Search Results (66)

We study one of the world’s largest cattle markets by revisiting and extending previous work on the forecasting of Brazil’s Boi Gordo Index (BGI). Using an updated daily dataset (July 2006–September 2025, inflation-adjusted), we evaluate classical and machine learning (ML) approaches for price prediction. Methods include Exponential Smoothing (Simple, Holt, and Holt–Winters), ARMA/ARIMA/SARIMA, GARMA variants, GARCH, Theta, Prophet, and XGBoost; models are compared under a strictly chronological 90/10 holdout (~476 test days) using RMSE, MAE, and MSE, with the AIC guiding within-family selection. Results show that, for the full out-of-sample window, GARMA delivers the best overall accuracy, with ARMA and Holt–Winters close behind, while Prophet and XGBoost perform comparatively worse in this volatile setting. Performance is horizon-dependent: in the first 180 test days, prior to the late-2024 level shift, Holt attains the lowest RMSE/MSE, and XGBoost achieves the lowest MAE. No method anticipates the October–November 2024 exogenous jump and subsequent correction, highlighting the difficulty of structural breaks and the need for timely re-specification. We conclude that GARMA is a robust default for long, turbulent windows, whereas smoothing and ML methods can be competitive on shorter horizons. These findings inform risk measurement and risk mitigation strategies in Brazil’s cattle futures market. Full article

The systematic failure of standard Value-at-Risk (VaR) models for the Tokyo Commodity Exchange (TOCOM) rubber futures contract poses significant challenges for risk management. This study addresses the issue by examining the market’s split trading sessions, which induce distinct overnight and intraday volatility regimes. We decompose daily returns into these two components and apply tailored Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family models. Our empirical results, strengthened by extensive robustness checks using EGARCH, IGARCH, and GJR-GARCH specifications, reveal that intraday volatility is persistent and influenced by leverage effects, whereas overnight volatility behaves as a jump-driven process unaccounted for by conventional models. Comprehensive VaR backtesting confirms that while traditional models accurately capture intraday risk, all standard daily models—including asymmetric variants—systematically and severely underestimate overnight risk. These findings demonstrate that aggregating returns into a single daily series conflates different volatility dynamics, leading to model failures. We propose a two-tiered risk management framework that separately applies conventional models to intraday risk and jump-aware measures for overnight risk. This approach aligns risk assessment with underlying market microstructure, improving model validity and capital adequacy for TOCOM rubber futures. Full article

Background: Exposure therapy is an established intervention for treating specific phobias. This study evaluates a Virtual Exposure Therapist (VET), a virtual reality (VR)-based system enhanced with artificial intelligence (AI), designed to reduce spider fear symptoms. Methods: The VET system delivers three progressive exposure scenarios involving interactive 3D spider models and features an adaptive relaxation mode triggered when physiological stress exceeds preset thresholds. AI integration is rule-based, enabling real-time adjustments based on session duration, head movement (degrees/s), and average heart rate (bpm). Fifty-five participants (aged 18–35) with self-reported moderate to high fear of spiders completed seven sessions using the VET system. Participants were not clinically diagnosed, which limits the generalizability of findings to clinical populations. Ethical approval was obtained, and informed consent was secured. Behavioral responses were analyzed using AR(p)–GARCH (1,1) models to account for intra-session volatility in anxiety-related indicators. The presence of ARCH effects was confirmed through the Lagrange Multiplier test, validating the model choice. Results: Results demonstrated a 21.4% reduction in completion time and a 16.7% decrease in average heart rate across sessions. Head movement variability declined, indicating increased user composure. These changes suggest a trend toward reduced phobic response over repeated exposures. Conclusions: While findings support the potential of AI-assisted VR exposure therapy, they remain preliminary due to the non-clinical sample and absence of a control group. Findings indicate expected symptom improvement across sessions; additionally, within-session volatility metrics (persistence/half-life) provided incremental predictive information about later change beyond session means, with results replicated using simple volatility proxies. These process measures are offered as complements to standard analyses, not replacements. Full article

Volatility modelling is a key feature of financial risk management, portfolio optimisation, and forecasting, particularly for market indices such as the JSE Top40 Index, which serves as a benchmark for the South African stock market. This study investigates volatility modelling of the JSE Top40 Index log-returns from 2011 to 2025 using a hybrid approach that integrates statistical and machine learning techniques through a two-step approach. The ARMA(3,2) model was chosen as the optimal mean model, using the auto.arima() function from the forecast package in R (version 4.4.0). Several alternative variants of GARCH models, including sGARCH(1,1), GJR-GARCH(1,1), and EGARCH(1,1), were fitted under various conditional error distributions (i.e., STD, SSTD, GED, SGED, and GHD). The choice of the model was based on AIC, BIC, HQIC, and LL evaluation criteria, and ARMA(3,2)-EGARCH(1,1) was the best model according to the lowest evaluation criteria. Residual diagnostic results indicated that the model adequately captured autocorrelation, conditional heteroskedasticity, and asymmetry in JSE Top40 log-returns. Volatility persistence was also detected, confirming the persistence attributes of financial volatility. Thereafter, the ARMA(3,2)-EGARCH(1,1) model was coupled with XGBoost using standardised residuals extracted from ARMA(3,2)-EGARCH(1,1) as lagged features. The data was split into training (60%), testing (20%), and calibration (20%) sets. Based on the lowest values of forecast accuracy measures (i.e., MASE, RMSE, MAE, MAPE, and sMAPE), along with prediction intervals and their evaluation metrics (i.e., PICP, PINAW, PICAW, and PINAD), the hybrid model captured residual nonlinearities left by the standalone ARMA(3,2)-EGARCH(1,1) and demonstrated improved forecasting accuracy. The hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model outperforms the standalone ARMA(3,2)-EGARCH(1,1) model across all forecast accuracy measures. This highlights the robustness and suitability of the hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model for financial risk management in emerging markets and signifies the strengths of integrating statistical and machine learning methods in financial time series modelling. Full article

The increasing interaction between the equity market and cryptocurrencies has raised concerns about volatility spillovers; however, empirical evidence about sectoral-specific spillover effects in emerging markets is scarce and hard to find. Existing research mainly concentrates on developed markets and aggregate equity indices, leaving a research gap in comprehending how sectoral indices variations impact market interactions in developing financial markets like Thailand. This article investigates the mean and volatility spillover effects between the Thai stock market and leading cryptocurrencies from April 2019 to April 2024. Applying bivariate VAR (1)-BEKK-GARCH (1,1) with an asymmetry model, this study examines the aggregate and sectoral-specific mean and volatility spillovers across major Thai stock market sectors. The findings reveal the significant mean spillover effect from cryptocurrencies to the Thai stock market with sectoral variation, while sectors such as industrials and financials exerted significant linkages, and the agricultural and food sector remains unaffected. Additionally, volatility spillovers were predominantly transmitted from the Thai equity market to cryptocurrency. Moreover, asymmetry effects were observed, with the asymmetry effects mainly transmitted from the Thai equity market to cryptocurrency. These findings provide critical insights for both individual and institutional investors on risk management and portfolio diversification while also helping policymakers with guidance on regulatory measures to mitigate systemic risks in emerging financial markets. Full article

Machine learning forecasting methods are compared to more traditional parametric statistical models. This comparison is carried out regarding a number of different situations and settings. A survey of the most used parametric models is given. Machine learning methods, such as convolutional networks, TCNs, LSTM, transformers, random forest, and gradient boosting, are briefly presented. The practical performance of the various methods is analyzed by discussing the results of the Makridakis forecasting competitions (M1–M6). I also look at probability forecasting via GARCH-type modeling for integer time series and continuous models. Furthermore, I briefly comment on entropy as a volatility measure. Cointegration and panels are mentioned. The paper ends with a section on weather forecasting and the potential of machine learning methods in such a context, including the very recent GraphCast and GenCast forecasts. Full article

This study investigates systemic risk, return patterns, and diversification within the Johannesburg Stock Exchange (JSE) during the COVID-19 pandemic, utilizing data-centric approaches and the ARMA-GARCH vine copula-based conditional value-at-risk (CoVaR) model. By comparing three investment strategies—industry sector-based, asset risk–return plot-based, and clustering-based—this research reveals that the industrial and technology sectors show no ARCH effects and remain isolated from other sectors, indicating potential diversification opportunities. Furthermore, the analysis employs C-vine and R-vine copulas, which uncover weak tail dependence among JSE sectors. This finding suggests that significant fluctuations in one sector minimally impact others, thereby highlighting the resilience of the South African economy. Additionally, entropy measures, including Shannon and Tsallis entropy, provide insights into the dynamics and predictability of various portfolios, with results indicating higher volatility in the energy sector and certain clusters. These findings offer valuable guidance for investors and policymakers, emphasizing the need for adaptable risk management strategies, particularly during turbulent periods. Notably, the industrial sector’s low CoVaR values signal stability, encouraging risk-tolerant investors to consider increasing their exposure. In contrast, others may explore diversification and hedging strategies to mitigate risk. Interestingly, the industry sector-based portfolio demonstrates better diversification during the COVID-19 crisis than the other two data-centric portfolios. This portfolio exhibits the highest Tsallis entropy, suggesting it offers the best diversity among the types analyzed, albeit said diversity is still relatively low overall. However, the portfolios based on groups and clusters of sectors show similar levels of diversity and concentration, as indicated by their identical entropy values. Full article

In this paper, we carry out a comprehensive comparison of Gaussian generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive stochastic volatility (ARSV) models for volatility forecasting using the S&P 500 Index. In particular, we investigate their performance using the physical measure (also known as the real-world probability measure) for risk management purposes and risk-neutral measures for derivative pricing purposes. Under the physical measure, after fitting the historical return sequence, we calculate the likelihoods and test the normality for the error terms of these two models. In addition, two robust loss functions, the MSE and QLIKE, are adopted for a comparison of the one-step-ahead volatility forecasts. The empirical results show that the ARSV(1) model outperforms the GARCH(1, 1) model in terms of the in-sample and out-of-sample performance under the physical measure. Under the risk-neutral measure, we explore the in-sample and out-of-sample average option pricing errors of the two models. The results indicate that these two models are considerably close when pricing call options, while the ARSV(1) model is significantly superior to the GARCH(1, 1) model regarding fitting and predicting put option prices. Another finding is that the implied versions of the two models, which parameterize the initial volatility, are not robust for out-of-sample option price predictions. Full article

As China’s financial markets become increasingly integrated and the carbon market undergoes financialization, the impact of carbon emission price fluctuations on financial markets has emerged as a key area of systemic risk research. This study employs the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model and the optimal Copula function to investigate the dynamic correlation between carbon prices and China’s financial markets. Building on this, the Monte Carlo simulation and Copula CoVaR models are used to explore the spillover effects of carbon price volatility on China’s financial markets. The findings reveal the following: (1) Carbon price fluctuations generate spillover effects on all financial markets, but the intensity varies across different markets. The foreign exchange market experiences the strongest spillover effect, followed by the bond market, while the stock and money markets are relatively less affected. (2) The optimal Copula functions differ between the carbon market and China’s financial markets, indicating heterogeneous characteristics across regional markets. (3) There is a degree of interdependence between the carbon market and various sub-markets in China’s financial system. The carbon market has the strongest positive correlation with the commodity market and a relatively high negative correlation with the real estate market. These findings underscore the importance of integrating carbon price volatility into financial risk management frameworks. For policymakers, it highlights the need to consider market stability measures when crafting carbon emission regulations. Market managers can leverage these insights to develop strategies that mitigate risk spillover effects, while investors can use this analysis to inform their portfolio diversification and risk assessment processes. Full article

It is well established that financial development and innovation promote economic growth through improving the allocation of capital, enhancing risk management, contributing to price discovery, and increasing market efficiencies. While a vast empirical literature is devoted to the nexus between financial development and economic growth, however, substantially less research has been done on the relationship between derivatives and growth, especially in the emerging-market context. Derivatives can be viewed as a specific category of financial innovation, which may advance economic growth through its specialised functions of risk management and price discovery. This paper contributes to bridging this gap in the literature by exploring the impact of exchange-traded futures derivatives on South African economic growth, output, and economic growth volatility. It employs ARDL bounds tests, Granger causality tests and GARCH volatility modeling to analyse the effects of exchange-traded futures derivatives on various measures of South African economic activity. The main result is that exchange-traded futures derivatives contribute positively to South African economic growth and economic activity. This may suggest that opportunities might exist in other emerging economies, with financial structures comparable to that of South Africa, to encourage the development of organised and well-regulated derivatives markets to unlock economic growth in these economies. Full article

This paper develops and implements an Autoregressive Integrated Moving Average model with an Adaptive Neuro-Fuzzy Inference System (ARIMA-ANFIS) for BTCUSD price prediction and risk assessment. The goal of these forecasts is to identify patterns from past data and achieve an understanding of the future behavior of the price and its volatility. The proposed ARIMA-ANFIS model is compared with a benchmark ARIMA-GARCH model. To evaluated the adequacy of the models in terms of risk assessment, we compare the confidence intervals of the price and accuracy measures for the testing sample. Additionally, we implement the diebold and Mariano test to compare the accuracy of the two volatility forecasts. The results revealed that each volatility model focuses on different aspects of the data dynamics. The ANFIS model, while effective in certain scenarios, may expose one to unexpected risks due to its underestimation of volatility during turbulent periods. On the other hand, the GARCH(1,1) model, by producing higher volatility estimates, may lead to excessive caution, potentially reducing returns. Full article

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented. Full article

This study rigorously investigates the impact of COVID-19 on Tunisian stock market volatility. The investigation spans from January 2020 to December 2022, employing a GJR-GARCH model, bias-corrected wavelet analysis, and an ARDL approach. Specific variables related to health measures and government interventions are incorporated. The findings highlight that confirmed and death cases contribute significantly to the escalation in TUNINDEX volatility when using both the conditional variance and the realized volatility. Interestingly, aggregate indices related to government interventions exhibit substantial impacts on the realized volatility, indicating a relative resilience of the Tunisian stock market amidst the challenges posed by COVID-19. However, the application of the bias-corrected wavelet analysis yields more subtle outcomes in terms of the correlations of both measures of volatility to the same metrics. Our econometric implications bear on the application of such a technique, as well as on the use of the realized volatility as an accurate measure of the “true” value of volatility. Nevertheless, the measures and actions undertaken by the authorities do not exclude fear and insecurity from investors due to another virus or any other crisis. The positive and long-term impact on the volatility of US equity market uncertainty, VIX, economic policy uncertainty (EPU), and the infectious disease EMV tracker (IDEMV) is obvious through the autoregressive distributed lag model (ARDL). A potential vulnerability of the Tunisian stock market to future shocks is not excluded. Government and stock market authorities should grapple with economic and financial fallout and always instill investor confidence. Importantly, our results put mechanisms such as overreaction to public news and (in)efficient use of information under test. Questioning the accuracy of announcements is then recommended. Full article

Stock market indices are important tools to measure and compare stock market performance. The Selective Stock Price (SSP) index reflects fluctuations in a set value of financial instruments of Santiago de Chile’s stock exchange. Stock indices also reflect volatility linked to high uncertainty or potential investment risk. However, economic shocks are altering volatility. Evidence of long memory in SSP time series also exists, which implies long-term persistence. In this paper, we studied the volatility of SSP time series from January 2010 to September 2023 using fractionally heteroskedastic models. We considered the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) innovations—the ARFIMA-GARCH model—for SSP log returns, and the fractionally integrated GARCH, or FIGARCH model, was compared with a classical GARCH one. The results show that the ARFIMA-GARCH model performs best in terms of volatility fit and predictive quality. This model allows us to obtain a better understanding of the observed volatility and its behavior, which contributes to more effective investment risk management in the stock market. Moreover, the proposed model detects the influence volatility increments of the SSP index linked to external factors that impact the economic outlook, such as China’s economic slowdown in 2012 and the subprime crisis in 2008. Full article

Volatility reflects the degree of variation in a time series, and a measurement of the stock performance in the energy sector can help one understand the pattern of fluctuations within this industry, as well as the factors that influence it. One of these factors could be the COVID-19 pandemic, which led to extreme volatility within the stock market in several economic sectors. It is essential to understand this regime of volatility so that robust financial strategies can be adopted to handle it. This study used stock data from the Yahoo! Finance API and data from the energy-price database from the US Energy Information Administration to conduct a comparative analysis of the volatility in the energy sector in Brazil and in the United States, as well as of the energy prices in California. The volatility in these time series were modeled using GARCH. The stock volatility regimes, both before and after COVID-19, were identified with a Markov switching model; the spillover index between the energy markets in the USA and in Brazil was evaluated with the Diebold–Yilmaz index; and the causality between the energy stock price and the energy prices was measured with the Granger causality test. The findings of this study show that (i) the volatility regime introduced by COVID-19 is still prevalent in Brazil and in the USA, (ii) the changes in the energy market in the US affect the Brazilian market significantly more than the reverse, and (iii) there is a causality relationship between the energy stock markets and the energy prices in California. These results may assist in the achievement of effective regulation and economic planning, while also supporting better market interventions. Also, acknowledging the persistent COVID-19-induced volatility can help with developing strategies for future crisis resilience. Full article