CRYPTOCURRENCY VOLATILITY AND RISK MODELING: MONTE CARLO SIMULATIONS, GARCH ANALYSIS, AND FINANCIAL MARKET INTEGRATION

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.

PurposeThis study aims to investigate the conditional volatility of the Asian stock market concerning Bitcoin and global crude oil price movement.Design/methodology/approachThis study uses the newest Dynamic Conditional Correlation (DCC)-Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to examine the conditional volatility of the stock market for Bitcoin and crude oil prices in the Asian perspective. The sample stock market includes Chinese, Indian, Japanese, Malaysian, Pakistani, Singaporean, South Korean and Turkish stock exchanges, with daily time series data ranging from 4 April 2015−31 July 2023.FindingsThe outcome reveals the presence of volatility clustering on the return series of crude oil, Bitcoin and all selected stock exchanges of the current study. Secondly, the outcome of DCC, manifests that there is no short-run volatility spillover from crude oil to the Malaysian, Pakistani and South Korean and Turkish stock markets, whereas Chinese, Indian, Japanese, Singapore stock exchanges show the short-run volatility spillover from crude oil in the short run. On the other hand, in the long run, there is a volatility spillover effect from crude oil to all the stock exchanges. Thirdly, the findings suggest that there is no immediate spillover of volatility from Bitcoin to the stock markets return volatility of China, India, Malaysia, Pakistan, South Korea and Singapore. In contrast, both the Japanese and Turkish stock exchanges exhibit a short-term volatility spillover from Bitcoin. In the long term, a volatility spillover effect from Bitcoin is observed in all stock exchanges except for Malaysia. Lastly, based on the outcome of conditional variance, it can be concluded that there was increase in the return volatility of stock exchanges during the period of the COVID-19 pandemic.Research limitations/implicationsThe analysis below does not account for the bias induced due to certain small sample properties of DCC-GARCH model. There exists a huge literature that suggests other methodologies for small sample corrections such as the DCC connectedness approach. On the other hand, decisive corollaries of the conclusions drawn above have been made purely based on a comprehensive investigation of eight Asian stock exchange economies. However, there is scope for inclusive examination by considering other Nordic and Western financial markets with panel data approach to get more robust inferences about the reality.Originality/valueMost of the empirical analysis in this perspective skewed towards the Nordic and Western countries. In addition to that many empirical investigations examine either the impact of crude oil price movement or Bitcoin performance on the stock market return volatility. However, none of the examinations quests the crude oil and Bitcoin together to unearth their implication on the stock market return volatility in a single study, especially in the Asian context. Hence, current investigation endeavours to examine the ramifications of Bitcoin and crude oil price movement on the stock market return volatility from an Asian perspective, which has significant implications for the investors of the Asian financial market.

Interconnections and contagion among cryptocurrencies, DeFi, NFT and traditional financial assets: Some new evidence from tail risk driven network

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

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. …

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.

This current study explores the application of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to forecast and model crude oil price volatility. Crude oil is a vital commodity whose price fluctuations significantly impact global economies, energy markets, and strategic decisions of both National Oil Companies (NOCs) and International Oil Corporations (IOCs). Using the GARCH(1,1) and GARCH(1,2) models, this study evaluates the effectiveness of these models in capturing the dynamic nature of oil price volatility. The findings indicate that while both models fit the data well, the GARCH(1,1) model is preferred due to its parsimonious nature and comparable forecast accuracy. Despite including an additional lag in the GARCH(1,2) model, it did not significantly outperform the GARCH(1,1) model in predictive performance. The study further analyzes the residuals and autocorrelation characteristics, highlighting the potential for model refinement. The study underscores the importance of selecting an appropriate model complexity, incorporating external factors, and exploring advanced methodologies to enhance forecast accuracy. These insights are critical for developing effective risk management strategies and informing policy decisions in volatile crude oil markets.

Bandung Regency located in West Java Province, Indonesia, has a tropical climate with high rainfall variation. This variable rainfall pattern is one of the main characteristics of tropical regions, where seasonal changes such as the rainy and dry seasons significantly impact annual rainfall patterns. In addition, high rainfall is often a trigger for natural disasters, such as floods and landslides, which can cause economic and social losses. Therefore, the ability to predict rainfall accurately is crucial, both for disaster risk mitigation and as a basis for decision-making in various sectors. This study aims to predict rainfall in Bandung Regency for the next year using a time series model approach, specifically a heteroscedastic model. The main focus of the study is to examine rainfall returns, or changes in rainfall over time while considering the nature of heteroscedasticity. In this condition, the variance of the data is not constant over time. The phenomenon of heteroscedasticity is common in rainfall data due to significant changes between seasons or extreme weather events. The study results indicate that the best model for predicting rainfall imbal hasil s is the Autoregressive Conditional Heteroskedasticity (ARCH) model. The selection of this model is based on the Akaike Information Criterion (AIC), which shows that the ARCH model outperforms the GARCH(1,1) model in handling variance instability in rainfall data. The advantage of the ARCH model lies in its ability to dynamically model variance instability, resulting in more accurate predictions. This model is not only capable of capturing high volatility patterns but also provides a more realistic estimate of large fluctuations that could occur in the future.

PurposeThe purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.Design/methodology/approachBoth regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.FindingsThe GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.Originality/valueThe regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

PurposeThis study constructs time series model, artificial neural networks (ANNs) and statistical topologies to examine the volatility and forecast foreign exchange rates. The Mauritian forex market has been utilized as a case study, and daily data for nominal spot rate (during a time period of five years spanning from 2014 to 2018) for EUR/MUR, GBP/MUR, CAD/MUR and AUD/MUR have been applied for the predictions.Design/methodology/approachAutoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models are used as a basis for time series modelling for the analysis, along with the non-linear autoregressive network with exogenous inputs (NARX) neural network backpropagation algorithm utilizing different training functions, namely, Levenberg–Marquardt (LM), Bayesian regularization and scaled conjugate gradient (SCG) algorithms. The study also features a hybrid kernel principal component analysis (KPCA) using the support vector regression (SVR) algorithm as an additional statistical tool to conduct financial market forecasting modelling. Mean squared error (MSE) and root mean square error (RMSE) are employed as indicators for the performance of the models.FindingsThe results demonstrated that the GARCH model performed better in terms of volatility clustering and prediction compared to the ARIMA model. On the other hand, the NARX model indicated that LM and Bayesian regularization training algorithms are the most appropriate method of forecasting the different currency exchange rates as the MSE and RMSE seemed to be the lowest error compared to the other training functions. Meanwhile, the results reported that NARX and KPCA–SVR topologies outperformed the linear time series models due to the theory based on the structural risk minimization principle. Finally, the comparison between the NARX model and KPCA–SVR illustrated that the NARX model outperformed the statistical prediction model. Overall, the study deduced that the NARX topology achieves better prediction performance results compared to time series and statistical parameters.Research limitations/implicationsThe foreign exchange market is considered to be instable owing to uncertainties in the economic environment of any country and thus, accurate forecasting of foreign exchange rates is crucial for any foreign exchange activity. The study has an important economic implication as it will help researchers, investors, traders, speculators and financial analysts, users of financial news in banking and financial institutions, money changers, non-banking financial companies and stock exchange institutions in Mauritius to take investment decisions in terms of international portfolios. Moreover, currency rates instability might raise transaction costs and diminish the returns in terms of international trade. Exchange rate volatility raises the need to implement a highly organized risk management measures so as to disclose future trend and movement of the foreign currencies which could act as an essential guidance for foreign exchange participants. By this way, they will be more alert before conducting any forex transactions including hedging, asset pricing or any speculation activity, take corrective actions, thus preventing them from making any potential losses in the future and gain more profit.Originality/valueThis is one of the first studies applying artificial intelligence (AI) while making use of time series modelling, the NARX neural network backpropagation algorithm and hybrid KPCA–SVR to predict forex using multiple currencies in the foreign exchange market in Mauritius.

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.