Bayesian Conditional Volatility Models of Skewed Generalized Error Distribution via Mode as the Stable Location Parameter

Global commodity markets, particularly crude oil markets, are inherently characterized by pronounced price volatility driven by geopolitical tensions, macroeconomic shocks, financial speculation, and structural changes in energy demand and supply.Accurately modeling and forecasting such volatility is essential for policymakers, investors, and risk managers seeking to design effective stabilization, hedging, and investment strategies.This study provides a comprehensive empirical investigation of oil price volatility by applying three prominent members of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family-namely the standard GARCH, Threshold GARCH (TGARCH), and Exponential GARCH (EGARCH) models-to monthly West Texas Intermediate (WTI) crude oil prices over the period from January 2008 to June 2024.The selected timeframe captures multiple episodes of extreme market turbulence, including the global financial crisis, oil price collapses, the COVID-19 pandemic, and recent geopolitical disruptions.The analysis proceeds through a structured econometric methodology, beginning with the transformation of price levels into return series, followed by stationarity testing, descriptive statistical analysis, and volatility modeling.Empirical results reveal strong volatility clustering and persistence in WTI oil returns, confirming the suitability of GARCH-type models for capturing oil price dynamics.While asymmetric specifications (TGARCH and EGARCH) provide valuable insights into the differential effects of positive and negative shocks, the findings indicate that the GARCH(1,1) model offers the most 207 -www.imcra.az.org,

Forecasting stock market volatility is an important and challenging task for both academic researchers and business practitioners. The recent trend to improve the prediction accuracy is to combine individual forecasts using a simple average or weighted average where the weight reflects the inverse of the prediction error. However, a problem in the existing forecast combination methods is that the weights remain fixed over time. This may prove inadequate, especially in economics data, where changes in policy regimes may induce structural change in the pattern of forecast errors of the different models, thereby altering the relative effectiveness of each model over time. In this paper, we present a new forecast combination approach where the forecasting results of the Generalized Autoregressive Conditional Heteroskedastic (GARCH), the Exponential GARCH (EGARCH), stochastic volatility(SV), and Moving average(MAV) models are combined based on time-varying weights that can be driven by regime switching in a latent state variable. The results of an empirical study indicate that the proposed method has a better accuracy than the GARCH, EGARCH, SV and MAV models, and also combining forecast methods with constant weights.KeywordsCombining forecastsGARCHStochastic volatilityRegime switchingStock market volatility

The Indonesian Sharia stock market has experienced significant growth over the past year, accompanied by an increase in market capitalization. However, high volatility remains a critical challenge for investors when deciding to invest in Sharia stocks. Modeling Sharia stock return volatility is essential to help investors minimize investment risks. This study aims to identify the most effective model for measuring volatility in the Sharia stock market by comparing classical models such as Generalized Autoregressive Conditional Heteroscedasticity (GARCH), asymmetric models including Exponential GARCH (EGARCH), Threshold GARCH (TGARCH), and Asymmetric Power GARCH (APGARCH), along with the Markov Switching GARCH (MSGARCH) and a Bayesian MSGARCH model that incorporates structural regime changes. The results indicate that the Bayesian MSGARCH model outperforms the other models in capturing the volatility of the Jakarta Islamic Index Sharia stock returns, achieving the lowest prediction error and improved accuracy in parameter estimation. Moreover, the study reveals that investment activities influence the volatility structure during periods of market appreciation and depreciation, with identifiable durations, thereby providing valuable insights for the formulation of effective investment strategies.

Stock is an investment in the capital market that is very promising for investors. Investors can also get high returns from the shares invested. However, this stock price is not always stable, it can go up and down drastically. The purpose of this study is to predict stock prices because they often experience instability. The method used in this research is using the Exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model with the Quasi Maximum Likelihood (QML) method. The result of this research is the implementation of this model. The EGARCH model used is the stock price index model that is formed, namely the autoregressive integrated moving average (ARIMA) (0, 1, 2) EGARCH (1.4). The conclusion from the results of the research that predictions using the ARIMA model (0, 1, 2) EGARCH (1, 4) is the best model in accommodating the asymmetric nature of the volatility of the stock price index. The results of this egarch model show more optimal prediction results seen from an error of 3% compared to other modes such as the arch model and the GARCH model.

This study examines the relationship between investor sentiment and stock market volatility in the West African Economic and Monetary Union (WAEMU) using data from the West African Regional Stock Exchange (BRVM). Based on daily data spanning the period 2010–2022, five volatility models are estimated and compared: Generalized Autoregressive Conditional Heteroskedasticity [GARCH(1,1)], Exponential Generalized Autoregressive Conditional Heteroskedasticity [EGARCH(1,1)], Asymmetric Power ARCH [APARCH(1,1)], Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity [FIGARCH(1,d,1)] and the RiskMetrics model. The empirical results indicate a high degree of volatility persistence, pronounced asymmetric effects, and the presence of long-memory dynamics in BRVM stock returns. Among the competing specifications, the EGARCH model with an asymmetric Student’s t distribution provides the best overall performance in terms of model fit and forecasting accuracy. Furthermore, the inclusion of an investor sentiment index leads to an improvement in volatility forecasts, highlighting the relevance of behavioral factors in explaining market risk dynamics. These findings suggest that investor sentiment plays an important role in volatility dynamics in emerging African stock markets, while also underscoring the need for caution in interpreting sentiment-based measures due to potential methodological limitations.

Revisiting volatility in global natural resources commodities? Evidence from global data

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

The objective of this article is to examine the impact of stock index futures on stock markets. Of particular interest is the evidence for change in overall volatility and liquidity after the introduction of stock index futures. The impact of derivatives trading on price volatility in the underlying spot market return is examined using the exponential GARCH (EGARCH) model which was proposed by Nelson (1991). Our empirical findings support the view that introducing futures trading decreases volatility in the spot market and the speed with which market information is reflected in spot market prices. However, volatility persistence increased in the post-futures period. In the light of these findings it can be said that the speed and nature of information differ between pre-futures period and post-futures period. JEL Classification : G13, G14, G32 Keywords : Futures Markets, Spot Markets, Volatility, GARCH Models, Emerging Markets DOI : 10.7176/RJFA/10-2-07

There is a strong connection between the Federal Reserve’s monetary policy and the trend of international food prices. Employing the average information share model, EGARCH(Exponential Generalized Autoregressive Conditional Heteroskedasticity), and DCC-MGARCH(Dynamic Conditional Correlation-Multivariate Generalized Autoregressive Conditional Heteroskedasticity) models, this study investigates the relationship between the U.S. dollar index, international grain futures prices, and spot prices in the context of Federal Reserve monetary policy adjustments from 2000 to 2023. The findings reveal that, first, under conditions of long-run cointegration, the U.S. dollar index exerts a strong pricing influence over international grain futures, while grain futures demonstrate a significant price discovery function over spot prices. Second, both international grain futures and spot markets exhibit asymmetric volatility, with price increases being more pronounced than decreases in response to external shocks. Additionally, the U.S. dollar index has a unidirectional and inverse influence on grain futures prices, while futures and spot prices interact bidirectionally and move in the same direction. This paper contributes to understanding the impact of Federal Reserve monetary policy adjustments on international food prices and offers policy insights for countries to manage food import risks and maintain price stability.

PurposeThis study investigates the effect of unproven energy reserve news on the volatility of energy firms' stocks. Thus, investors' perception of unproven energy reserves is revealed. Additionally, the study aims to determine whether the effect of the news changes according to time and volatility level.Design/methodology/approachThe general autoregressive conditional heteroskedasticity (GARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models consist of the energy reserve exploration news in Turkey for the period 2009–2022 and the volatility of 14 energy stocks.FindingsThe results indicate energy exploration news's negative and significant effect on volatility. According to empirical results, energy stock volatility is most affected in the first ten days. Besides, the results show that the significant models of energy reserve news in low-volatility stocks are proportionally higher than in high-volatility stocks.Research limitations/implicationsOnly unproved reserve news is included in the analysis, as sufficient confirmed reserves could not be reached during the sampling period. Further studies can compare proven and unproved reserve news effects. Additionally, a similar analysis can be conducted between Turkey and another country with a similar socio-economic character to examine different investor behaviors.Practical implicationsThis research includes indications on managing investors' reactions to unproven energy reserve news.Originality/valueThis study contributes to the literature by analyzing unproven reserves. Contrary to previous studies, examining stock volatility also makes the study unique.

Over the past decade, Malaysia’s Islamic capital market is emerging in achieving a total worth of 1.9 million or 61 percent of the overall Malaysian capital market as per December 2018. The establishment of Islamic Real Estate Investment Trust (REIT) gained a demand from investors in the Islamic capital market that claims to be a safe investment as it attached to the real estate to generate the source of income. Nevertheless, the Islamic REITs are structured and operating in accordance with the Shariah principle laid out by the Malaysia securities commission, as it is beneficial to the potential investors given its high liquidity and diversification opportunity compared to investing in physical property. In addition, although Islamic REIT is deemed to have a stable return given the real estate portfolio, there is still risk inherent such as an impact of the external forces. Therefore, the impact of macroeconomic factors shocks towards Islamic REITs is significant to the investors, policy makers and government to outline their relationship and facilitate their future growth. However, the evidence published on the listed Islamic REITs stock return in Malaysia is very limited and has seldom been modelled. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model employed in this study to analyze the Islamic REIT stock return. The empirical finding show that the Islamic REITs exhibit an unstable behavior and volatility would take a longer time to respond to a shock in the market. Nevertheless, the magnitude of changes in price level of Islamic REITs tends to be greater in responding to new market information. Furthermore, it points out that the leverage effect of all the macroeconomic shocks towards Axis REIT and mix macroeconomic finding leverage effect for Aqar REIT and KLCC REIT in Malaysia. Nutshell, this study provides a discussion of Islamic finance to set a basis for Malaysian Islamic REIT, the regulatory framework, and conceptual model property trust funds in Malaysia.

Finding low-dimensional chaos is a relevant issue as it could allow short-term reliable forecasting. However, the existence of chaos in shipping freight rates remains an open and outstanding matter as previous research used methodology that can produce misleading results. Using daily data, this paper aims to unveil the nonlinear dynamics of the Baltic Dry Index that has been proposed as a measure of the shipping rates for certain raw materials. We tested for the existence of nonlinearity and low-dimensional chaos. We have also examined the chaotic dynamics throughout three sub-sampling periods, which have been determined by the volatility pattern of the series. For this purpose, from a comprehensive view we apply several metric and topological techniques, including the most suitable methods for noisy time series analysis. The proposed methodology considers the characteristics of chaotic time series, such as nonlinearity, determinism, sensitivity to initial conditions, fractal dimension and recurrence. Although there is strong evidence of a nonlinear structure, a chaotic and, therefore, deterministic behavior cannot be assumed during the whole or the three periods considered. Our findings indicate that the generalized autoregressive conditional heteroscedastic (GARCH) model and exponential GARCH (EGARCH) model explain a significant part of the nonlinear structure that is found in the dry bulk shipping freight market.

Many empirical studies have analysed the effect of good news and bad news on equity market return volatility using both developed and emerging markets data, with scant literature for frontier stock markets. This study evaluates how news affects stock market return volatility in a frontier market using Uganda data. It specifically analyses the reaction of stock return volatility to news filtering into a frontier market using the exponential generalized autoregressive conditional heteroscedasticity (GARCH) model on daily data ranging from 1 September 2011 to 31 December 2017. Estimates of the shape parameter from generalized error distribution indicate the existence of leptokurtic return distribution. Results from the exponential GARCH model show that the effect of bad news and good news on the frontier market return volatility differs, thus suggesting existence of leverage effect in the period studied. Overall results from the study suggest that positive news impacts stock market returns volatility more than negative news of the same magnitude. An important implication of our results is that investors, analysts, brokers and dealers should be conscious of the nature of news filtering into the stock market as such information might improve their expected volatility forecast.

This book introduces empirical methods for analyzing energy markets. Even beginners in econometrics and mathematical finance must be able to learn how to utilize these methodologies and how to interpret the analysis results. This book provides some example analyses of the North American, European, and Asian energy markets. The reader will experience some theories and practices of energy trading and risk management. This book reveals the characteristics of energy markets using quantitative analyses. Examples include unit root, cointegration, long-term equilibrium, stochastic arbitrage simulation, multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models, exponential GARCH (EGARCH) models, optimal hedge ratio, copula, value-at-risk (VaR), expected shortfall, vector autoregressive (VAR) models, vector moving average (VMA) models, connectedness, and frequency decomposition. This book is suitable for people interested in the empirical study of energy markets and trade.KeywordsEnergy marketEnergy tradingRisk managementArbitrageRisk measurement

A large body of research suggests that the conditional volatility of asset prices displays long-memory or long-range persistence. Furthermore, as we demonstrate below, this type of persistence cannot be appropriately modelled by autoregressive conditional heteroskedastic (ARCH), generalized ARCH (GARCH), exponential GARCH (EGARCH) or standard (short-memory) stochastic volatility .models.