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Article
Business, Economics and Management
Econometrics and Statistics

Yunpeng Zhao

Abstract: This article applies the Fama-MacBeth two-step regression technique to investigate the effect of excess cash holdings on stock returns. By integrating both theoretical and empirical methods, the study explores how excess cash impacts stock valuations. Analyzing financial data from non-financial firms listed on the Shanghai and Shenzhen A-share markets between 2011 and 2020, the research estimates the influence of excess cash holdings. It creates a long-short investment portfolio based on excess cash holdings using monthly trading data from A-shares spanning July 2012 to June 2022. Evaluations using the Fama-MacBeth three-factor, five-factor, and Carhart four-factor framework reveal that companies possessing elevated levels of surplus cash tend to experience notably greater monthly equity returns than their counterparts with limited excess liquidity. This result holds true across various models. Additionally, the study shows a significant positive correlation between excess cash holdings and stock returns, affirming that excess cash can reliably predict future stock performance. Market conditions, the quality of information disclosure, financing constraints, and ownership type also significantly influence this relationship. Both state-owned and private companies with higher excess cash holdings tend to outperform those with lower cash reserves. This study enhances our understanding of the determinants of stock returns and confirms the positive correlation between excess cash holdings and anticipated returns in the Chinese stock market.
Article
Business, Economics and Management
Econometrics and Statistics

Bidyut Kumar Ghosh

Abstract:

India’s inbound tourism potential could not be fully realised even though it has rich heritage resources, expanding air networks, and sustained policy attention. To identify the key determinants of foreign tourism demand, this study applies an interpretable machine learning framework using a panel data of 61 source countries to India over 2002–2024. Using a gravity-based tourism demand model, the analysis estimates an XGBoost regression for predicting tourism demand based on origin-country income, India’s hotel capacity, domestic and international aircraft movements, UNESCO heritage sites, mega-events, inflation, and governance indicators. Accumulated Local Effects (ALE) and SHAP values were used as interpretable tools. Results show that source-country income and air connectivity are the most influential drivers of arrivals, while heritage sites and hotel rooms display clear saturation and diminishing returns, and governance and inflation exert only mild or non-linear effects. Mega-events provide small and inconsistent short-run gains without strong persistence. The findings indicate that India’s future tourism gains lie less in further capacity expansion and more in strengthening air connectivity, strategically targeting emerging middle-income markets, and upgrading quality, governance, and price stability to convert existing assets into sustained, spatially dispersed arrivals.

Article
Business, Economics and Management
Econometrics and Statistics

Felix Reichel

Abstract: Fixed effects models often rely on the within transformation, which constructs demeaned arrays prior to forming cross-products. This paper develops an estimator that avoids the for- mation of demeaned arrays by exploiting grouped summaries built from per-unit sufficient statistics. A complete derivation shows that the grouped Gram representation reproduces the classical estimator exactly. The difference lies in memory access patterns and byte movement. The grouped estimator concentrates operations into unit-level accumulations, avoiding the writes associated with array centering. Gains arise once the panel reaches a scale where mem- ory traffic governs run time. Simulations examine coefficient accuracy, bootstrap dispersion, run time, and memory use.
Article
Business, Economics and Management
Econometrics and Statistics

Alberto Jose Miranda Fretes

Abstract: Understanding how subway stations affect nearby crime is important for urban planners, transit agencies, and public safety officials who must allocate limited resources. Prior research suggests that transit nodes can increase crime by concentrating potential targets, but findings vary depending on station design, ridership levels, and time of day. This study examines whether within-place changes in subway ridership are associated with changes in recorded crime across New York City from 2020 to 2024. The unit of analysis is the quarter-mile "egohood," a buffer around each Census block centroid. Data come from NYPD complaint records, MTA ridership counts, and American Community Survey demographics. Using two-way fixed-effects models that control for stable neighborhood traits and citywide year shocks, the analysis finds that increases in ridership within the same egohood are associated with modest increases in recorded crime. Station presence alone does not predict crime once time-invariant characteristics are held constant. These findings suggest that managing passenger flows, rather than station footprint, should guide safety planning. Practical steps include improved lighting, visible staffing during peak hours, and coordination between transit agencies and local police.
Article
Business, Economics and Management
Econometrics and Statistics

Kabiru Mohammed Yahaya

,

Charles Nwekeaku

Abstract:

This study examined the impact of the National Poverty Eradication Programme (NAPEP) on youth employment in Bauchi State, Nigeria. The study adopted a quantitative research design, using a structured questionnaire administered to 264 respondents selected through multistage sampling. Data were analyzed using descriptive and inferential statistics, including frequency distributions, percentages, and chi-square tests. The results revealed that NAPEP contributed moderately to youth employment generation, particularly through skills acquisition and micro-credit schemes, though sustainability remained low. Challenges identified included inadequate funding, poor monitoring, and political interference. The study concludes that while NAPEP had positive short-term outcomes, its long-term impact on poverty reduction and youth employment in Bauchi State was limited. It recommends stronger institutional coordination, improved funding, and the integration of private sector partnerships to sustain youth empowerment initiatives.

Article
Business, Economics and Management
Econometrics and Statistics

Nikhil Bhardwaj

,

Munish Sahrawat

,

Eshan Gambhir

Abstract: The global financial crises of 2008 and COVID-19 triggered market volatility, disrupting trade and foreign direct investment (FDI) flows, and impacting financial integration among economies. This study investigates the degree of financial integration between India and selected global economies—US, UK, China, Hong Kong, and Japan—during crises, using daily closing stock index data from January 2002 to June 2022. Econometric tools, including the Johansen Co-integration Test, Granger Causality Test, and Augmented Dickey-Fuller Unit Root Test, are applied to analyse short- and long-term financial linkages. The Johansen Co-integration Test results reveal long-term integration among all economies, with significant co-integrating equations detected (Trace Statistic = 98.18, Max-Eigen Statistic = 35.37) during the post-COVID period. However, the Granger Causality Test shows fluctuating short-term causal relationships, particularly with India and China shifting from bi-directional to uni-directional causality post-COVID. Standard deviations across indices, such as China (1.73) and India (1.51), highlight market volatility. The correlation matrix reveals a high correlation between India and the US (0.93 pre-COVID, 0.98 post-COVID), indicating limited opportunities for portfolio diversification. The results emphasise that sustained financial integration reduces diversification benefits and increases the potential for volatility spillovers during crises. Policymakers must identify highly connected markets and implement risk mitigation strategies to avoid systemic shocks. This study offers actionable insights for investors to navigate interconnected markets during turbulent times and provides guidance for future policy frameworks to enhance financial stability.
Article
Business, Economics and Management
Econometrics and Statistics

Massimo Arnone

,

Alberto Costantiello

,

Carlo Drago

,

Angelo Leogrande

Abstract: This paper investigates the influence of environmental, social, and governance (ESG) factors on financial development, using Domestic Credit to the Private Sector by Banks (DCB) as the core indicator of credit market development. To effectively market the research within the broader literature on finance and ESG issues, the authors employ an approach combining econometric analysis, K-Nearest Neighbors (KNN), cluster analysis, and network analysis. By analyzing the impact through the estimation of the model parameters through the impact of instrumental variable estimation on the model parameters (using Two-Stage Least Squares (IV), Random Effects (IV), and First-Differenced (IV) methods), the study confirms that access to clean fuels and natural resource depletion impact the model margins significantly. However, across all the models used in the analysis, the impact of access to clean energy is positive. By analyzing the significance of the issue using the KNN model throughout the research process on the impact of ESG on credit market dynamics across countries, the research demonstrates that the issue is significant. By performing hierarchical cluster analysis on the significance of the research by considering the significance of the issue in its contribution to the impact on credit market dynamics in countries, in terms of climate stress issues being core in influencing the dynamics of credit in countries, through network analysis mapping performed by carrying out research on the topic.
Article
Business, Economics and Management
Econometrics and Statistics

Nicola Magaletti

,

Giancarlo Caponio

,

Angelo Amodio

,

Valeria Notarnicola

,

Mauro Di Molfetta

,

Angelo Leogrande

Abstract: This paper focuses on the design and development of a decision support system (DSS) for the governance of intralogistics processes and, in particular, devoted to optimize capacity management and the workload of activities characterizing freight entry. This research activity was carried out as part of the Logistics Research and Development 4.0 Project launched by La Logistica Srl, a new player in the distribution of hydro-thermo sanitary products, with the support of the Puglia Region. The purpose of this study is to provide managers with a range of customized process information to improve workforce efficiency and management in receiving, controlling, and storing goods entering the newly established logistics hub. Other researchers’ work had shortcomings, as did the lack of this study’s practical approach. This study aims to overcome these constraints. To do so, the study introduces the Content Load Parameter (CLP) index. This index integrates three variables relevant to defining the workload, such as quantity, size and weights of the goods to be handled, using a single standard value. This makes it easier for managers to estimate the required capacity all along the work cycle. As part of the system development, a module analyzes and simulates operational scenarios. Simulation facilitates the management of analysis capacity by allowing alternatives to be compared and evaluated to bridge the gap between demand and availability of production capacity in various situations. Scenario simulation, combined with tools for concise and effective visualization of results, therefore allows organizations to identify critical capacity points and take preventative measures to manage overhead and minimize consequences. In summary, this study demonstrates how integrating the Content Load Parameter index into a decision support system can significantly contribute to making intralogistics process management more effective. By addressing quantifiable workload parameters and facilitating scenario-based operational analysis, the proposed system provides managers with useful information for capacity optimization. These advances not only overcome the limitations of previous research but also help develop resilient and efficient logistics operations, thus strengthening the critical role of empirically informed decision-making in contemporary logistics governance.
Article
Business, Economics and Management
Econometrics and Statistics

Dan Liu

,

Guangzhi Shang

Abstract: While product returns pose challenges for retailers, prior research suggests that high-quality return services can turn these experiences into opportunities to strengthen customer loyalty and encourage repeat purchases. However, existing studies have largely treated returns as a uniform phenomenon, focusing on their overall impact on repurchase behavior while overlooking the distinct effects of different return types. This study addresses this gap by categorizing returns based on customer attributions of blame—specifically, self-attributed, seller-attributed, and intermediary-attributed returns—and examining how these attributions influence future purchasing behavior. The findings reveal significant variations in consumer responses depending on the perceived cause of the return. Customers who attribute a return to their own mistakes (self-attributed) demonstrate a notable increase in future repurchases. In contrast, returns attributed to seller-related issues (seller-attributed) significantly reduce repurchasing behavior. Meanwhile, returns with ambiguous attributions involving intermediaries (intermediary-attributed) do not have a statistically significant impact on future purchases. By addressing the overlooked role of return attributions, this study advances the understanding of return service recovery and provides actionable insights for businesses seeking to optimize return policies, enhance customer retention, and allocate resources more effectively.
Article
Business, Economics and Management
Econometrics and Statistics

Marcelo Santana Silva

,

Luís Oscar Silva Martins

,

Fábio Matos Fernandes

,

Lucas da Silva Almeida

,

Maria Cândida Arraes de Miranda Mousinho

,

Rilton Gonçalo Bonfim Primo

,

Ednildo Andrade Torres

Abstract: This study examines the determinants of renewable energy consumption among BRICS countries (Brazil, Russia, India, China, South Africa, Saudi Arabia, Egypt, the United Arab Emirates, Ethiopia, Iran, and Indonesia) between 2000 and 2022. Using static (Fixed and Random Effects) and dynamic (First-Difference GMM) panel data models, the research investigates how economic, institutional, and social factors influence renewable energy transition. The results reveal structural heterogeneity within the bloc. Among the founding members, renewable energy consumption is positively associated with governance quality and trade openness, while GDP per capita exhibits a negative relationship, consistent with the Environmental Kuznets Curve hypothesis. In contrast, the new members show strong energy dependence and limited institutional capacity, with dynamic models confirming high persistence in energy consumption and weak responsiveness to economic and policy changes. Variables such as education and life expectancy were omitted in the dynamic specification due to limited temporal variation, without compromising model consistency. Diagnostic tests (Hansen, Sargan, and AR(2)) confirm the robustness of the estimates. Overall, the findings highlight the importance of strengthening institutional governance, technological innovation, and intra-bloc cooperation to advance energy transition and achieve sustainable development across the BRICS economies.
Article
Business, Economics and Management
Econometrics and Statistics

Uğur Tahsin Şenel

,

Nursal Arıcı

,

Müslüme Narin

,

Hüseyin Polat

Abstract: This study develops a comprehensive two-stage hybrid framework to forecast food prices in Turkey, addressing inflation prediction challenges critical for sustainable food security in emerging economies. In the first stage, systematic relationship and causality analyses—comprising correlation, ARDL, cointegration, and Granger causality tests—identified ten key predictors from the Turkish Statistical Institute and Central Bank datasets. In the second stage, ten predictive models, including ensemble (Gradi-ent Boosting, Random Forest, SVR), traditional (ARIMA, Linear Regression), and deep learning approaches (LSTM, NARX-RNN, ANFIS), were evaluated using rice prices as a pilot case. Ensemble models demonstrated clear superiority, with Gradient Boosting achieving optimal single-split performance (R² = 0.9990) and high cross-validation consistency (mean R² = 0.9742 ± 0.03). Support Vector Regression (R² = 0.9896 ± 0.02) and Random Forest (R² = 0.9811 ± 0.02) showed statistically equivalent performance, reinforcing ensemble robustness. NARX-RNN analysis revealed a six-month lag in economic shock transmission, providing a practical policy intervention window. SHAP-based interpretability identified insurance, healthcare, transportation, educa-tion, and social protection expenditures as major drivers of food price formation, un-derscoring Turkey's cross-sector inflation mechanisms. These findings integrate econometric rigor with machine learning transparency, offering practical tools for sustainable inflation management and early warning systems in volatile emerging markets.
Article
Business, Economics and Management
Econometrics and Statistics

Shaoqian Tang

,

Ningjiang Huang

Abstract: New account fraud poses a persistent challenge in modern banking systems due to the sparsity, heterogeneity, and incompleteness of user information. Existing methods often struggle with missing data, limited cross-view representation, and weak adaptability to evolving fraud patterns. To address these issues, we propose NAFNet, a deep learning framework that integrates dynamic feature imputation, multi-view encoding, and attention-based representation learning. NAFNet employs a learnable imputation module guided by statistical priors, encodes heterogeneous views via dedicated encoders with bilinear fusion, and enhances global dependency modeling through attention-augmented neural layers. A fine-tuned training regime ensures robustness and generalization. Experiments show that NAFNet offers substantial improvements over conventional methods, demonstrating its effectiveness in complex, real-world fraud detection scenarios.
Article
Business, Economics and Management
Econometrics and Statistics

Ningjiang Huang

,

Shaoqian Tang

Abstract: Hierarchical multi-label financial event detection in Chinese news is difficult because of limited data, vague semantics, and label inconsistency between general and specific categories. Transformer-based models often fail to capture financial language details such as negation and modality, and they struggle to maintain consistency across label hierarchies. This paper presents HARTE, a Hierarchical Adaptive Risk-Aware Transformer Ensemble that combines risk-aware representation, hierarchical decoding, and uncertainty integration in one framework. HARTE uses a contextual risk encoder with adaptive attention and BiLSTM-gated fusion to represent risk semantics, dual-level contrastive learning to improve feature discrimination under limited supervision, and progressive knowledge distillation to align probabilities and attention for efficient transfer. It also ensures hierarchical consistency with structured gating and fuses multiple encoders through uncertainty weighting. These designs allow HARTE to improve semantic clarity, structural consistency, and reliability for financial event detection with scarce annotations.
Article
Business, Economics and Management
Econometrics and Statistics

Kola Adegoke

,

Olajide Alfred Durojaye

,

Olawale Emmanuel Oyebode

,

Abimbola Adegoke

,

Adeyinka Adegoke

Abstract: Hospital consolidation has increased in the USA, raising concerns about reduced competition and higher costs. This study investigates whether recent consolidations have enhanced efficiency or boosted market power. Data from 2017 to 2024, collected from RAND Hospital Data, which combines Medicare Cost Reports and hospital ownership information, were analyzed using a difference-in-differences approach to assess efficiency changes before and after hospitals joined multihospital systems. The treatment group consisted of hospitals affiliated with a hospital system between 2019 and 2020, while standalone hospitals served as the comparison group. The analysis examined overall, operating, and cash flow margins. Fixed-effects models with clustered standard errors accounted for hospital-level differences. Results showed a significant increase in overall margins (β = 0.0064, SE = 0.0028, p = 0.021) and operating margins (β = 0.0068, SE = 0.0025, p = 0.006), but no significant change in cash flow margins (β = 0.0019, p = 0.415) for hospitals that joined systems between 2019 and 2020. Pre-trend lines support causal inference. These findings suggest efficiency improvements rather than increased market dominance. The results differ from previous studies on cost inflation but reflect recent efficiency gains under new regulations following the public healthcare law.
Article
Business, Economics and Management
Econometrics and Statistics

Selim Jürgen Ergun

,

M. Fernanda Rivas

Abstract: Vietnam is an energy-intensive economy that has a rapidly growing industry. This fact has increased the urgency for firm-level sustainable energy management practices, especially given the country’s low ranking in global environmental performance. In this study, we investigate the firm-level determinants of sustainable energy management adoption in Vietnam, focusing on structural characteristics, innovation capabilities, and external linkages. Using data from the 2023 World Bank Enterprise Survey, we apply both a logit regression model and a Random Forest algorithm, a novel combination in the study of determinants of sustainable energy management adoption. The logit model identifies significant positive relationships between sustainable energy management adoption and factors such as firm size, R&D investment, international quality certification, and export orientation. Managerial experience shows a non-linear relationship with sustainable energy management adoption, whereas foreign ownership influences it only when combined with R&D investment. The Random Forest model complements these findings by revealing nonlinear relationships and highlighting the predictive importance of variables like international certification, managerial expe-rience, and manufacturing sector affiliation. Together, the models show that internal capabilities and external pressures drive the adoption of sustainable energy management. Our results suggest that policy interventions should be designed with sector- and firm-specific contexts in mind to foster more sustainable firms.
Article
Business, Economics and Management
Econometrics and Statistics

Malefane Harry Molibeli

,

Gary van Vuuren

Abstract: We present a unified framework for modeling the term structure of interest rates using both the affine term structure models (ATSM) with jumps and regime-switches. The novelty lies in combining affine jump diffusion models with regime-switching dynamics within a unified framework, allowing for state-dependent jump behavior while preserving analytical tractability. This integration enables the model to simultaneously capture nonlinear market regimes and discontinuous movements in interest rates—features that traditional affine models or regime-switching models alone cannot jointly represent. Estimation is carried out using the unscented Kalman filter (UKF) with the believe that it is capable of handling nonlinearity, therefore should estimate the non-Gaussian dynamics well. The yield curve fitting demonstrate that both models fit our data well. RMSEs show that the regime-switching affine jump diffusion (RS-AJD) models outperforms the affine jump diffusion (AJD) in-sample.
Article
Business, Economics and Management
Econometrics and Statistics

Piotr Semkiw

,

Dariusz Gerula

Abstract: The aim of this study was to analyse the economic conditions of the beekeeping sector in Poland between 2019 and 2024, with particular emphasis on production costs, price formation mechanisms, the foreign trade balance, and the structure of honey supply. The analysis was based on data from public institutions, beekeeping organisations, in-dividual beekeepers, and the authors’ own research and analyses. The results indicate a clear increase in domestic honey production, which reached 31 thousand tonnes in 2024, confirming the growing potential of the sector. Poland is among the largest honey producers in the European Union. The market structure is dominated by direct sales; however, as production scale increases, wholesale channels become more important. Apiary size remains a key factor influencing unit costs and profitability – commercial apiaries benefit from economies of scale, while smaller operations have limited in-vestment capacity. During the analysed period, the sector faced significant cost pres-sures driven by high inflation and rising prices of beekeeping production inputs. The market analysis shows increasing competitive pressure, particularly in the wholesale segment, intensified by low-priced imported honey. The oversupply of popular honey types reduces profitability and weakens beekeepers’ bargaining position. The future development of the sector should focus on increasing the added value of production, diversifying distribution channels, expanding premium segments, and building strong and competitive brands. Ensuring the stability of the sector is crucial not only for the agri-food economy but also for ecosystem balance and food security. In this context, proactive measures and the consideration of appropriate market protection instruments are essential to mitigate the effects of market imbalances and enhance the sector’s re-silience to future economic shocks.
Article
Business, Economics and Management
Econometrics and Statistics

Juk-Sen Tang

,

Hongwei Lu

,

Tianyi Gong

,

Junhong Chen

Abstract: In the context of China’s pursuit of high-quality economic development, enhancing agricultural productivity is crucial for ensuring food security and promoting common prosperity. This paper constructs a systematic IV-LP-ACF-SAR econometric framework to analyze agricultural Total Factor Productivity (TFP) growth using panel data from 31 Chinese provinces spanning 2014 to 2023 (n=341 observations). The framework employs the Instrumental Variable (IV)-based Levinsohn-Petrin (LP) proxy variable method under the Ackerberg-Caves-Frazer (ACF) system to estimate a Translog production function while addressing endogeneity using multiple spatial weight matrices. TFP growth is decomposed into Technical Change (TC), Technical Efficiency (EC), and Scale Efficiency (SC). A Spatial Autoregressive (SAR) model with Dynamic Common Correlated Effects (DCCE) explores spatial spillover effects and regional heterogeneity. Results show that China’s agricultural TFP remained largely stagnant from 2014 to 2023 with an average annual growth rate of -0.18%, where Technical Efficiency decline (-0.33% annually) was the main constraint. Technical Change remained neutral, while Scale Efficiency contributed positively (+0.15% annually). Mechanization showed the highest output elasticity (0.99), while fertilizers, pesticides, and labor exhibited negative marginal returns. Spatial analysis revealed significant negative Scale Efficiency spillovers with regional patterns of “scale synergy in the Northeast/Northwest” and “efficiency synergy in East/North China.” These findings suggest that productivity policy should shift toward a dual-driver model combining efficiency enhancement and optimal scaling, with differentiated regional policies and inter-provincial coordination mechanisms necessary to mitigate negative spillovers and enhance sustainable agricultural growth quality.
Article
Business, Economics and Management
Econometrics and Statistics

Alireza Hassani

,

Milad Javadi

,

Mohammad Naisipour

Abstract: This investigation examines the efficacy of the Time Series Informer (TSI) architecture in forecasting stock prices, positioning it as a pivotal instrument within business intelligence (BI) paradigms. Amid the escalating intricacy and nonlinear dynamics inherent to financial markets, deep learning frameworks have emerged as preeminent modalities for delineating sequential dependencies. Employing a comprehensive historical dataset of stock prices sourced from Google, the present analysis juxtaposes the TSI with the Long Short-Term Memory (LSTM) model. Performance is rigorously benchmarked through dual quantitative indices: The Root Mean Square Error (RMSE) and the Pearson correlation coefficient. Supplementary assessments encompass convergence trajectories, computational parsimony, and temporal overheads associated with model training. Empirical findings substantiate the superior predictive fidelity and correlative fidelity of TSI vis-à-vis LSTM, underscoring its adeptness at encapsulating protracted temporal interdependencies in financial chronologies. Visualization of convergence profiles evinces accelerated and more resilient optimization dynamics for TSI. Collectively, this multifaceted juxtaposition elucidates the model's viability for pragmatic stock market prognostication, thereby illuminating the transformative prospective of advanced neural architectures in fortifying strategic business intelligence infrastructures.
Article
Business, Economics and Management
Econometrics and Statistics

Israel Maingo

,

Thakhani Ravele

,

Caston Sigauke

Abstract: This paper studies the volatility dynamics of the JSE Top40 Index by estimating a univariate GAS model with time-varying location, scale, and shape parameters (identity score scaling) and comparing its density and point-forecast performance against a standalone ARMA(3,2)-EGARCH(1,1) model and a hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost framework. The GAS model is estimated on 3,515 daily observations, and several conditional densities are examined. The Student-t GAS model (GAS-STD) obtains the lowest information criteria within the GAS family (AIC = 10,188.142; BIC = 10,243.626) and exhibits statistically significant persistence in location and scale dynamics. Statistical diagnostics provide evidence of correct density calibration (Normalised Log Score = 1.1932; Uniform score = 0.4417), although residual skewness remains (IID-Test skewness p=0.0134). Out-of-sample analysis shows that GAS-STD performs strongly in density and risk forecasting, producing accurate 5% VaR and ES paths and passing coverage backtests (Kupiec LRuc p=0.8414; DQ p=0.2281). However, short-horizon point forecasts are best delivered by the hybrid ARMA-EGARCH-XGBoost model (RMSE = 0.1386), with Diebold-Mariano tests confirming a transitive ranking: Hybrid > ARMA-EGARCH > GAS-STD. Simulation experiments highlight the sensitivity of tail behaviour to degrees-of-freedom (e.g., kurtosis ν=5≈7.32). Overall, GAS-STD is a strong density and risk model for the JSE Top40, while the hybrid framework excels in short-term volatility forecasting.

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