GARCH Research Articles

A Bayesian non-stationary heteroskedastic time series model for multivariate critical care data.

We propose a multivariate GARCH model for non-stationary health time series by modifying the observation-level variance of the standard state space model. The proposed model provides an intuitive and novel way of dealing with heteroskedastic data using the conditional nature of state-space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. We use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution of the latent state. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data and analyze a data set obtained from an intensive care unit in a Montreal hospital and the MIMIC dataset. We further show that our proposed models offer better performance, in terms of WAIC than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non-stationary time series data. Model comparison can then be easily performed using the WAIC.

A Classical Modernization of the V‐Model

AbstractThis paper provides new iconography for the Systems Engineering “V‐Model” or “Vee‐Model.” The “Arch Model” resets and refreshes the original iterative intent of the “V‐Model” in a modern context integrated with digital engineering (DE). We will highlight common misperceptions that reduced the efficacy of the “V‐Model” and explore how a “classical Roman engineering” metaphor can inspire a modern view of systems development based on historically successful, foundational engineering.

Contagion and interdependencies between BRICS-plus Countries on the Markets of Commodities and Derivative Financial Instruments

Purpose: This study was started on the main macroeconomic data (2010-2019), coming from the countries of the BRICS-plus group. While a significant contribution of these emerging economies to global economic output has generally been observed, this has also been accompanied by persistent domestic imbalance. Design/Methodology/Approach: Regarding the model, we state and contextualize the (long-term) risk co-incidence of the set of macroeconomic variables for this coalition of countries. Particular attention was paid to a valuation, description and forecasting model based on the calculation of the Dynamic Conditional Correlation (DCC) in a Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) process on the time series of credit default swaps (CDS). Findings: The empirical analysis and calculations carried out have verified the significance of the parameters and confirmed the conditional dynamic correlation between the economies of the Brics “expanded”, especially in the presence of shocks, which also involve mutual contagion (temporary increase in DCC) and even interdependence (increasing DCC leads to new, less unstable levels). Implications/Originality/Value: The research offers a look at the most current trends in terms of international economic balances and the entire global system, focusing on commodity markets, financial derivatives and the impacts of trade at the dawn of the new BRICS-plus coalition.

Modelling Asymmetric Volatility in the Crypto Currency and its Dynamic Relationship with Stock Market

The paper investigates the asymmetric volatility effect of five major cryptocur- rencies and their bilateral linkages with major indices in the Indian stock market. To inves- tigate the bilateral relationship of crypto currency with stock indices, researchers used two major stock indices in the Indian stock market namely, BSE Sensex and NSE Nifty. The study used GARCH, EGARCH and TGARCH models, asymmetric to model the asymmetric volatility effect in the conditional volatility of crypto currencies and stock indices. Johansen’s cointegration and Vector Error Correction Model is used for examining the presence of cointe- gration between selected variables and to analyse the strength of causality among them. The study finds the evidence of cointegration between cryptocurrencies and stock market indices, implying that cryptocurrencies are related to stock indices. Further there is unidirectional relationship among stock and crypto market and crypto currencies having short-lived re- sponse to shocks in stock markets. Even with these currencies’ explosive growth, there are still not many research examining their connection to stock markets. This study will help investor’s those who making investment in currency market or in the stock market to eval- uate the pattern of volatility, interconnection among them, so that they can make crucial investment decisions and diversification strategies. This will help them to gain knowledge about how these two markets move together so they may avoid underestimating risk when building portfolios that contain both kinds of assets.

TRUENESS AND PRECISION OF DIFFERENT DIGITAL SCAN SYSTEMS IN A TWO IMPLANT COMPLETE ARCH MODEL: AN IN-VITRO STUDY

Background: One of the major concerns in implant-retained prostheses is their accuracy which plays an essential role in implant success and prosthesis adaptation. Although many contemplates stated the indications and merits of different digital scanner systems, little is identified about their trueness and precision in scanning dental implants of implant-retained prostheses. Objectives: This contemplate aimed to evaluate and compare the trueness and precision of two unalike most recent digital scan systems in a mandibular two-implant complete arch model. Materials and Methods: A completely edentulous mandibular cast was utilized into which two conventional dental implant analogs were drilled in its inter-foramina area from which the distance between the analogs was measured by a caliper (Control). The same space was assessed via scanning the whole assembly 13 scans/each digital scanner system. The final distance of each scan attained from both systems was then compared with the control. The accuracy of each system was assessed in terms of trueness and precision. Results: Slight advancement of the Dof Freedom X5 premium digital scanner system than the Medit T300-T500 dental digital scanner regarding trueness although they were still insignificantly different, as P=0.66. The Medit digital scanner system was significantly better than the Dof Freedom one concerning precision, as P=0.001. Conclusion: The two dental laboratory digital scanner systems employed are reliable tools for scanning and reproducing digital dental records accurately for an implant-supported prosthesis. Furthermore, the Medit dental digital scanner system seemed to be more accurate in terms of precision than the Dof Freedom one.

Application of Copula Models in Stock Market Analysis

Objectives. The objective of the study is to use copula models to analyze shares of the Russian stock market and describe changes in the relationship between the shares before and during the coronavirus infection (COVID-19).Methods. An algorithm for using copulas and functions of the R programming language in its implementation is presented. To model the dynamics of financial series the ARMA-GJR-GARCH process (autoregressive moving average Glosten-Jagannathan-Runkle model with generalized autoregressive conditional heteroskedasticity) is used. The selection of optimal families and parameters of copula models is carried out. The adequacy of the obtained models is checked and the results of the study of the relationship between the series are analyzed.Results. An algorithm has been developed for a relatively new approach to using copulas in conjunction with the ARMA-GJR-GARCH model. The approach was used to study the impact of coronavirus in the context of the Russian economy. It is revealed that during the COVID-19 period the dependence between different stocks increases. It is shown that the effect of volatility in financial series increases after the outbreak of the pandemic.Conclusion. The research algorithm using copula models in conjunction with the ARMA-GJR-GARCH process has shown its feasibility. This approach can be used with other GARCH-type models to study finance and other areas.

State-dependent intra-day volatility pattern and its impact on price jump detection - Evidence from international equity indices

Current price jump tests assume a constant intra-day volatility pattern (IVP) over sample period. We test this assumption by allowing IVP to depend on some state variables such as the sign of previous returns or the relative levels of volatility. Estimation results from 5-min GARCH model for four equity indices show that squared-return-based IVP weights increase in early morning hours when previous returns are negative, suggesting an asymmetric IVP. For a jump-robust IVP estimator, distinct responses are found for days with Realized Variance (RV) increasing from the previous day. Our results are consistent with and complement recent studies on time-varying IVP. Price jumps obtained using the state-dependent IVP are more prudent, show lower degree of clustering and are less concentrated over trading hours.

Research on Hedging Ratio of Stock Index Futures to ETF Fund

Exchange Traded Funds (ETF) can largely avoid non-systematic risk, but investors often cannot avoid systemic risk, and the hedging function of stock index futures can do this. Therefore, hedging ETF with stock index futures has become a good investment strategy. Based on the trading data of the China Securities Index (CSI) 300 stock index futures and CSI 300 Exchange-Traded Fund (ETF), this paper analyzes the optimal hedging ratio of CSI 300 stock index futures by Ordinary Least Squares (OLS) and dynamic Error Correction Model - Generalized Autoregressive Conditional Heteroskedasticity (ECM-GARCH) model and compares the hedging performance predicted by the model to avoid the systematic risk of ETF. The results show that the hedging effect of the dynamic hedging model is better than that of the static model, and the ability to avoid systemic risk is also better. The predictions of both models show that stock index futures hedge ETFs very well. The dynamic model is more able to reduce the heteroscedasticity of the transaction data.

Utilizing the GARCH Model for Analysis and Prediction of Stock Market Trends

This study utilizes the Generalized Auto-regressive Conditional Heteroskedasticity (GARCH) model to analyze the Shanghai Stock Exchange Composite Index and the Shenzhen Composite Index. It computes the returns and logarithmic returns, fits the GARCH model with a student-t distribution, and calculates the standardized residuals of the stock. Tests for normality and heteroskedasticity of residuals are conducted, follows by the creation of auto-correlation and partial auto-correlation plots to aid in volatility forecasting. The findings indicate that both returns of stock distributions exhibit multiple peaks and significant fluctuations, revealing that there exists pronounced volatility clustering and strong abrupt changes. Historical fluctuations significantly affect current fluctuations, showing a clustering effect. Volatility in returns has been very persistent, reflecting strong speculation and elevated overall risk. Histograms and skewness assessments show a left-skewed distribution for both indices, with a kurtosis greater than three, indicating a "fat-tailed" distribution. The positive mean values imply that China's economy is growing constantly, while the low standard deviation implies the immaturity of China's stock market. These insights highlight the dynamic behaviors and risk profiles in Chinas major stock indices, offering a deeper understanding of their speculative nature and economic implications. The Advantages and disadvantages of GARCH models and limitations of a single model are acknowledged in the report.

Testing the Adaptive Market Hypothesis and Time-Varying Efficiency in the Indian Equity Market

The study examines the adaptive market hypothesis (AMH) as an evolutionary principle of the alternative efficient market hypothesis in the Indian stock market (Sensex and Nifty50) on the daily return from April 2014 to May 2020. Based on AMH, investors behave, learn, and adapt to market conditions. This distinction of dynamic market conditions is divided into bull and bear market classifications. We apply three variations of the variance ratio test and the returns have been whitened using the Autoregressive model with generalized autoregressive conditional heteroskedasticity (AR-GARCH) approach to examine the nonlinear predictability test. Further, we evaluate a fixed-length subsample window framework to detect the time-varying predictability and examine whether market conditions affect stock return predictability and market condition. The study confirms inefficient market behaviour during crises, fear, panic, macroeconomic events and each market adapts differently to certain market conditions. Furthermore, the return series exhibits significant periods of efficiency and inefficiency consistent with the adaptive market hypothesis. The evidence of our findings sheds light on efficient market behaviour in dynamic market conditions and market environments for researchers, investors in investment strategies and policy intervention in risk containment measures and control market manipulation.

Analysis of the Medical Industry in the Stock Market under the Influence of the Pandemic in China

This paper is working to analyze the influence of COVID-19 on the medical industry in Chinas stock market. Because the pandemic has influenced our society and development impressively, using statistical methods to analyze its influence is a necessary method to estimate the risk of investment. Some common statistic analyzing methods, the ARIMA model and GARCH model, will be used in this paper, and the data of the stock price of a medical manufacturing company Zhangzhou Pientzhng Phrmctcl Co Ltd during the COVID-19 is collected and introduced in the models. Meanwhile, machine learning is also implemented in the prediction and analysis of the data. The results of these two models both demonstrate the high volatility in the stock market under the influence of pandemic, which is meaningful for further research about the risks of future investment in medical industry of Chinas stock market.

Enhancing Forecasting Accuracy in Commodity and Financial Markets: Insights from GARCH and SVR Models

The aim of this study is to enhance the understanding of volatility dynamics in commodity returns, such as gold and cocoa, as well as the financial market index S&P500. It provides a comprehensive overview of each model’s efficacy in capturing volatility clustering, asymmetry, and long-term memory effects in asset returns. By employing models like sGARCH, eGARCH, gjrGARCH, and FIGARCH, the research offers a nuanced understanding of volatility evolution and its impact on asset returns. Using the Skewed Generalized Error Distribution (SGED) in model optimization shows how important it is to understand asymmetry and fat-tailedness in return distributions, which are common in financial data. Key findings include the sGARCH model being the preferred choice for Gold Futures due to its lower AIC value and favorable parameter estimates, indicating significant volatility clustering and a slight positive skewness in return distribution. For Cocoa Futures, the FIGARCH model demonstrates superior performance in capturing long memory effects, as evidenced by its higher log-likelihood value and lower AIC value. For the S&P500 Index, the eGARCH model stands out for its ability to capture asymmetry in volatility responses, showing superior performance in both log-likelihood and AIC values. Overall, identifying superior modeling approaches like the FIGARCH model for long memory effects can enhance risk management strategies by providing more accurate estimates of Value-at-Risk (VaR) and Expected Shortfall (ES). Additionally, the out-of-sample evaluation reveals that Support Vector Regression (SVR) outperforms traditional GARCH models for short-term forecasting horizons, indicating its potential as an alternative forecasting tool in financial markets. These findings underscore the importance of selecting appropriate modeling techniques tailored to specific asset classes and forecasting horizons. Furthermore, the study highlights the potential of advanced techniques like SVR in enhancing forecasting accuracy, thus offering valuable implications for portfolio management and risk assessment in financial markets.

Hybrid Fourier asymmetric-garch estimation of value at risk and expected shortfall: Empirical evidence from crude oil prices

We propose a hybrid Fourier approximation in an autoregressive fractional integrated moving average (ARFIMA) model, to account for periodic unoberved components in financial time series. We apply this hybrid model on parametric estimation of value at risk (VaR) and expected shortfall (ES). Using crude oil returns, we show that Fourier approximation inclusion significantly accounts for unobserved periodic components in a VaR estimation using exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model under generalized error distribution (GED). Similarly, in VaR estimation, Fourier approximation inclusion significantly accounts for unobserved periodic components using asymmetric power generalized autoregressive conditional heteroscedasticity (APARCH) model under skewed normal distribution (SNORM). For ES estimation, Fourier approximation inclusion only significantly accounts for unobserved periodic components of APARCH under SNORM.

Adaptive Bayesian speckle reduction in the 2D DOST domain using 2D MC-GARCH-M model: Preserving image edges and textural information

Image denoising and image quality enhancement are major issues in image processing. Additive and multiplicative noise removal is one of the main image enhancement approaches. In this paper, we propose a novel 2D Merged Complex Generalized Autoregressive Conditional Heteroscedasticity Mixture (MC-GARCH-M) model for 2D complex stochastic processes. This model effectively captures non-Gaussian statistics and all three types of dependencies within the processes (RRD, IID, and RID) using the proposed linear mapping transformation T. Our statistical analysis shows that the 2D MC-GARCH-M model provides the best fit to the non-Gaussian statistics of the mapped matrix of 2D DOST coefficients compared to Gaussian, Generalized Gaussian, and Stable distributions. We confirm the presence of heteroscedasticity in the mapped matrix using the Engle hypothesis test, verifying ARCH/GARCH effects. The 2D MC-GARCH-M model, with its location-dependent conditional variances, provides a flexible approach for noise removal and modeling complex stochastic processes. Experimental results on artificially speckled aerial and actual SAR images demonstrate that our method outperforms state-of-the-art approaches in terms of speckle removal and preserving the edges and textural information of the image. Key innovations include: a new statistical analysis using linear mapping T showing non-Gaussian heavy-tailed distributions; an adaptive Bayesian estimator, MCMAP, based on the heteroscedastic model for speckle noise removal; and the method's applicability to images with varying mutual information (MI) between real and imaginary parts of 2D DOST coefficients. Our method is adaptive and robust to initial parameter settings, effectively utilizing magnitude and phase information, providing an optimal closed-form solution, reducing memory and computational requirements, and demonstrating robustness to speckle power levels. While requiring more computational resources compared to thresholding methods, our approach is less demanding than other Bayesian algorithms, making it suitable for offline processing.

Understanding Investor Sentiment: Analyzing Its Influence on Stock and Cryptocurrency Markets During the Russia–Ukraine War

ABSTRACTThis paper examines the shifts in investor sentiment during the Russia–Ukraine war and its consequent impact on market volatility. By employing a comprehensive dataset that includes the S&P 500 index, historical Bitcoin prices, the Investor Sentiment Index, the Industrial Production Index, and the US Consumer Price Index, this study applies several econometric models such as generalized autoregressive conditional heteroskedasticity (GARCH) models, regression analyses, vector error correction models (VECM), and the Granger causality model. The analysis spans from January 2021 to March 2023. The findings indicate that investor sentiment significantly influences returns in both stock and cryptocurrency markets, having a positive effect. These results underscore the importance for investors and policymakers to monitor investor sentiment during periods of conflict to understand its potential impact on financial markets. This research offers valuable insights that can guide investment decisions and inform policy interventions.

Financial technology and ESG market: A wavelet-DCC GARCH approach

This paper examines the co-movement between FinTech and ESG markets from a time-frequency domain perspective. We use an approach suggested by Vacha and Barunik (2012) and include wavelet coherence analysis and dynamic conditional correlation from a multivariate GARCH model (DCC GARCH). We find a significant bi-directional positive relationship between the FinTech and ESG indices. We also find the DCC GARCH process to be mean reverting. The correlations between FinTech and ESG indices, based on both the wavelet coherence and DCC GARCH models, are found to fluctuate over time with the one based on DCC GARCH being higher on the average compared to the one based on wavelet coherence. Finally, we find that the correlations are significant for almost all frequencies except for the 256-day frequency. For the lower frequencies, such as 512-day (approximately 2-year frequency), the correlation increases.

Stock Market Resilience: Evaluating Islamic and Conventional Indices through COVID-19 Waves

The study examined the impact of the five COVID-19 waves on Pakistan's conventional (KSE-100) and Islamic (KMI-30) stock indices from March 3, 2020, to August 30, 2022. The DCC GARCH (1, 1) model found weak, predominantly negative connections between COVID-19 cases each day and stock returns. Visual data indicated a slight decrease in both indices as cases increased, reflecting previous findings on pandemics' adverse effects on stock markets. A thorough examination of the linkages between COVID-19 cases and financial indicators using Wavelet Coherence analysis highlighted intricate connections that are important to policymakers and financiers. Pakistan's KSE100 and KMI-30 indices showed a constant significant positive dynamic conditional association that persisted throughout the investigation. This challenges the perception that the Islamic index serves as a safe haven during financial crises. According to the research, Islamic stock markets, as reflected by the KMI-30, were not as protective or as good at hedging during crises like the COVID-19 pandemic. In fact, they were more susceptible to economic downturns. When navigating the effects of global health crises on financial markets, investors and policymakers must have a thorough understanding of these dynamics.

Modeling and forecasting the volatility of some industry development indicators in Ethiopia using multivariate GARCH models

Industry development indicators refer to a set of measures used to assess the performance and growth of industries. The main aim of this study was to assess the relationship between industry development indicators in Ethiopia using a multivariate GARCH model based on World Bank data from 1982 to 2021. A time series technique using annual data for the period 1982–2021 is utilized, and multivariate generalized autoregressive conditional heteroscedasticity was performed for volatility modeling. The results of the diagonal BEKK (1, 1)-GARCH model showed that there is strong evidence for a GARCH effect and the presence of a weaker ARCH effect, Equations show a statistically significant co-variation in shocks, which depends more on their lags than on past errors. Consequently, development indicator shocks are influenced by past information. The cross-volatility effects are higher than the own-volatility effects in Industry GDP, manufacturing GDP, and manufacturing exports. However, past volatility shocks in industry growth have less effect on cross-volatility than its own volatility shock. The implication of the study is that both domestic policymakers and development partners should support and motivate the growth of manufacturing sectors and manufacturing exports, since this is a necessary condition for promoting industry growth.

Equilibrium bifurcation and extreme risk in the EU carbon futures market

Considering the long-term memory and volatility clustering of the European Union (EU) Carbon Emission Allowances (EUA) futures returns, based on the economy–energy–environment system perspective and the assumption of investors' heterogeneity, this study proposes a joint modeling approach combining the fractionally integrated generalized autoregressive conditional heteroscedasticity model (FIGARCH) and the stochastic cusp catastrophe model (SCC) to examine the equilibrium bifurcations and extreme risks in the EU carbon futures market. The relevant results are threefold. (1) The SCC model has good fitting effect and interpretability, and is an effective method for investigating catastrophe reactions under time-varying volatility conditions. (2) In the EUA futures market, chartists are mainly affected by short-term price and trading volume changes, which leads to the emergence of equilibrium bifurcations, while fundamentalists make investment decisions based on the economy, the energy market, and market supply–demand, which affects the asymmetry of equilibrium bifurcations. (3) Using the catastrophe criterion (i.e., Cardan's discriminant of the equilibrium surface equation), we identify148 equilibrium bifurcation time points in the EUA futures market from December 3, 2009 to September 16, 2020, most of which are concentrated in two upward periods with an average scale of extreme risks is about 32.51 %. Our analysis provides theoretical support for regulatory authorities to stabilize the carbon futures market and build a collaborative extreme risk management framework covering energy and macroeconomics, also proposing suggestions for traders to effectively prevent extreme risks.

Dynamic Correlations Between Carbon Futures and Energy Futures Markets

An essential instrument for reducing carbon emissions worldwide is the carbon market. Comprehending the dynamic relationships between carbon and energy futures prices is crucial as carbon trading picks up promote globally. This research examines how two energy futurescrude oil and natural gasinteract with carbon futures in the American and European markets between November 21, 2013, and March 28, 2024. We examine correlations between futures returns across different regions using the Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model. Our findings reveal significant, albeit fluctuating, correlations influenced by external market events. Interestingly, compared to crude oil futures, there is a stronger dynamic link between carbon futures and natural gas futures, especially in the European market, demonstrating strong long-term persistence.