Preface

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.

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.

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.

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,

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.

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.

This paper estimates and compares alternative distribution density forecast methodology of three generalised autoregressive conditional heteroscedasticity (GARCH) models for Botswana and Namibia stock market returns. The symmetric GARCH and asymmetric Glosten Jagannathan and Runkle (GJR) version of GARCH (GJR-GARCH) and exponential GARCH methodology are employed to investigate the effect of stock return volatility in both stock markets using Gaussian, Student-t and generalised error distribution densities. The evidence reveals that the current shocks to the conditional variance will have less impact on future volatility in both markets. News impact is asymmetric in both stock markets leading to the existence of leverage effect in stock returns. Besides, both markets exhibit reverse volatility asymmetry, contradicting the widely accepted theory of volatility asymmetry. Regarding forecasting evaluation, the results reveal that the symmetric GARCH model coupled with fatter-tail distributions present a better out-of-sample forecast for both stock markets.

Speech spectral modeling and enhancement based on autoregressive conditional heteroscedasticity models

Data Driven Value-at-Risk Forecasting Using a SVR-GARCH-KDE Hybrid

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

Nearly 1% of the world population in all ages suffer from epilepsy. An automatic seizure detection system is an important tool, which helps diagnose epilepsy. In this study, a new approach for epileptic detection based on generalised autoregressive conditional heteroscedasticity (GARCH) model is proposed. First, the electroencephalogram (EEG) signals are decomposed into the frequency sub-bands using wavelet transform. To choose an efficient statistical model for EEG signal wavelet coefficients, the statistical characteristics of these coefficients are studied. The authors show that these coefficients are heteroscedastic. To capture this important property, GARCH model, that is, heteroscedastic, is employed for these coefficients. Moreover, the authors show that GARCH model is compatible with other properties of wavelet coefficients such as heavy tail marginal distribution. GARCH parameters are calculated for each sub-band to represent the wavelet coefficients' distribution of EEG signals. These parameters are then utilised for EEG classification. Next, Markov random field is used to feature selection. The features found are then fed to multilayer perceptron classifier with three discrete outputs: healthy volunteers, epilepsy patients during seizure-free interval and epilepsy patients during seizure. The results clearly indicate that the performance of the new method in classification of EEG signals outperforms previous methods.

This paper proposes a two-component realized exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model – an extension of the realized EGARCH model – for the joint modeling of asset returns and realized measures of volatility. The proposed model assumes that the volatility of asset returns consists of two components: a long-run component and a short-run component. The model’s unique ability to capture the long-memory property of volatility distinguishes it from the standard realized EGARCH model. The model is convenient to implement within the framework of maximum likelihood estimation. We apply the two-component realized EGARCH model and a restricted version of the model (the two-component realized EGARCH model with only short-run leverage) to four stock indexes: the Standard & Poor’s 500 index, the Hang Seng index, the Nikkei 225 index and the Deutscher Aktienindex. The empirical study suggests that the two-component realized EGARCH model and its restricted version outperform the realized GARCH model, the realized EGARCH model and the realized heterogeneous autoregressive GARCH model in terms of in-sample fit. Further, an out-of-sample predictive analysis demonstrates that the two-component realized EGARCH model and its restricted version yield more accurate volatility forecasts than the alternatives.

In order to model and forecast exchange rates in both developed and emerging countries, majority of time series analysts have employed various technical and fundamental approaches, the forecast outcome differs depending on the approach chosen or implemented. In this view, this study is about hybridization of Autoregressive Integrated Moving Average (ARIMA) with Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in forecasting exchange rate using monthly data of the Nigerian Naira against the U.S. Dollar for the period of January 2002 to February 2020. The stationarity of the exchange rate series is examined using unit root test of Augmented Dickey Fuller (ADF) test and Kwaitkowski-Philips-Schmidt-Shin (KPSS) which showed that the series is non stationary. To make the exchange rate series stationary, the data was transformed by first differencing and appropriate ARIMA models were obtained using Box-Jenkins method. ARIMA (0,1,1) and ARIMA(0,1,2) models were selected using AIC criteria and the residuals of these models were found to be serially correlated and heteroscedastic; hence the need for the hybridization of ARIMA with GARCH model. Therefore ARIMA models were hybridized with GARCH(1,1) to form ARIMA(0,1,1)-GARCH(1,1) and ARIMA(0,1,2)-GARCH(1,1). The results of forecast performance indicates that the best model is ARIMA(0,1,1)–GARCH(1,1) which has the lowest Root Means Square Error (RMSE) and Mean Absolute Error( MAE).

The objective of this study was to model the behavior of the Current Account Balance of Payments (CAB) for Indonesia. It also calculated the conditional Value at Risk (VaR) as a measure of the risk level of the CAB. An ARDL (Autoregressive Distributed Lag) model and an EGARCH (Exponential Generalized Autoregressive Conditional Heteroskedasticity) model were used to estimate the CAB behavior for the annual data 1985-2018. The research found that exchange rates, growth of gross domestic product, inflation, total reserves, and unemployment are essential in determining the behavior and volatility of the CAB. The VaR calculated based on the conditional standard deviation that resulted from the EGARCH estimation shows that most of the time the Indonesian CAB is in safe conditions. However, the VaR has been violated by the actual CAB several times, and the violations coincide with various macroeconomic shocks. The Central Bank of Indonesia could calculate the VaR threshold using this method to evaluate the risky nature of the current account deficit. This study provides an alternative procedure to analyze and assess the current account balance risk to mitigate the impact of macroeconomic shocks.

This paper collects a total of 541 groups of the RMB exchange rate to build the model of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) for forecasting of RMB exchange rate against US dollar. The empirical results show that the GARCH models can fit the series well and the prediction effects of both the GARCH (1, 1) model and the GARCH-M model are good.