Forecasting Stock Market Volatility

Steel structures such as transmission towers may have cracks and other damages during the service period. When the structure vibrates, the cracks will open and close, which makes the structure have nonlinear characteristics of variant stiffness. In order to identify this type of nonlinear damage, a time-domain damage identification method based on the residual deviation distance (RDD) of the autoregressive conditional heteroskedasticity (ARCH) model is proposed. First, the basic theory of the ARCH model is introduced, and the methods of model order determination and parameter estimation are given. Then, the time-domain nonlinear damage characteristics are analyzed, and the second-order variance (SOV) index based on the ARCH model is introduced. Considering that both the ARCH model coefficient and the RDD contain nonlinear information, a conversion index is constructed using the Euclidean distance (ED) of the ARCH model coefficients before and after the damage. On this basis, an RDD conversion index is further proposed to improve the identification accuracy. Finally, a three-storey frame experiment and a complex transmission tower model experiment are used to verify the effectiveness of the proposed method. The experimental results show that the proposed RDD conversion index can better identify the location of structural damage, and the identification results of the RDD conversion index are obviously better than those of the SOV conversion index and the ED conversion index.

For the limitations of vibration signals caused by non-stationary autoregressive (AR) model which can not effectively describe the signal characteristics, it is presented a fault diagnosis based on autoregressive conditional heteroskedasticity (ARCH) model. This method firstly uses ARCH model to fit various fault signals and regard the proceeds of the model parameters as the characteristics of fault diagnosis, using RBF neural network classification as fault diagnosis method. The experimental results verify the feasibility and effectiveness of the ARCH model, and at the same time it makes the comparison with the method based on same AR model and another modified method based on AR model. The results show that the method has significantly improvements in the diagnosis rate.

In this paper we compare a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the US stock market volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, in the MRS-GARCH models all parameters switch between a low and a high volatility regime. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis. The forecasting performances of the competing models are evaluated both with statistical and risk-management loss functions. Under statistical losses, we use both tests of equal predictive ability of the Diebold-Mariano-type and test of superior predictive ability. Under risk-management losses, we use a two-step selection procedure where we first check which models pass the tests of correct unconditional or conditional coverage and then we compare the best models under two subjective VaR-based loss functions. The empirical analysis demonstrates that MRS-GARCH models do really outperform all standard GARCH models in forecasting volatility at horizons shorter than one week under both statistical and VaR-based risk-management loss functions. In particular, all tests reject the presence of a better model than the MRS-GARCH with normal innovations. However, at forecast horizons longer than one week, standard asymmetric GARCH models tend to be superior.

Forecasting stock market volatility using Realized GARCH model: International evidence

Exchange rate volatility has long been a central concern in international finance due to its implications for trade, investment, and monetary policy. This article presents a comprehensive theoretical review of modeling exchange rate volatility using ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized ARCH) frameworks, emphasizing recent advancements over the past decade (2015–2025). Beginning with the foundational concepts introduced by Engle (1982) and Bollerslev (1986), the paper outlines the mathematical structure and interpretative significance of ARCH and GARCH models in capturing volatility clustering, persistence, and time-varying variance in exchange rate returns. A detailed comparison is provided between standard models and their extensions, including GARCH-M, EGARCH, and TGARCH, which incorporate features like risk premia and asymmetric responses to shocks. Recent empirical applications are discussed to highlight how these models have been expanded to include macroeconomic variables (via GARCH-MIDAS), account for structural breaks, and better capture tail risk using alternative error distributions such as the Normal Tempered Stable. Furthermore, the article explores how GARCH-based models are applied beyond traditional currency pairs, including in cryptocurrency markets and during crisis periods, underscoring their adaptability. Despite certain limitations, such as sensitivity to structural changes and assumptions of symmetric responses, ARCH/GARCH models remain foundational in volatility forecasting due to their tractability, empirical robustness, and capacity to incorporate evolving market dynamics. The article concludes that while modern econometrics has introduced increasingly complex hybrid models, the core principles of ARCH and GARCH continue to offer a reliable and interpretable framework for understanding exchange rate volatility. Keywords: Exchange rate volatility, ARCH model, GARCH model, Risk premium, Asymmetric volatility, Financial econometrics

An important development in the modelling of exchange rate volatility is the use of artificial neural networks (ANN) to create enhanced generalised autoregressive conditional heteroskedasticity (GARCH) models. Conventional GARCH models are good at capturing the clustering of volatility in financial time series, but they have trouble understanding complex linkages and non-linear patterns in the data. This paper aims to investigate the hybrid approach in modelling exchange rate volatility of two currency pairs: South African Rand against Brazilian Real (ZAR/REAL) and South African Rand against Chinese Yuan (ZAR/YUAN) using monthly observations over the period of January 1996-March 2024. The paper introduced ANN as an additional factor to both symmetric and asymmetric GARCH models that capture most common stylised facts about exchange rate volatility and leverage effects. The GARCH (1,1)-ANN, EGARCH (1,1)-ANN, and GJR-GARCH (1,1)-ANN models were used, and their performance was assessed using mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results revealed that the EGARCH (1,1)-ANN model had the best overall performance when compared to the other hybrid models based on all three evaluation measures for both the currency pairs’ data. The paper recommends further similar studies to predict future exchange rate trends and also incorporating other nonlinear methods.

This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which implies that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the UK foreign exchange market experienced a similar pattern of volatility shifts and suffered smaller but longer volatility than the Korean one. The volatility shifts are estimated using a Markov switching GARCH model and a Bayesian method is suggested.Keywords: Bayesian Inference, Markov Switching GARCH Models, Exchange Rate Volatility, Credit CrisisJEL classification: C11, C22, F31(ProQuest: ... denotes formulae omitted.)1. INTRODUCTIONThe Korean foreign exchange market has experienced two crises during the last two decades, as shown in Figure 1. The exchange rate was managed by the government before the Asian financial crisis in 1997-8. The Korean currency, or the won, depreciated sharply during the crisis and showed a trend of appreciating during the next decade. The foreign exchange market suffered from another foreign capital flight during the global credit crisis in 2008-9. Contrary to the case of the 1997-8 crisis, the 2008-9 credit crisis stemmed from the developed economies. However, the credit crisis led many developing countries, including South Korea, to an economic or financial crisis. Many policies were implemented to stabilize the financial and foreign exchange markets in Korea. The Bank of Korea has swiftly lowered the policy rate from 5.25% to 2% for 4 months since October 2008. The government announced the Financial Market Stabilization Measures, which included government warrants of the foreign currency debt of the commercial banks and provision of dollar liquidity to them, on October 19, 2008. The Bank of Korea has also made a 30-billion US dollar swap arrangement with the Federal Reserve on October 30, 2008 and other deals with the People's Bank of China and the Bank of Japan on December 12, 2008. From October 2008 to February 2009, it provided around 30-billion dollar liquidity to financial institutions which had difficulties in overseas fund raising.This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis and investigates what determined the volatility. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which suggests that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the dollar-pound exchange rate experienced a similar pattern of volatility shifts to that of the won-dollar exchange rate. But, the UK foreign exchange market suffered smaller but longer volatility than the Korean one.Since the Autoregressive Conditional Heteroskedastic (ARCH) model was suggested by Engle (1982), the conditional heteroskedastic models have been updated and developed to analyze the volatility of the financial markets. Researchers, including Bollerslev (1986), generalized the ARCH model to GARCH (generalized ARCH) and its variants, such as IGARCH, GARCH-M, and EGARCH. The models are known to describe well the many features of volatility, such as volatility clustering and the leverage effect.1 However, as Schwert (1990) and Engle and Mustaffa (1992) show, the GARCH models imply too much persistence in the conditional variance. To overcome this shortcoming, Cai (1994) and Hamilton and Susmel (1994) incorporate the Markov switching component into the ARCH model. Gray (1996) and Dueker (1997) generalize their model to Markov switching GARCH (hereafter, MS-GARCH) models. …

Purpose – In the last decade, digital innovations in the field of finance emerge mainly due to Blockchain technology. The most widely used product of Blockchain technology in the world is cryptocurrencies. Bitcoin draws attention to both market capitalization and transaction volume. The analysis of the volatility of Bitcoin has great significance both theoretically and practically. Therefore, the research aims to determine the most suitable volatility model in Bitcoin investment analysis and present a model suggestion that can be used for predicting the future. Design/methodology/approach – In this study, daily logarithmic return series between 29.04.2013-17.04.2019 are used to analyze Bitcoin volatility. While calculating the return series, daily closing prices of Bitcoin are based on. As a research method, generalized autoregressive conditional heteroskedastic (GARCH) models are tested. In this study, ARCH, GARCH, GJR / TARCH, EGARCH, APARCH, and CGARCH type models are compared for volatility modeling of Bitcoin logarithmic return series. Findings – The study found that the best method for the analysis of Bitcoin volatility is the EGARCH model. Another important finding of the study is that negative shocks are more effective on Bitcoin returns than positive shocks. Discussion – The study contributes to the literature in terms of analyzing the dynamics of Bitcoin volatility, which is a new and digital product, with various models and current data set. Bitcoin investors and researchers can predict returns by using the volatility equation in result of this research. Another output of the study is that negative news effects Bitcoin returns more than positive news. Using this information, traders will be able to take positions on Bitcoin prices.

The impact of changes in government policies on economic performance (the ARCH model)

Portfolio Performance of the SDR and Reserve Currencies: Tests Using the Arch Methodology

Gear wear is inevitable during the service life of gearboxes and may lead to catastrophic failure. As an important micro-level wear feature, tooth surface roughness directly affects the gear wear progression (lubrication regimes, wear mechanisms and wear rates) and lifespan of a gearbox. Therefore, it is important to monitor surface roughness changes. The tooth surface roughness induces random vibration signals with cyclic amplitude modulation. Reported works used an indicator of second-order cyclostationarity (ICS2) to assess such signals. However, the ICS2 gives a poor correlation with surface roughness. This paper presents the use of an Autoregressive Conditional Heteroskedasticity (ARCH) model to represent the random vibration signals with cyclic amplitude modulation. ARCH model parameter serves as an indicator to assess the changes in gear tooth surface roughness. A laboratory dataset was used to validate the effectiveness of the ARCH model in assessing surface roughness level. Results have shown that using the ARCH model returns a more accurate assessment result than the ICS2.

Stock price prediction and volatility modeling are important for making financial decisions, especially in emerging markets like the Nairobi Securities Exchange (NSE). This study examines how well the Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models perform in forecasting stock prices and modeling volatility. The ARIMA (2,1,0) model was selected as the best fit using the Akaike Information Criterion (AIC), showing strong performance in capturing long-term price trends. However, an analysis of the residuals showed signs of volatility clustering, meaning ARIMA alone could not capture short-term fluctuations. To solve this, the study added a GARCH (1,1) model, which effectively captured changing volatility and improved prediction accuracy. The combined ARIMA-GARCH model reduced the Root Mean Squared Error (RMSE) from 3.1211 to 2.5786, demonstrating the value of including volatility modeling in financial time series. The results highlight the need for strong statistical models in emerging markets, where stock prices are often affected by external shocks and market inefficiencies. This research offers useful insights for investors, policymakers, and financial analysts by supporting better risk management and more accurate forecasting. Future studies could expand the model to include more stocks, macroeconomic data, and machine learning techniques to further improve results.

Uncertainty is often associated with travel-time prediction. Traditional point prediction methods only provide point values that are unable to offer enough information on the reliability of prediction results. The recent development of statistical volatility models has given us an effective way to capture uncertainties in data. Generalized autoregressive conditional heteroskedasticity (GARCH) models have been widely used in transportation systems as a way to account for this uncertainty by providing more accurate prediction intervals. However, a GARCH model arguably does not consider the trend and seasonality in data. If there is a trend or seasonality, the performance of the GARCH model may be affected. In the context of travel-time prediction, this paper proposes two component GARCH models that are able to model trend and seasonal components through decomposition. The travel-time data obtained along a freeway corridor in Houston, TX, USA, were used to empirically test the performance of the proposed models. The study results indicate that the proposed models perform well when capturing uncertainties associated with travel-time prediction.

Orientation: Macroeconomic news announcement poses a risk to stock returns, especially that of United States (US) on emerging markets because of globalisation.Research purpose: The purpose was to investigate the impact that US macroeconomic news announcements have on the Johannesburg Stock Exchange (JSE).Motivation for the study: Investment in financial markets is volatile. Globalisation means that greater economies’ macroeconomic news announcements could impact emerging financial markets. Knowing which announcements have an influence could improve investment decisions.Research design, approach and method: This study is qualitative, following secondary data analysis. Analysis was carried out using volatility modelling, paired with an event study to add robustness.Main findings: The generalised autoregressive conditional heteroskedastic (GARCH) models indicated that US macroeconomic news announcements made in relation to unemployment were statistically significant, with a negative impact on the JSE. This was supplemented by the event study in which interest rate announcements that were made in August 2008 (during the global financial crisis) were found to have a statistically significant impact on the JSE. The coronavirus disease 2019 (COVID-19) pandemic did not appear to have a statistically significant impact in the results obtained from the event study.Practical/managerial implications: Investment industry professionals and policymakers should consider unemployment announcements from the US to enhance investment decisions while managing stock market volatility.Contribution/value-add: The results make a novel contribution towards the findings during the initial COVID-19 period and generalisability of the method as well as the theoretical expansion of the theoretical application of globalisation on stock markets.

Cryptocurrencies have rapidly emerged as a significant financial asset class, influencing global monetary systems and financial markets. However, their extreme volatility, speculative nature, and evolving regulatory landscape pose challenges to investors, policymakers, and financial analysts. This study presents an in-depth quantitative analysis of cryptocurrency volatility and risk assessment, focusing on Bitcoin (BTC-USD) and its correlation with traditional financial assets, including the EUR/USD exchange rate and S&P 500 index. Our research employs Generalized Autoregressive Conditional Heteroskedasticity (GARCH) modeling to measure the dynamic volatility patterns of Bitcoin, revealing the asset’s substantial fluctuations over time and its sensitivity to market shocks. Additionally, we utilize Monte Carlo simulations to forecast potential future price movements of Bitcoin, highlighting risk scenarios and the probability distribution of price trajectories over a one-year period. The Value-at-Risk (VaR) model is implemented to estimate potential losses within a given confidence interval, providing a robust measure of downside risk. Furthermore, the study examines the integration of cryptocurrency markets with traditional financial instruments by analyzing cross-asset correlations and volatility spillover effects. The findings suggest that while Bitcoin remains a highly volatile asset, its correlation with the broader financial system is increasing, indicating a potential shift towards mainstream financial adoption. The results contribute to the ongoing debate on whether cryptocurrencies serve primarily as speculative instruments or as viable components of diversified investment portfolios. These insights are valuable for institutional investors, risk managers, and policymakers in designing more effective risk mitigation strategies for cryptocurrency investments.