which is particularly critical for stock markets, suggests that past price movements are already integrated into current values. Therefore, it is not possible to systematically predict future returns by looking only at past data (Ikeora et al., 2016; Trang, 2022).

This theory becomes even more interesting when Islamic stock markets are considered. Islamic indices are constructed through Sharia screening rules that exclude companies that do not meet activity-based and financial ratio criteria. As a result, these indices differ from traditional indices in terms of leverage, diversification, and sector composition (Sakınç and Sakınç, 2024; Ülev and Selçuk, 2022). Some studies also show that Islamic indices may behave differently during periods of stress, exhibiting lower volatility or different correlation patterns compared to traditional markets (Chazi et al., 2023; Tabash et al., 2023). The Islamic finance system, notable for these differences, is growing rapidly. Total Islamic financial assets rose from $2.70 trillion in 2020 to $3.88 trillion in 2024, with Islamic fund assets reaching $193.6 billion. Equities constitute the largest share of these assets (Islamic Financial Services Board (IFSB), 2025). Post-COVID evidence also shows strong regional interconnectedness within Islamic equity markets, although the way shocks propagate differs from traditional systems (Rehman et al., 2024).

Nevertheless, research on weak-form efficiency in Islamic stock markets is still limited in scope compared to extensive studies on traditional markets (Al-Khazali et al., 2016; Mensi et al., 2017; Sakınç and Sakınç, 2024). Most of these studies are primarily based on unit root and similar time series tests. While useful, these methods may be less informative in situations commonly seen in long samples when financial series exhibit structural breaks, non-linearities, regime shifts, and crisis-specific volatility and correlation changes (Çevik, 2018; Chazi et al., 2023; Rehman et al., 2024; Tabash et al., 2023).

In this context, this study tests the weak-form EMH for nine Dow Jones Islamic Market indices: DJICA, DJICHKU, DJIJP, DJIMIND, DJIMKW, DJIMTR, IMUS, DJIUK, and DJMY25D. The analysis combines machine learning-based forecasting with wavelet transform coherence (WTC) in a multi-country and multi-index setting. This allows us to assess weak-form efficiency from multiple angles and account for structural changes, nonlinear dynamics, and crisis-period behavior.

The remainder of the paper is organized as follows. Section 2 reviews the literature. Section 3 presents the data. Section 4 explains the methodology. Section 5 reports the findings. Section 6 presents the conclusions.

A large body of research has examined the random walk hypothesis, or weak-form EMH, in conventional stock markets across developed and emerging economies. By contrast, studies on Islamic stock markets remain relatively limited. The evidence is also far from uniform. Some studies support weak-form efficiency, others reject it, and some report mixed results across countries, indices, sectors, or sample periods. This pattern appears in both conventional and Islamic markets. For clarity, the literature is reviewed under three headings: studies supporting weak-form EMH in conventional markets, studies rejecting it or reporting mixed evidence, and studies on Islamic markets together with the methodological issues that motivate the present study.

A number of studies in the literature have provided significant evidence consistent with weak-form efficiency in traditional markets. For example, Fattahi (2010) showed that the German DAX index followed a random walk, while Kok and Munir (2015) reached a similar conclusion for financial stocks in Malaysia. Weak-form efficiency has also been reported for specific indices and markets such as Indonesia, Borsa Istanbul, Casablanca, and some developed country ETFs and stock markets (Malini, 2019; Gazel, 2020; Karademir and Evci, 2020; Benthabet and Benthabet, 2023; Özmerdivanlı, 2024). Showalter and Gropp (2019) also present strong evidence of weak-form efficiency in the US market when transaction costs and risk are taken into account.

Some recent studies also approach market efficiency from new methodological angles. Bagwan et al. (2025) discuss EMH through fractional difference equations, while Adegboyo and Sarwar (2025) examine volatility dynamics in the Nigerian market using asymmetric GARCH specifications. Although these studies differ in focus, they show that support for weak-form efficiency remains present in parts of the literature, especially when market structure, risk, and model choice are taken into account.

A second line of research rejects weak-form efficiency or finds only partial support. Early evidence from markets such as Karachi and Ghana suggests that stock prices do not follow a random walk (Ahmad and Erdem, 1996; Frimpong and Oteng-Abayie, 2007). Similar conclusions are reported for India, Nigeria, Tehran, the Gulf region, Jordan, Bangladesh, Tanzania, Türkiye, Vietnam, Nepal, China, and several emerging markets more broadly (Khan et al., 2011; Gimba, 2012; Saeedi et al., 2014; Raquib and Alom, 2015; Ikeora et al., 2016; Awan and Subayyal, 2016; Ogbulu, 2016; Kumar and Jawa, 2017; Pervez et al., 2018; Katabi and Raphael, 2018; Hailu and Vural, 2020; Diallo et al., 2021; Risal and Koju, 2021; Trang, 2022; Luo et al., 2022; Nik and Marko, 2023; Joshi, 2024; El-Diftar, 2024). In these studies, returns often appear to depend on past information, which is inconsistent with weak-form efficiency.

There is also a sizeable group of studies reporting mixed results. Hepsağ and Akçalı (2015) show that efficiency differs across G7 and E7 countries. Khan and Khan (2016) find inefficiency in daily and weekly Pakistani returns but not in monthly returns. Çevik (2018) reports that the BIST-100 is efficient in high-volatility periods but not in low-volatility periods. Other studies show that efficiency changes across crises, recovery periods, development levels, data frequencies, and empirical methods (Marsani et al., 2022; Lee and Choi, 2023; Tutar and Dalgar, 2023; Al-wazier, 2024). Taken together, this literature suggests that weak-form efficiency is highly sensitive to market conditions, sample periods, and methodology.

Research on Islamic stock markets is smaller in volume and still inconclusive. This is important because Islamic financial markets operate under Shariah principles that prohibit interest, excessive uncertainty, and speculative trading. These features may affect how information is incorporated into prices and may also shape volatility, co-movement, and investor behaviour, especially during periods of stress. Related evidence from investor-level and crisis-period studies also suggests that information channels and market responses can change across regimes and horizons (Naveed et al., 2020; Naveed and Ali, 2024).

Empirical findings on Islamic equity-market efficiency remain mixed. Al-Khazali et al. (2016) argue that conventional indices are generally more efficient than Islamic ones, although Islamic indices may become more efficient during crises. Mensi et al. (2017) show that efficiency in Islamic sectoral indices changes over time. Ali et al. (2018) report relatively stronger efficiency in Islamic markets from developed and BRICS economies, whereas Bouoiyour et al. (2018) find lower efficiency in emerging Islamic markets. Hassan and Ahmad (2020), Khan et al. (2021), and Sakınç and Sakınç (2024) report evidence against weak-form efficiency in several Shariah-compliant indices, while Buğan et al. (2021) and Ülev and Selçuk (2022) show that results vary across regimes, market groups, and index sets.

Recent studies also point to the value of methods that can capture time variation and crisis-specific dynamics. Ali et al. (2022) document pandemic-period co-movements in Islamic and conventional indices using wavelet coherence. Kazak et al. (2025b) show that global uncertainty indicators affect Islamic equity indices, although the strength of this effect differs across indicators. More broadly, time-frequency, connectedness, and machine-learning studies in related financial settings show that dependence structures, spillovers, and forecast performance can vary markedly across horizons and market conditions (Ali et al., 2024a, b; Aharon et al., 2025; Kazak et al., 2025a; Naveed et al., 2025). This is important because the Islamic-market literature still relies heavily on traditional tools such as unit root, variance ratio, serial correlation, autocorrelation, and runs tests.

Overall, the literature does not offer a clear consensus on weak-form EMH in Islamic stock markets. Results differ across countries, indices, periods, and methods. One reason may be that conventional tests are often not well suited to financial series marked by structural breaks, nonlinearities, and crisis-driven shifts. For this reason, using approaches such as machine learning and wavelet-based analysis may provide a more informative assessment of weak-form efficiency. This is where the present study aims to contribute.

This study examines the behavior of nine global Dow Jones Islamic Market Indices DJICA, DJICHKU, DJIJP, DJIMIND, DJIMKW, DJIMTR, IMUS, DJIUK, DJMY25D under the weak-form EMH. All indices used in our study were selected to represent the major Islamic markets across different regions in different regions, and the data were downloaded directly from the S&P Global and Refinitiv Eikon databases and contained no missing observations or transformations, thereby ensuring the full reproducibility of the results. The dataset, obtained from S&P Global and Refinitiv Eikon databases and compiled using daily closing prices, includes the following date ranges for each index: DJICA: 06/2004–04/2025; DJICHKU: 06/2010–04/2025; DJIJP: 05/2004–04/2025; DJIMIND: 10/2010–04/2025; DJIMKW: 01/2008–04/2025; DJIMTR: 12/2004–04/2025; IMUS: 05/2004–04/2025; DJIUK: 05/2004–04/2025; and DJMY25D: 06/2009–04/2025. Daily closing prices were used for all indices. Due to data availability constraints, it was not possible to obtain data earlier than 2004 for any of the indices. However, each index was analyzed separately within its respective data range, enabling a comparative assessment of the activity levels of Islamic capital markets in different regions over time. Detailed information on the variables used is presented in Table 1.

This study examines weak-form efficiency in a broad set of Islamic stock indices using a combined empirical framework. Next-day returns are forecast through ANN models and compared with the random walk benchmark, while time-varying dependence is evaluated through wavelet-based analysis. In this way, the study provides a more integrated assessment of weak-form efficiency across markets and periods, including crisis episodes.

The descriptive statistics show that 5-day return volatility differs across the Islamic indices in the sample, while next-day returns remain close to zero in most cases. Volatility is generally low, but the positive skewness values suggest that sharp increases in volatility occur from time to time. Next-day returns, on the other hand, are mostly slightly negatively skewed. Overall, the results point to some cross-market variation in volatility, whereas average returns remain quite limited.

In this study, we first use the Fourier-ADF test, introduced by Enders and Lee (2012), to analyze the stationarity of the series. The Fourier-ADF test evaluates the null hypothesis of a unit root against the alternative of stationarity while allowing for smooth structural changes through Fourier (sine and cosine) terms. This feature is particularly useful for long financial samples in which breaks may occur gradually rather than abruptly.

The technique was preferred to conventional unit-root tests, such as ADF or KPSS, because it allows for smooth and gradual structural breaks by including trigonometric terms. This kind of flexibility enables the detection of nonlinear and cyclical variations in financial time series that traditional tests might have missed, leading to more reliable assessments of stationarity in markets that are generally characterized by regime shifts and volatility clustering.

The empirical strategy is organized around three related questions that arise in weak-form efficiency assessments, especially under crisis conditions. First, do the return and volatility series exhibit random-walk or stationarity properties once smooth breaks are allowed for (Fourier-ADF)? Second, even if weak-form tests suggest limited predictability, does any forecasting model generate practically meaningful out-of-sample gains relative to standard random-walk-type benchmarks (ANN forecasting stage)? Third, do volatility and return linkages strengthen at particular horizons and periods, such as crisis windows, in a way that is not visible in purely time-domain averages (WTC time–frequency evidence)? This structure allows the methods to be complementary rather than repetitive.

Following the basic unit root testing, three main methodological approaches were applied sequentially in this study:

1. The Artificial Neural Network (ANN) model for forecasting,

2. The Fourier Granger causality approach, and

3. The Wavelet Transform Coherence (WTC) analysis for time–frequency dependence.

This sequencing is intentional: we start with baseline weak-form diagnostics, then evaluate operational predictability out-of-sample, and finally examine whether crisis-period dynamics vary across horizons in the time–frequency domain.

In the next stage of the study, forecasts are generated using ANN-based machine-learning models. At this stage, a multilayer artificial neural network (ANN, MLP) model is used to predict the next day's return based on the daily returns of the financial indices in the panel. All data used in the model consist of daily price change percentages (log returns) and are found to be stationary in levels based on the stationarity analysis (Fourier-ADF). Therefore, we did not apply additional normalization or standardization, because the inputs are already expressed as stationary log returns on a comparable scale, and we aimed to keep the data treatment consistent across indices to preserve comparability of forecasting performance.

The ANN employs a feedforward network architecture in which data are propagated forward across layers. In this model, data are first received in the input layer, then processed through one or more hidden layers, and finally obtained in the output layer. The number of hidden layers and the number of neurons in each hidden layer determine the complexity and learning capacity of the model. A multilayer neural network is modeled as follows (Heidari et al., 2016; Teixeira Zavadzki de Pauli et al., 2020):

In this study, the model architecture consists of:

1. Input layer: lagged daily returns,

2. One hidden layer: 20 neurons using ReLU activation,

3. Output layer: a single neuron with linear activation for regression output,

4. Loss function: Mean Squared Error (MSE),

5. Optimizer: Adam optimizer for adaptive learning and efficient convergence,

6. Epochs: 200, Batch size: 32.

The network weights were updated using the backpropagation algorithm and the Adam (Adaptive Moment Estimation) optimization algorithm. The main purpose of Adam optimization is to provide faster, more balanced learning than classical optimization methods by combining momentum (the average of past gradients) with adaptive learning rates (step sizes that vary by parameter) when updating network weights. The dataset was split into training and test sets in a 75:25 ratio. The split was implemented chronologically to respect the time-series nature of daily returns: the first 75% of observations were used for training and model selection, while the final 25% were reserved as a genuine out-of-sample test set. Within the training portion, a validation set was used to guide hyperparameter tuning and to apply early stopping based on validation loss. Accordingly, cross-validation and all tuning decisions were confined to the training sample, and the test set was used only once for the final performance evaluation reported in the results section. Hyperparameters (such as the number of hidden layers, number of neurons, and learning rate) were selected through guided tuning using validation performance, with candidate settings evaluated systematically to balance fit and generalization.

This evaluation design also helps prevent information leakage by reserving the test set exclusively for final out-of-sample assessment. The ANN model was therefore implemented using a chronological train-test split, and the test sample was kept untouched until the final evaluation stage. To improve robustness, hyperparameter tuning and validation were performed within the training sample using 5-fold cross-validation and early stopping. In addition, dropout regularization (0.2) was used to limit overfitting.

At the subsequent stage of the analysis, we employed the panel Fourier Granger causality approach, originally proposed by Enders and Jones (2014) and later enhanced by Nazlioglu et al. (2016) and Yilanci and Gorus (2020) through the inclusion of Fourier functions to examine causal relationships among the variables. While Granger causality is not a direct weak-form efficiency test, it provides complementary evidence on the direction and stability of volatility–return dynamics. In our setting, it helps evaluate whether short-horizon volatility (X9) contains incremental information for next-day returns (Output), which is directly relevant for interpreting predictability claims under stress periods.

In this analysis, our aim is to examine the causal effect of X9 on Output. The following equation is used to test for causality from the independent variable to the dependent variable (Equation (1)):

This approach has been preferred over the standard Granger causality test because it accounts for cross-sectional heterogeneity and smooth structural breaks over time. Moreover, by including Fourier terms, it captures gradual changes in the causal relationships rather than abrupt breaks, which is particularly valuable in financial markets characterized by regime evolution and global shocks.

In the final stage, Wavelet Transform Coherence (WTC) analysis was used to examine volatility-return relationships across time and frequency. Following Torrence and Webster (1999), wavelet coherence was computed as follows (Equation (2)):

Values close to zero indicate weak coherence, while values close to one indicate strong coherence. This step helps identify when and at which horizons volatility-return linkages become more pronounced.

The FF Fourier-ADF unit root test was applied under both constant and trend specifications to examine the stationarity properties of X9 and Output. Since these series are used in the subsequent causality and WTC analyses, establishing their order of integration is an important first step. The results are summarized in Table 2.

As shown in Table 2, the findings are fully consistent across the two specifications. Both X9 and Output are stationary in levels for all nine countries under the constant and trend models. This indicates that the series are suitable for the subsequent empirical analyses.

Following the unit root tests, a multilayer artificial neural network (ANN/MLP) model was applied to the nine Dow Jones Islamic indices to predict next-day returns based on past returns. Forecast performance was evaluated on the holdout test sample using RMSE, MAE, and out-of-sample (⁠$R2$⁠). To assess whether ANN offers any improvement over a standard benchmark, the results were also compared with those of the random walk model, and the differences in forecast accuracy were tested using the Diebold and Mariano (1995) (DM) test. The combined results are reported in Table 3.

Table 3 shows that the ANN model produces lower RMSE and MAE values than the random walk benchmark for all indices. However, the out-of-sample (⁠$R2$⁠) values remain close to zero and are negative throughout, which suggests that next-day returns are still difficult to predict in practical terms. The DM statistics are negative and statistically significant for all indices, indicating that ANN reduces forecast loss relative to the random walk model. Even so, these gains should be read as limited improvements in forecast accuracy rather than strong evidence of return predictability. Overall, the results remain broadly consistent with weak-form market efficiency.

Analysis of comparative line and scatter plots and of error histograms for actual and predicted returns shows that the model's predictions cluster around the mean of the observed values and exhibit no systematic predictive power. The forecast graphs of the indices evaluated in the study are also provided in the Supplementary Material (access details are provided in the Data Availability statement). As observed in these graphs, the ANN model closely tracks observed movements in normal periods but deviates slightly during crisis episodes, reflecting limited short-term predictability, consistent with the weak-form EMH. This pattern is theoretically plausible because crisis periods are often associated with abrupt information arrivals, changing expectations, and heightened market uncertainty, which can destabilize short-horizon return dynamics and make one-step-ahead forecasts more difficult (e.g. Gormsen and Koijen, 2020; Ang and Bekaert, 2002). Empirical evidence in finance also suggests that machine learning methods can improve predictive accuracy by capturing nonlinear relationships, but such gains should be interpreted carefully in light of market-state dependence and changing risk conditions (Gu et al., 2018; Atsalakis and Valavanis, 2009). From a practical perspective, these observed crisis-period deviations imply that ANN-based forecasts may be more useful as complementary tools for incremental error reduction and risk monitoring, rather than as stand-alone timing signals during stress episodes. This interpretation is also consistent with recent evidence that uncertainty and risk indicators materially affect Islamic equity markets and have direct implications for investors and policymakers (Kazak et al., 2025a, b). Accordingly, the crisis-period evidence reinforces our conclusion that any predictive gains remain limited and should not be interpreted as strong evidence against weak-form market efficiency.

The graphs comparing the observed returns in the test set with forecasts from the artificial neural network (ANN) and random-walk models across all indices are provided in the Supplementary Material. As shown, the predictions from both models have limited success in capturing actual returns. Forecasting performance deteriorates, particularly when confronted with extreme values and abrupt changes. Accordingly, this finding indicates that the ANN model cannot predict next-day returns from past price movements in the test set, which holds for all indices. In other words, a weak form of market efficiency is valid in Islamic stock markets.

In subsequent tests, the relationships between X9 and the Output variables were analyzed. First, the Fourier Granger causality test is conducted, and results are presented in Table 4.

Table 4 reports the Fourier Granger causality results for the effect of X9 on Output across countries. The Wald statistic and related p-values, supported by the bootstrap method, show that X9 has a significant causal effect on Output in many countries. In particular, for Canada, China (Hong Kong), India, Kuwait, the United Kingdom, and the United States, both the asymptotic and bootstrap p-values are statistically significant (p < 0.05), indicating rejection of the null hypothesis (H0) and a causal relationship from X9 to Output. Although the bootstrap p-values for Japan and Malaysia are significant, the asymptotic p-values do not reach statistical significance, suggesting that the causal relationship may vary across countries depending on sample size and methodological sensitivity. In Türkiye, because both p-values were not statistically significant, no causal relationship from X9 to Output could be detected.

Finally, wavelet transform coherence (WTC) analysis was used to examine the time-frequency co-movement between volatility (X9) and next-day returns (Output). As shown in the Supplementary Material (access details are provided in the Data Availability statement), warmer colors indicate stronger coherence, while arrows summarize the phase relationship between the two series. Overall, the results point to episodic rather than persistent co-movement across the nine Islamic indices. In most cases, coherence appears in localized clusters and becomes more visible at medium horizons, especially during periods of market stress. For Canada and China/Hong Kong, the volatility-return relationship is generally limited and fragmented across time and scale. Japan and India also show time-varying coherence, with more visible clusters at medium horizons during particular subperiods rather than throughout the sample. A similar pattern appears in Kuwait and Malaysia, where coherence remains weak or intermittent and does not indicate a stable relationship. Türkiye, the United Kingdom, and the United States display relatively broader and more pronounced coherence clusters, especially at medium horizons and during stress periods. Even in these cases, however, the relationship is not uniform across the sample. Taken together, the WTC findings suggest that volatility-return linkages in Islamic equity indices are mostly horizon-specific and temporary, rather than consistent with persistent predictability.

Following the index-level WTC figures, we provide a compact cross-region summary to make the global comparison explicit. While the figures document when and at which horizons volatility (X9) and next-day returns (Output) co-move, a single overview table helps assess whether the strength, dominant horizon, and phase tendency of these linkages differ across major crisis windows. Table 5 therefore synthesizes the WTC evidence by reporting, for each index and crisis period, (1) the strength category, (2) the dominant time horizon (short/medium/long), and (3) the prevailing phase tendency.

Table 5 highlights that volatility–return linkages during crises are not uniform across indices or horizons. In the Global Financial Crisis and the Euro Area debt episode, the dominant coherence is typically concentrated in longer horizons (L) for several major markets (e.g. DJICA, DJIUK, IMUS), whereas some indices show no statistically significant coherence within the cone of influence for the same windows (e.g. DJICHKU, DJIMIND, DJMY25D in 2007–2009). During the COVID-19 window, the dominant horizon shifts toward medium and long bands for many indices, and the phase tendency is more frequently mixed, consistent with heightened and time-varying uncertainty. In the 2022–23 window, the summary suggests greater heterogeneity in both dominant horizons and phase tendencies, with some indices exhibiting shorter-horizon dominance (S) and in-phase tendencies (IP), indicating that crisis-specific conditions can alter the time scale at which volatility and returns co-move.

Regional and global crises such as the 2008 global financial crisis, the COVID-19 shock, and the 2022–2023 geopolitical-energy turbulence appear in the WTC results as localized volatility-return co-movements rather than a stable pattern over the full sample. This is consistent with the Islamic-market literature, which shows that efficiency can vary across markets, regimes, and horizons. Al-Khazali et al. (2016), Mensi et al. (2017), Buğan et al. (2021), and Ülev and Selçuk (2022) all point to time-varying or market-specific efficiency patterns, while Bouoiyour et al. (2018) and Sakınç and Sakınç (2024) emphasize cross-market differences in weak-form efficiency.

The horizon structure of the WTC findings also helps explain why the literature reports mixed evidence. In our results, coherence tends to cluster at particular horizons and then fade, rather than forming a continuous forecasting signal. This is in line with Mensi et al. (2017) and Buğan et al. (2021), and also fits more recent work showing that volatility-correlation patterns in Islamic markets change across crisis periods and should be examined with time-varying methods (Chazi et al., 2023; Rehman et al., 2024; Tabash et al., 2023).

Read together with the Fourier-based Granger results, the picture becomes clearer. In some indices, volatility helps predict next-day returns, while in others the effect is not statistically supported. This again matches earlier studies showing that Islamic equity markets do not follow a single efficiency profile (Al-Khazali et al., 2016; Bouoiyour et al., 2018; Ülev and Selçuk, 2022; Hassan and Ahmad, 2020; Khan et al., 2021; Sakınç and Sakınç, 2024). Our findings suggest that, when predictability appears, it is usually limited to specific windows and horizons rather than indicating persistent weak-form inefficiency.

The forecasting results tell a similar story. ANN produces lower forecast errors than the random walk benchmark, but the out-of-sample R² values are still close to zero and in some cases negative. So, even if the model performs better in statistical terms, this does not mean that returns become meaningfully predictable in practice. As Showalter and Gropp (2019) also note, a better fit does not automatically translate into an economically useful trading opportunity. Taken together, the findings suggest that weak-form efficiency is still broadly consistent with the data, even though crisis periods may create short-lived dependence that does not persist long enough to generate systematic excess returns (Emenike and Joseph, 2018; Hailu and Vural, 2020).

This study examined weak-form efficiency in nine Dow Jones Islamic stock indices using unit root testing, Fourier-based Granger causality, ANN forecasting, and wavelet transform coherence analysis. The aim was to assess whether return predictability is persistent and whether volatility-return linkages become more visible during crisis periods.

The findings point to a clear overall pattern. Weak-form efficiency remains broadly consistent with the data. Although ANN produces lower forecast errors than the random walk benchmark, the out-of-sample explanatory power remains very limited. The WTC results show that volatility-return linkages become more visible during major stress episodes, but these effects are localized and short-lived rather than stable over time.

The study contributes to the literature by examining a broad set of Islamic indices within a single framework and by showing that efficiency in these markets is better understood as time-varying and crisis-sensitive. This helps explain why earlier studies report mixed findings across markets and periods.

The results also carry practical implications. During crisis periods, Islamic equity markets may deserve closer attention, since temporary dependence becomes easier to observe in such episodes. For investors and fund managers, the main message is one of caution. Short-lived co-movements may become more noticeable under stress, but they do not seem stable enough to offer a reliable basis for persistent excess returns.

Overall, the evidence suggests that Islamic equity markets remain broadly compatible with weak-form efficiency, even though crisis periods may create temporary and horizon-specific departures.

The supplementary material for this article can be found online: https://doi.org/10.7910/DVN/8BRAQZ