GARCH Research Articles

Forecasting the Volatility of CSI 300 Index with a Hybrid Model of LSTM and Multiple GARCH Models

Forecasting the Volatility of CSI 300 Index with a Hybrid Model of LSTM and Multiple GARCH Models

Searching for safe haven assets against American and European stocks during the Russo-Ukrainian War

Purpose This study aims to evaluate the safe haven property of several assets against the US and European stock markets during the Russo-Ukrainian War in a time–frequency framework. Design/methodology/approach This study uses the wavelet-based dynamic conditional correlation-generalized autoregressive conditional heteroskedasticity (DCC-GARCH) methodology and wavelet coherence on daily returns for the S&P500, STOXX600 and 13 possible save haven assets. Findings The results show that wheat and corn are the best assets to use as hedges and safe havens for all types of investors. The second-ranked are energy commodities, which are hedges and safe havens for long-term investors. Gold, silver and palladium display hedging and safe haven qualities for medium- and long-term investment. However, cryptocurrencies, the Dow Jones sustainability index and Islamic indices do not act as safe havens for most holding periods. Practical implications These findings have significant implications for portfolio investment strategies in times of geopolitical risks. Originality/value The contributions of this study are twofold. First, several assets from different classes were analyzed as possible candidates for safe havens. Second, to the best of the authors’ knowledge, this is the first study to analyze safe haven property through different investment horizons for the US and the European stock market indices during the Russo-Ukrainian War.

A Comprehensive Study of Stock Market Volatility: Types, Determinants, and Measurement Methods

The Volatility, a critical aspect of financial markets, quantifies the uncertainty associated with asset price movements. This paper provides a comprehensive review of volatility, encompassing its definition, types, determinants, and measurement methods. Various factors, including macroeconomic indicators, market sentiment, liquidity, global events, and corporate actions, influence volatility. A range of methods, such as standard deviation, historical volatility, implied volatility, GARCH models, EWMA, and range-based volatility, are employed to measure volatility. Understanding volatility is essential for investors, traders, and risk managers to make informed decisions and manage risk effectively. Future research can delve into advanced volatility models, volatility spillovers, investor behavior, and the relationship between volatility and asset pricing.

Long-Run Volatility Memory Dynamics and Inter-Market Linkages in GCC Equity Markets: Application of DCC-FIGARCH Models

Abstract The study investigates volatility persistence, long-term memory and time-varying conditional correlations among the stock markets of the Gulf Cooperation Council (GCC) countries. Daily equity index data between 2012 and 2024 were analyzed using univariate fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) models to examine long-memory behavior and multivariate dynamic conditional correlation (DCC) models to assess conditional correlations between these markets. For each of the GCC equity markets, the analysis highlighted large degrees of long-memory and volatility persistence. Finally, the DCC model shows that strong and dynamic Intermarket links among the GCC, especially between KSA and UAE, exist and reflect significant volatility spillover from good economic ties. This study fills the gap in the literature by providing a comprehensive understanding of long-run volatility memory and inter-market associations in the GCC stock markets.

The GARCH-EVT-Copula Approach to Investigating Dependence and Quantifying Risk in a Portfolio of Bitcoin and the South African Rand

This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α=1.007, implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio’s diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure.

Intrados FRCM-strengthening of a masonry bridge: Experimental and analytical investigations

This paper will present the results of an experimental campaign aimed to study the structural behavior of solid clay brick masonry arch models strengthened at the intrados with Fiber Reinforced Cementitious Matrix (FRCM). The arch models’ peculiarities are: i) the presence of the haunching made of hydraulic lime mortar-based conglomerate, and ii) the geometry that reproduces a 1:2 scaled longitudinal section of a typical Italian railway single span bridge. The arch models are tested, imposing loading-unloading cycles to analyze the effectiveness of the strengthening system. The results are expressed in terms of failure mode, load carrying capacity and ductility, which shows the increase in the strength and displacement capacity of the strengthened model. Finally, limit analysis was performed to validate the experimental results and to assess the maximum fiber strain and the corresponding stress at the peak load.

Low-carbon economic optimization strategy for industrial loads in parks considering source-load-price multivariate uncertainty

A low-carbon economic optimization method is proposed for industrial loads in parks considering multivariate uncertainty. Model of dynamic load node carbon intensity is proposed considering the uncertainty of clean energy and dynamic conventional units carbon intensity based on system currents. The robustness is improved based on multi-interval uncertainty set. The gap is filled by hybrid copula model with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) prices in the uncertainty model. The GARCH is used to built the marginal distribution function of prices, and a hybrid copula model is proposed to obtain the joint probability density function based on the weights calculated by Euclidean distance. The LNCI probability distributions of the regulation potential of loads are proposed with the virtual energy storage and the virtual power model to improve the descriptive ability of uncertainty based on the expansion and contraction functions. Finally, the typical scenarios are extracted based on Monte Carlo and Wasserstein measures. The Column sum Constraint Generation algorithm and strong duality theory are used to get the robust-stochastic optimization. The method proposed in the paper has a positive effect on enterprises to rationalize their production schedules, reduce electricity and carbon emissions costs and increase the revenue from participating in grid regulation.

Predicting Portfolios Using Fuzzy Logic and Optimization Techniques: A Case Study of BSE-IT Listed Companies

Stock price trends were considered in this study, the companies in the BSE-IT index, with a view to optimizing portfolio allocation based on risk tolerance. The GARCH model has been applied here to allow an investigation into the volatility of the stock returns and to set up different clusters using K-Means clustering that group together companies owning the same attributes related to volatility for strategic classification. Data collection and processing occur between April 1, 2014, and March 31, 2024, for reasons of reliability and relevance. Descriptive statistics report on the variance of stock performance across companies; different risk-return profiles are thus exposed. The GARCH model measures each stock's long-term variance, along with sensitivity to past shocks, and overall volatility persistence, making this an excellent inventory for risk assessment. K-Means clustering groups companies based on similar volatility patterns, thereby informing portfolio construction. Findings present how clustering with econometric modeling may assist in the production of optimal portfolios that depend on specified risk capacities, thus efficiently managing and implementing an IT investment strategy.

Analytic Moments of TGARCH(1,1) Models with Polynomially Adjusted Densities

Abstract This article extends He, Silvennoinen, and Teräsvirta (2008, J Finan Econ, 6, 208–230) and Francq and Zakoïan (2010, GARCH Models) by providing analytical expressions for the moments of the unconditional distribution of the TGARCH(1,1) under alternative specifications for the conditional mean and different skewed distributions for the innovations. We consider polynomially adjusted (PA) densities, such as the PA Logistic, PA hyperbolic secant, and the PA Gaussian, along with the skewed Student-t. Our results show that (i) the main driver of the skewness of the TGARCH(1,1) is the skewness of the innovations, while the excess kurtosis has a comparatively lesser impact. However, both skewness and kurtosis of the innovations significantly affect the TGARCH(1,1) kurtosis; (ii) if the conditional mean is not constant, returns can be asymmetric even if innovations are symmetric; (iii) skewed innovations can generate cross-correlations different from zero, indicating leverage effect, even when the volatility model is symmetric. Finally, we illustrate our theoretical results with an empirical application to stock indices.

Dynamic analysis and application of network structure control in risk conduction in the industrial chain

According to control theory, a dynamical system is controllable if, with a suitable choice of inputs, it can be driven from any initial state to any desired final state within a finite time. Most dynamic characteristics of real networks are nonlinear, so achieving target control is more practical and necessary. The network’s control energy is also a problem that must be considered. Whether and how to control the complex system of the industrial chain has high theoretical and practical significance. In this study, we use the GARCH model, DCC model, and network structure control theory comprehensively to study the price fluctuation risk of the mining stock market from the perspective of the industry chain and network control dynamics and obtain interesting results. (1) Risk conduction among stocks has a prominent industry-driving effect, and the risk conduction ability of upper and middle stocks is stronger. (2) The risk regulation cost, time cost, and node number cost of the whole-industry chain are all higher than those of the two-tier chain, which indicates that the correlation complexity of the network has a positive relationship with risk control. (3) Key risk nodes play an essential role in risk control, so monitoring key stocks from the industrial chain perspective is necessary to control risks in time. This work can provide valuable suggestions for market regulators and policy-makers in terms of risk management and control.

Influence of political stability on the stock market returns and volatility: GARCH and EGARCH approach

Political instability has increased drastically in Pakistan during the last few decades. This may intensify the fear of investors and eventually affect investment decisions. Therefore, the stock market’s reaction to political stability must be explored and appropriate policy measures should be prescribed. This paper examines the effect of political stability on stock market returns and volatility using time series data from Pakistan for the period from January 02, 2004, to May 31, 2018. The study uses the Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential Generalized Autoregressive Conditional Heteroskedastic (EGARCH) models to achieve the main objectives. The findings of the GARCH and EGARCH models confirm that political stability has a positive and significant influence on both stock market returns and volatility in Pakistan. In addition, the EGARCH findings indicate that negative shock (political instability) creates more volatility in the stock market than positive shock (political stability). The results of this study reveal that financial market investors are affected more by political instability. In conclusion, this study suggests that political stability is an essential factor affecting financial market volatility, and it leads to stable financial markets. It also emphasizes that political instability needs to be resolved to achieve stable financial markets.

Asymmetric Effects and Volatility Clustering in NSE NIFTY 50: A Comparative Analysis of GARCH Models

This study aims to analyze the volatility patterns, Clustering, and asymmetric effects in the NSE NIFTY 50 index. It involves using daily returns data from the NSE NIFTY 50 from 01 Jan 2010 to 31 Dec 2023. Daily closing prices are obtained from the official NSE website, and returns are calculated based on these prices. EGARCH (1, 1), TARCH (1, 1), GARCH (1, 1), GARCH-M (1,1), and models are utilized to predict volatility, capturing volatility clustering and leverage effects. Using both the Akaike and Schwarz criteria, EGARCH (1,1) was demonstrated to be the best model. The findings reveal that Fluctuations in the Indian stock market, particularly shown in the NIFTY index of the NSE were the highest in the year 2020 due to the COVID-19 pandemic. Past NIFTY returns demonstrate a GARCH effect on today’s NIFTY returns. The results of the research suggest that the impact of negative and positive shocks on the stock returns series varies. Volatility is largely caused by negative news compared to positive news. It is suggested that the model exhibits a leverage effect and that different types of information produce various types of shock to the volatility of the Nifty index return. The findings show that investors of NSE, particularly those involved with the NIFTY50, face heightened volatility and increased risk, especially during periods of significant events.

The shifted GARCH model with affine variance: Applications in pricing

This paper introduces a modification to the affine GARCH model of Heston and Nandi (2000). The new model is designed to allow for a non-zero lower bound for the variance achieved by adding two parameters to the existing model. The affine structure of the moment-generating function is preserved at the level of variance, while an approximation is studied for log prices. The construction resembles the shifted continuous-time Heston (1993) model. Maximum likelihood estimation is performed on real data, and the model is shown to improve the fitting of the implied volatility surface, particularly for deep out-of-the-money options.

A long short-term memory enhanced realized conditional heteroskedasticity model

This paper examines the potential of using realized volatility measures for capturing financial markets’ uncertainty. Earlier studies show the usefulness of the high-frequency data based Generalized AutoRegressive Conditional Heteroskedasticity (RealGARCH) model for enhancing volatility forecasting accuracy; however, this model focuses only on linear and short-term dependencies of realized volatility measures on the underlying volatility. Recognizing the critical economic implications of this limitation, the long short-term memory neural network is integrated into RealGARCH, aiming to explore the full impact of realized volatility on volatility modeling and forecasting via capturing the nonlinear and long-term effects. A comprehensive empirical study using 31 indices from 2004 to 2021 is conducted. The results demonstrate that our proposed framework achieves superior in-sample and out-of-sample performance compared to several benchmark models. Importantly, it retains interpretability and effectively adapts to the stylized facts observed in volatility, emphasizing its significant potential for enhancing economic decision-making and risk management.

Nonlinear simultaneous resonance behaviors of a shallow arch model under the moving load

By applying a moving load with the uniform velocity, this paper investigates nonlinear behaviors of a shallow arch model allowing for describing the effects of the initial configuration of the structure. Two different cases are taken into account, namely, simultaneous primary resonances of the first and third modes; simultaneous resonances of the first mode for two-term excitations. First, nonlinear ordinary differential equations (ODEs) of the shallow arch are derived by using Galerkin method. Through introducing different time scales, the ODEs are solved based on the widely utilized method of multiple time scales (MMTS). In this way, the modulation equations for the two cases are derived, on the basis of which the steady state frequency- and force-response curves are obtained. Meanwhile, phase portraits, power spectra and two-parameter bifurcation diagram are also given to assist in analysis on nonlinear behaviors. The results show that the large vibration of the shallow arch under the moving load may occur and primary resonance peaks of the different modes are located in distinct positions.

FORECAST ACCURACIES OF HYBRID OF BILINEAR AND EXPONENTIAL SMOOTH TRANSITION AUTOREGRESSIVE MODELS WITH GARCH MODELS

The study looks at the forecast accuracies of GARCH and Bilinear models on the one hand, and hybrids of Bilnear with GARCH (BL-GARCH) and ESTAR with GARCH (ESTAR-GARCH) models on the other hand. Necessary mathematical or theoretical frameworks were set up for the four models and were illustrated with inflation rate data from Nigeria (1994–2019). Stationarity tests conducted (Unit Root Test) show that at level (original data) the series is chaotic and volatile (non-stationary), but at the first difference the series is stationary. This, therefore, paved the way for the analysis. In and out of sample, the forecast accuracies of all the models used were checked and compared. Information criteria such as AIC, BIC, and FPE were used, where it was seen that ESTAR-GARCH performs best. Also, the performance measure indices used revealed that ESTAR-GARCH was very outstanding. The same goes for variance analysis (ESTAR-GARCH had the least variance). The results show that the two hybrid models give exceptional performances; also, the GARCH model's performance is fairly good but not comparable to the hybrids. Exponential GARCH models perform better than Bilnear-GARCH models and GARCH models. However, the ESTAR-GARCH and BL-GARCH models are comparable and could be interchangeably used by would-be forecasters, investors, academia, and other would-be users.

Heterogeneous Responses of Energy and Non-Energy Assets to Crises in Commodity Markets

In this study, we investigate the heterogeneity in energy and non-energy commodities by analyzing their four realized moments: returns, realized volatility, realized skewness and realized kurtosis. Utilizing monthly data, we examine two commodity categories over various crisis periods. This study examines a comparative approach to descriptive statistics across different crisis periods and the full sample and assesses the out-of-sample significance of heteroscedasticity using GARCH models. The findings reveal significant heterogeneity in both energy and non-energy commodities, with energy commodities exhibiting higher average returns and volatility. Crisis periods markedly influence the statistical properties of these commodities. GARCH models outperform ARMA models in forecasting realized moments, particularly for non-energy commodities. This research contributes to the literature by providing robust evidence of heterogeneity in commodity markets and highlights the importance of considering all four realized moments in such analyses.

Bayesian Modeling of INGARCHX Models for Cellulitis Related to Meteorological Factors in Mahasarakham and Roi-Et HospitalsMahasarakham and Roi-Et Hospitals

The objective of this research is to develop integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models to represent the weekly incidence of cellulitis cases in relation to two exogenous variables: seasonality and the weekly average of either relative humidity or maximum temperature. The key to the proposed model is its capacity to explain overdispersion and lag dependence. For predictions and model parameters, we employ the Bayesian Markov Chain Monte Carlo (MCMC) approach, as supported by both a simulation study and an empirical study. To assess different models, we apply the deviance information criterion (DIC) criterion to the weekly cellulitis case sample data with two independent variables. In addition, we offer a one-week prediction to help Mahasarakham and Roi-Et Hospitals manage the increasing volume of hospital admissions by estimating the weekly cellulitis case incidence rate.

Forecasting stock index closing points using ARIMA-GARCH with a rolling data window

This research develops and examines the efficacy of a hybrid ARIMA-GARCH model, augmented by a rolling data window approach, to enhance the accuracy of stock index prediction, specifically focusing on the NEPSE index. Accurate predictions of stock indices are of paramount importance to investors, analysts and policy makers to navigate and circumvent the market uncertainties. The AutoRegressive Integrated Moving Average (ARIMA) model captures linear trends and temporal dependencies in time series data, while the General AutoRegressive Conditional Heteroskedasticity (GARCH) model addresses volatility clustering—ubiquitous character of financial time series—thereby providing a comprehensive framework for prediction. Utilizing a dataset comprised of daily closing points of NEPSE index approximately three years and nine months, the study identifies the ARIMA (5,1,0)-GARCH (1,1) model as optimal fit, upon integrating 180-day rolling data window. This model achieved a Mean Percentage Error of -0.0058% and a correlation of 0.995, which is indicative of superior fit to the underlying time series data. These findings underscore the hybrid model’s capacity to adaptively respond to dynamic market conditions and acclimatize prediction parallel to most recent market trends and volatility. This research is useful for optimizing investment strategies for those invested in Nepalese stocks. Also, this research lays a foundational framework for future investigations into application of this advanced forecasting method in other emerging markets, financial instruments and indices.

Methodological insights regarding the impact of COVID-19 dataset on stock market performance in African countries: A computational analysis

This research aims to evaluate the impact of the COVID-19 pandemic on stock markets in Africa. The study analyzes the stock market returns in nine selected African countries (South Africa, Morocco, Tunisia, Botswana, Nigeria, Uganda, Kenya, Mauritius, and Tanzania) before, during, and after the COVID-19 pandemic. We investigate the impact of COVID-19 on stock market returns and the effect of the worst-hit country's volatility on other African countries' stock market returns utilizing autoregressive conditional heteroscedasticity (ARCH), generalized ARCH (GARCH), and threshold ARCH (TARCH) tests. Additionally, we explore the implications for foreign investors in terms of portfolio diversification and risk management, contributing to the existing literature on the effects of the COVID-19 crisis on financial markets and investment risk. Thereby, we provide insights into African stock markets' interconnectedness and help foreign investors reduce their losses and manage risks associated with the COVID-19 pandemic. Finally, we discuss the need for further research.