Generalized Autoregressive Conditional Heteroskedasticity Model Research Articles

Forecasting tail risk of skewed financial returns having exponential‐polynomial tails

AbstractAggregated long and short trading risk positions of speculative assets over time are likely to be unequal. This may be because of irrational decisions of traders and investors as well as catastrophic events that lead to pronounce or salient market crashes. Returns of such assets are therefore more likely to have one polynomial tail and one exponential tail. The generalized hyperbolic (GH) skewed Student‐t distribution is known to handle such situations quite well. In this paper, we use generalized autoregressive conditional heteroscedasticity (GARCH) models to empirically show the superiority of the GH skewed Student‐t distribution in forecasting the extreme tail risks of cryptocurrency returns in the presence of substantial skewness in comparison with some competing distributions. Furthermore, we show the practical significance of the GH skewed Student‐t distribution‐based risk forecasts in computing daily capital requirements. Evidence from the study suggests that the GH skewed Student‐t distribution model tends to be superior in forecasting volatility and expected shortfall (ES) but not value‐at‐risk. In addition, the distribution yields higher value‐at‐risk (VaR) exceptions but surprisingly avoids the red zone of the Basel II accord penalty zones and produces lower but optimal daily capital requirements. Therefore, in the presence of substantially skewed returns having exponential‐polynomial tails, we recommend the use of the GH skewed Student‐t distribution for parametric GARCH models in forecasting extreme tail risk.

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.

Online Muscle Activation Onset Detection Using Likelihood of Conditional Heteroskedasticity of Electromyography Signals.

The real-time, accurate detection of muscle activation onset (MAO) is significant for EMG-triggered control strategies in embedded applications like prostheses and exoskeletons. This paper investigates sEMG signals using the generalized autoregressive conditional heteroskedasticity (GARCH) model, focusing on variance. A novel feature, the likelihood of conditional heteroskedasticity (LCH) extracted from the maximum likelihood estimation of GARCH parameters, is proposed. This feature effectively distinguishes signal from noise based on heteroskedasticity, allowing for the detection of MAO through the LCH feature and a basic threshold classifier. For online calculation, the model parameter estimation is simplified, enabling direct calculation of the LCH value using fixed parameters. The proposed method was validated on two open-source datasets and demonstrated superior performance over existing methods. The mean absolute error of onset detection, compared with visual detection results, is approximately 65 ms under online conditions, showcasing high accuracy, universality, and noise insensitivity. The results indicate that the proposed method using the LCH feature from the GARCH model is highly effective for real-time detection of muscle activation onset in sEMG signals. This novel approach shows great potential and possibility for real-world applications, reflecting its superior performance in accuracy, universality, and insensitivity to noise.

Quantitative Assessment and Impact Analysis of Land Surface Deformation in Wuxi Based on PS-InSAR and GARCH Model

Land surface deformation, including subsidence and uplift, has significant impacts on human life and the natural environment. In recent years, the city of Wuxi, China has experienced large-scale surface deformation following the implementation of a groundwater abstraction ban policy in 2005. To accurately measure the regional impacts and understand the underlying mechanisms, we investigated the spatiotemporal characteristics of surface deformation in Wuxi from 2015 to 2023 using 100 Sentinel-1A SAR images and the Persistent Scatterer InSAR (PS-InSAR) technique. The results revealed that surface deformation in Wuxi exhibited significant spatial and temporal variations, with some areas experiencing alternating trends of subsidence and uplift rather than consistent unidirectional change. To uncover the factors influencing this volatility, we conducted a comprehensive analysis focusing on groundwater, precipitation, and soil geology. This study found strong correlations between the groundwater level changes and surface deformation, with the soft soil geology of the area, characterized by alternating layers of sand and clay, further increasing the surface volatility. Moreover, we innovatively applied the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, typically used in financial analyses, to analyze the subsidence displacement time series in Wuxi. Based on this model, we propose a new “Amplitude Factor” index to evaluate overall surface deformation volatility in the city. Our qualitative assessment of surface stability based on the Amplitude Factor was consistent with research findings, demonstrating the accuracy and effectiveness of the proposed model. These results provide valuable insights for urban planning, construction, and safety control, highlighting the importance of continuous monitoring and analysis of surface deformation volatility for the city’s future development and safety.

Decoding herding dynamics in the generative AI investment amid key technological advancements: A timeline perspective

This study, using two herding dynamics metrics and Glosten–Jagannathan–Runkle Generalized Autoregressive Conditional Heteroskedasticity (GJR-GARCH) model, forecasts market trends, captures asymmetric volatility, and reveals the generative AI (GenAI) ecosystem's impact on individual assets’ returns. Results of this study highlight distinctive traits of each GenAI equity, crucial for strategic positioning, especially for investors in tech stocks tied to GenAI. Herding behavior exhibits greater strength in the initial four months post-announcement of ChatGPT, gradually diminishing. GJR-GARCH reports that most of GenAI stocks do not exhibit statistically significant leverage effects. These findings provide valuable insights to navigate the dynamic landscape of GenAI investments.

VIX option pricing through nonaffine GARCH dynamics and semianalytical formula

AbstractThis paper develops analytical approximations for volatility index (VIX) option pricing under nonaffine generalized autoregressive conditional heteroskedasticity (GARCH) models as advocated by Christoffersen et al. We obtain the approximation formulae for pricing VIX options and then evaluate their performance with three expansions under four empirically well‐tested models. Our numerical experiments find that the weighted expansion generated by the fat‐tailed weighting kernel can significantly reduce approximation error over the Gram‐Charlier expansion; the Taylor expansion of conditional moments can lead to divergence for parameters with certain high persistence in the affine GARCH, nonlinear asymmetric GARCH, and Glosten‐Jagannathan‐Runkle GARCH models, while surviving during high persistence in the exponential GARCH.

The volatility of global energy uncertainty: Renewable alternatives

Fluctuations in energy markets affect all economic activities by affecting energy prices and investment decisions. This study is the first attempt to investigate the energy-related uncertainty (volatility) in the world using the newly developed energy-related uncertainty index (EUI). The ARCH (autoregressive conditional heteroskedasticity) and GARCH (generalized autoregressive conditional heteroskedasticity) models are applied for this investigation between 1996 and 2021. The ARCH model reveals that global energy uncertainty is highly volatile, with a coefficient of 0.63. As policy implications, fostering the transition process to renewable energy and a green economy is recommended. The rise of renewable energy can reduce energy dependency and uncertainty in energy markets since they are less sensitive to exogenous shocks and fossil fuel price fluctuations. Understanding this uncertainty helps policymakers develop more effective energy policies, increase energy security and a sustainable environment, and maintain economic stability. The proposal to increase renewable energy in this study also aligns with the United Nation's SDG7 (Affordable and Clean Energy), which aims to improve the share of renewable energy by 2030.

Asymmetric Volatility in Stock Market: Evidence from Selected Export-based Countries

In a country, the financial markets depend on several economic factors. One of these important factors is the export of the country. The stock index of the country tends to be raised due to the exports, though it may occur after some time rather than immediately. In this study, an attempt has been made to predict the best model of volatility in top export countries, Germany, China, the United States, Japan and Hong Kong by taking into account the closing price of the stock index of the sampled countries for a period ranging from the year 2000 to 2020. The returns from the stock markets are asymmetric; negative returns are found to be followed by a greater increase in volatility than the corresponding positive returns. Therefore, both symmetric and asymmetric generalised autoregressive conditional heteroscedasticity (GARCH) models have been applied to predict the volatility. The symmetric model used is GARCH (1,1) and asymmetric models used in the study are exponential GARCH (1,1) and GJR-GARCH (1,1). The study shows that EGARCH model has outperformed the GARCH and GJR-GARCH models in estimating the volatility in four stock indices ( Hanif & Pok, 2010 ; Kışınbay, 2010 ; Lin, 2018 ), and GJR-GARCH has outperformed in estimating volatility in one stock index ( Oberholzer & Venter, 2015 ; Shamiri & Hassan, 2007 ). The benefit of this study is to help portfolio managers, investors and corporations in making investment-related decisions. JEL Codes: C20, C31, C58, G12

Domestic and Global Causes for Exchange Rate Volatility: Evidence From Turkey

Understanding which factors influence exchange rate movements is important for understanding economic development, trade patterns, investment decisions, and for designing economic policies. In this study, we allow for monetary, domestic and global financial variables to assess the relevant importance of each of the variables to exchange rate volatility in the case of Turkey. The paper investigates the dynamics of exchange rate volatility of the Turkish lira in a complementary perspective by employing both Generalized autoregressive conditional heteroskedasticity (GARCH) method and Lyapunov exponents over the period from March 1, 2019 to November 11, 2021. Firstly, decomposing the impact of domestic and global financial variables, the results of the GARCH model indicate that the exchange rate volatility is affected by Volatility index (VIX) and Credit default swaps (CDS). This result suggests that the exchange rate shocks experienced are mainly caused by global factors, therefore policymakers should focus on volatility spillovers caused by global financial markets. Secondly, detected positive maximal Lyapunov exponent shows that complexity in foreign exchange markets has been increased, market expectations lead to multiple-equilibria and diverging volatility eventually will generate recurrent spikes in currency value. These complementary findings have important implications for interventions of Central banks and preventing systemic risks, as well as portfolio and risk management. JEL Classification: C32, G14, G15.

Sovereign Credit Default Swap Market Volatility in BRICS Countries Before and During the COVID-19 Pandemic

SCDS (Sovereign Credit Default Swaps) are becoming more widely used as a country risk indicator after 2008 and stand out for providing real-time information rather than periodic reporting. The COVID-19 pandemic has led to economic disruptions and a decline in international trade. Understanding how the Pandemic affects SCDS return volatility in emerging economies like BRICS forms the motivation for our research. With this study, we aim to determine the impact of the COVID-19 Pandemic on SCDS return volatility in Brazil, Russia, India, China and South Africa, known as the BRICS countries. We used the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model to analyze the data, which consisted of the daily closing price data for SCDS. The date of the first COVID-19 case in each country has been taken as the beginning of the COVID-19 Pandemic in each country. The results of the estimated GARCH models show that the volatility processes of the SCDS return series differ between periods. EGARCH model results indicate that shocks created by news in these countries during the Pandemic have a small and persistent effect on Brazil and Russia's SCDS return volatility, while they have a large and enduring effect on China and South Africa's SCDS return volatility. The findings will guide policymakers and portfolio managers in determining risk management models.

Analysis of China's carbon market price fluctuation and international carbon credit financing mechanism using random forest model.

This study aims to investigate the price changes in the carbon trading market and the development of international carbon credits in-depth. To achieve this goal, operational principles of the international carbon credit financing mechanism are considered, and time series models were employed to forecast carbon trading prices. Specifically, an ARIMA(1,1,1)-GARCH(1,1) model, which combines the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Autoregressive Integrated Moving Average (ARIMA) models, is established. Additionally, a multivariate dynamic regression Autoregressive Integrated Moving Average with Exogenous Inputs (ARIMAX) model is utilized. In tandem with the modeling, a data index system is developed, encompassing various factors that influence carbon market trading prices. The random forest algorithm is then applied for feature selection, effectively identifying features with high scores and eliminating low-score features. The research findings reveal that the ARIMAX Least Absolute Shrinkage and Selection Operator (LASSO) model exhibits high forecasting accuracy for time series data. The model's Mean Squared Error, Root Mean Squared Error, and Mean Absolute Error are reported as 0.022, 0.1344, and 0.1543, respectively, approaching zero and surpassing other evaluation models in predictive accuracy. The goodness of fit for the national carbon market price forecasting model is calculated as 0.9567, indicating that the selected features strongly explain the trading prices of the carbon emission rights market. This study introduces innovation by conducting a comprehensive analysis of multi-dimensional data and leveraging the random forest model to explore non-linear relationships among data. This approach offers a novel solution for investigating the complex relationship between the carbon market and the carbon credit financing mechanism.

THE IMPACT OF THE COVID-19 PANDEMIC AND THE RUSSIAN INVASION OF UKRAINE ON GOLD MARKETS

Purpose – The study examines global Gold market performance and correlations between COVID-19, the Russian invasion, inflation, investors’ fear, asymmetric shocks, and the VIX (volatility index) impact on volatility. Research Methodology – This research uses an econometric approach to analyse the impact of COVID-19 and the Russian invasion on Gold market performance – specifically the ARCH (Autoregressive Conditional Heteroskedasticity) – GARCH (Generalized Autoregressive Conditional Heteroskedasticity) Model and the Threshold-Asymmetric ARCH Model. Findings – The study reveals that the COVID-19 pandemic and the Russian invasion of Ukraine have significantly impacted Gold market dynamics. Inflation significantly impacts volatility, emphasising the need for monitoring inflation rates. Investor fear increases demand during uncertainty periods, while negative shocks have a higher asymmetric effect. The VIX positively affects Gold market volatility, suggesting a perceived safe-haven status during increased volatility. Research Limitations – Gaps in the data related to COVID-19 cases, geopolitical events, and Gold market performance could potentially introduce inaccuracies, biases or limitations to the analysis. Practical Implications – The study’s findings have practical implications for investors, analysts, and policymakers involved in the financial investment of Gold markets. Originality/Value – This study provides new insights into the relationships between inflation, investor fear, asymmetric shocks, and the impact of the VIX on Gold market dynamics during economic and geopolitical uncertainty.

Volatility transmission between upstream and midstream energy sectors

This research studies volatility dynamics of the returns to upstream (exploration and production) and midstream (pipeline and storage) energy (oil and gas) sectors over time and across sectors. We find significant structural breaks in volatility of upstream sector returns possibly triggered by major events, while no breaks are detected in the midstream sector. These results indicate the midstream sector is fairly insulated from major events relative to the upstream sector. Results based on a bivariate generalized ARCH model, which controls for breaks, indicate that the conditional variance of the upstream sector is significantly more affected by midstream volatility than vice versa. This finding could be due to the fundamental difference in functions performed by the midstream and upstream sector firms. These patterns in volatility dynamics have practical significance for financial market participants.

Forecasting volatility of stock indices: Improved GARCH-type models through combined weighted volatility measure and weighted volatility indicators

This paper proposes an unbiased combined weighted (CW) volatility measure and weighted volatility indicators (WVI) that integrates the return- and range-based volatility measures to model the dynamics volatility of stock returns. The main feature of the CW measure is that it is formulated based on the weighted inter- and intra-price information to quantify the volatility directly, while the WVI effectively identifies signals on the shift of volatility. Empirical analysis using five stock indices demonstrates that the CW measure, utilising squared returns in combination with range-based Garman-Klass volatility measure, exhibits the lowest losses based on root mean squared error and quasi-likelihood when compared to 5-minute realised volatility as a proxy for true volatility. Furthermore, we investigate the feasibility of incorporating the CW measure and WVI as the exogenous variable(s) in the generalised autoregressive conditional heteroscedasticity (GARCH)-type models to enhance the forecasting performance. The findings indicate that the GARCH-CW-WVI and EGARCH-CW-WVI models exhibit superior in-sample model fit based on the Akaike information criterion than the existing GARCH and EGARCH models. Moreover, our proposed models also offer the best out-of-sample forecasts evaluated using various loss functions and further tested using Hansen’s model confidence set based on the mean squared error loss. Different risk levels of value-at-risk (VaR) and expected shortfall (ES) forecasts based on GARCH-CW-WVI and EGARCH-CW-WVI models are computed and examined with various backtests to confirm the accuracies of VaR and ES forecasts.

Prediction of volatility and seasonality vegetation by using the GARCH and Holt-Winters models.

Seasonality and volatility of vegetation in the ecosystem are associated with climatic sensitivity, which can have severe consequences for the environment as well as on the social and economic well-being of the nation. Monitoring and forecasting vegetation growth patterns in ecosystems significantly rely on remotely sensed vegetation indices, such as Normalized Difference Vegetation Index (NDVI). A novel integration of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and the Holt-Winters (H-W) models was used to simulate the seasonality and volatility of the three different agro-climatic zones in Jharkhand, India: the central north-eastern, eastern, and south-eastern agro-climatic zones. MODIS Terra Vegetation Indices NDVI data MOD13Q1, from 2001 to 2021, was used to create NDVI time series volatility and seasonality modeled by the GARCH and the H-W models, respectively. GARCH-based Exponential GARCH (EGARCH) [1,1] and Standard GARCH (SGARCH) [1,1] models were used to check the volatility of vegetation growth in three different agro-climatic zones of Jharkhand. The SGARCH [1,1] and EGARCH [1,1] models for the western agro-climatic zone experienced the best indicator as it has maximum likelihood and minimal Schwarz-Bayesian criterion and Akaike information criterion. The seasonality results showed that the additive H-W model showed better results in the eastern agro-climatic zone with the optimized values of MAE (16.49), MAPE (0.49), NSE (0.86), RMSE (0.49), and R2 (0.82) followed by the south-eastern and central north-eastern agro-climatic zones. By utilizing the H-W and GARCH models, the finding demonstrates that vegetation orientation and monitoring seasonality can be predicted using NDVI.

Predicting coal workers' pneumoconiosis trends: Leveraging historical data with the GARCH model in a Chinese Miner Cohort.

Coal workers' pneumoconiosis (CWP) is one of the most common and severe occupational diseases worldwide. The main risk factor of CWP is exposure to respirable mine dust. Prediction theory was widely applied in the prediction of the epidemic. Here, it was used to identify the characteristics of CWP today and the incidence trends of CWP in the future. Eight thousand nine hundred twenty-eight coal workers from a state-owned coal mine were included during the observation period from 1963 to 2014. In observations, the dust concentration gradually decreased over time, and the incidence of tunnels and mine, transportation, and assistance workers showed an overall downward trend. We choose a better prediction model by comparing the prediction effect of the Auto Regression Integrate Moving Average model and Generalized Autoregressive Conditional Heteroskedasticity model. Compared with the Auto Regression Integrate Moving Average model, the Generalized Autoregressive Conditional Heteroskedasticity model has a better prediction effect. Furthermore, the status quo and future trend of coal miners' CWP are still at a high level.

Vine Copula Approach to Understand the Financial Dependence of the Istanbul Stock Exchange Index

AbstractRecently, the complex dependence patterns among various stocks gained more importance. Measuring the dependency structure is critical for investors to manage their portfolio risks. Since the global financial crisis, researchers have been more interested in studying the dynamics of dependency within stock markets by using novel methodologies. This study aims to investigate a Regular-Vine copula approach to estimate the interdependence structure of the Istanbul Stock Exchange index (ISE100). For this purpose, we consider 32 stocks related to 6 sectors belonging to ISE100. To reflect the time-varying impacts of the 2008–2009 global financial crisis, the dependence analysis is conducted over pre-, during-, and post-global financial crisis periods. Portfolio analysis is considered via a rolling window approach to capture the changes in the dependence. We compare the Regular-Vine-based generalized autoregressive conditional heteroskedasticity (GARCH) against the conventional GARCH model with different innovations. Value at risk and expected shortfall risk measures are used to validate the models. Additionally, for the constructed portfolios, return performance is summarized using both Sharpe and Sortino ratios. To test the ability of the considered Regular-Vine approach on ISE100, another evaluation has been done during the COVID-19 pandemic crisis with various parameter settings. The main findings across different risky periods illustrate the suitability of using the Regular-vine GARCH approach to model the complex dependence among stocks in emerging market conditions.

Volatility Spill-Over and Financial Contagion Effect of Conventional Stock on Islamic Equity in Nigeria: Evidence from Covid-19

This study empirically investigated volatility spill-over and financial contagion effect between conventional stocks and shariah compliant equities before and during covid-19 pandemic in Nigeria. Banking and insurance sectoral stocks indices were selected to represent conventional equities while Nigerian stock exchange lotus islamic index represent islamic stocks. Daily closing stock price data from 02-01-2018 to 26-02-2020 for pre-covid and 27-02-2020 to 31-12-2021 for pre-covid and during covid were considered. DCC-GARCH model (Dynamic conditional correlation- Generalized Autoregressive Conditional Heteroskedasticity Model) was deployed to examine the spill-over effect while t-test was applied to check the consistency of the DCC coefficient before and during the pandemic. The result of the multivariate GARCH show that both banking and insurance stocks have long run volatility spillover effect on lotus islamic index, the result also revealed no significant increase in conditional correlation during covid-19 pandemic which indicate absence of financial contagion from the conventional to islamic stocks. The results provide important information to researchers, investors, and policymakers

Asymmetric beta-binomial GARCH models for time series with bounded support

In this paper, we introduce a new class of asymmetric beta-binomial generalized autoregressive conditional heteroscedastic (GARCH) models for bounded integer-valued time series, which can capture the asymmetric impact of positive and negative observations. We study the stationarity conditions of the process and derive the moment and covariance functions. Furthermore, we estimate the unknown parameters using the conditional maximum likelihood (CML) method. The asymptotic properties of the estimators are discussed, as well as their finite-sample performance. Finally, we illustrate the model to real time series data in the field of meteorology.

High-Frequency Volatility Modeling of Chinese Agricultural Products Market Based on Garch-Type Models

The modeling of high-frequency volatility is of utmost importance in comprehending market dynamics and the characteristics of risk. The adoption of high-frequency volatility modeling in the agricultural sector has the potential to enhance risk management for food production enterprises through the utilization of hedging strategies to mitigate the impact of food price changes. The GARCH (Generalized Autoregressive Conditional Heteroskedasticity) class of models is well-suited for the analysis and prediction of volatility in financial time series. These models effectively capture the highest level of volatility observed in the time series data. Therefore, this research utilizes one-minute trade data of the Wind Agriculture Index (886045.WI) to examine the efficacy and predictability of several GARCH class volatility models. When it comes to fitting the data within the sample, the TGARCH model demonstrates superior performance compared to both the GARCH and EGARCH models. The fluctuations in the price changes of the Wind Agriculture Index exhibit characteristics of time variability and clustering, which can be attributed to the relatively low barriers for entry and exit in the agricultural planting sector. Simultaneously, within the agricultural market, an imbalance is observed whereby the influence of positive information on price volatility surpasses that of negative information.