Stock Price Forecasting Using A Dependence Structure

Purpose- The primary purpose of this study is to model Bitcoin price volatility and forecast its future price returns using advanced econometric models such as ARCH and GARCH. The study aims to enhance risk management strategies and support informed investment decisions by addressing the time-varying nature of Bitcoin’s volatility. The research explores the persistence of volatility shocks and the clustering of price movements to provide insights into market dynamics. Methodology- This research examines daily Bitcoin closing prices over the period from January 2020 to October 2024. The data was preprocessed to ensure reliability, including applying logarithmic transformations to standardize the data and eliminate trends. Stationarity tests, such as the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and KPSS tests, were conducted to confirm the series' stationarity. The ARCH-LM test was utilized to detect volatility clustering which is essential for validating the use of ARCH and GARCH models. Following this, ARIMA models were employed to define mean equations and GARCH models were used to estimate conditional variance and capture volatility dynamics. The dataset was split into training and validation subsets with data from July to October 2024 reserved for validation. Findings- The findings demonstrate that Bitcoin’s price movements exhibit significant volatility clustering and persistence of shocks which are key characteristics effectively captured by ARCH and GARCH models. These models provide valuable insights into the volatility patterns of Bitcoin, supporting their application in cryptocurrency analysis. Despite their robustness, the models face limitations in precise return forecasting during highly volatile periods, suggesting the need for further refinement or integration with advanced approaches. Conclusion- The research concludes that ARCH and GARCH models are effective tools for understanding and forecasting Bitcoin’s volatility. The study underscores the importance of acknowledging volatility persistence and clustering effects when analyzing cryptocurrency price behavior. However, it also highlights areas for improvement in econometric modelling by including the exploration of hybrid models and the integration of macroeconomic factors to enhance forecasting accuracy. Keywords: Bitcoin, ARCH models, GARCH Models, forecasting, ARIMA models JEL Codes: C58, G10, G12

A class of robust M-estimators for generalised autoregressive conditional heteroscedastic (GARCH) type models are used for the prediction of value-at-risk (VaR) of Karachi Stock Exchange (KSE). To better understand the impact of global financial crisis on KSE, the daily stock return data is divided into three sub-periods: the pre-crisis period (3 January 2005 to 31 December 2007), the crisis period (2 January 2008 to 30 June 2009), and the post-crisis period (1 July 2009 to 31 December 2013). Symmetric and asymmetric GARCH models that capture the most common stylised facts about index returns such as volatility clustering and leverage effect are fitted to these time periods and in-sample and out-of-sample estimates of VaR are obtained. Our results show that M-estimators provide accurate and reliable estimates of VaR in low and high volatile time. Our findings also show that the asymmetric model provides better fit than the symmetric model for the KSE.

Modeling Time Varying Volatility and Asymmetry of Karachi Stock Exchange (KSE)

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.

BackgroundThis paper examines the pattern of the volatility of the daily return of select commodity futures in India and explores the extent to which the select commodity futures satisfy the Samuelson hypothesis.MethodsOne commodity future from each group of futures is chosen for the analysis. The select commodities are potato, gold, crude oil, and mentha oil. The data are collected from MCX India over the period 2004–2012. This study uses several econometric techniques for the analysis. The GARCH model is introduced for examining the volatility of commodity futures. One of the key contributions of the paper is the use of the β term of the GARCH model to address the Samuelson hypothesis.ResultThe Samuelson hypothesis, when tested by daily returns and using standard deviation as a crude measure of volatility, is supported for gold futures only, as per the value of β (the GARCH effect). The values of the rolling standard deviation, used as a measure of the trend in the volatility of daily returns, exhibits a decreasing volatility trend for potato futures and an increasing volatility trend for gold futures in all contract cycles. The result of the GARCH (1,1) model suggests the presence of persistent volatility and the prevalence of long memory for the select commodity futures, except potato futures.ConclusionsThe study sheds light on significant characteristics of the daily return volatility of the commodity futures under analysis. The results suggest the existence of a developed market for the gold and crude oil futures (with volatility clustering) and show that the maturity effect is only valid for the gold futures.

The investors, policy makers and researchers give lot of attention towards evaluation of risk while analysing the stock market. The quality of risk measures very largely depends on how well the econometric model captures behaviour of underlying asset. The paper examines the relationship between returns and volatility, volatility clustering, leverage effect and the persistence of volatility for the Indian stock markets viz. National Stock Exchange(NSE) and Bombay Stock Exchange (BSE) for period from 1990 to 2016. The main focus of this research paper is to examine the nature of the volatility in the Indian stock markets. In this study ARCH and GARCH models have applied to study the behaviour of stock market volatility. This study shows that GARCH (1, 1) model is more satisfactorily explains volatility clustering and its high persistence for better decision making purpose.

A class of robust M-estimators for generalised autoregressive conditional heteroscedastic (GARCH) type models are used for the prediction of value-at-risk (VaR) of Karachi Stock Exchange (KSE). To better understand the impact of global financial crisis on KSE, the daily stock return data is divided into three sub-periods: the pre-crisis period (3 January 2005 to 31 December 2007), the crisis period (2 January 2008 to 30 June 2009), and the post-crisis period (1 July 2009 to 31 December 2013). Symmetric and asymmetric GARCH models that capture the most common stylised facts about index returns such as volatility clustering and leverage effect are fitted to these time periods and in-sample and out-of-sample estimates of VaR are obtained. Our results show that M-estimators provide accurate and reliable estimates of VaR in low and high volatile time. Our findings also show that the asymmetric model provides better fit than the symmetric model for the KSE.

The volatility of cryptocurrency markets has increased substantially in recent years, particularly for Ethereum (ETH), which exhibits fat-tailed distributions and persistent volatility clustering that traditional linear models are unable to capture. This study aims to analyze and model the volatility of ETH/USD using high-frequency hourly data to determine the most appropriate volatility model for describing Ethereum’s intraday market dynamics. The dataset consists of 8,760 hourly closing prices from October 31, 2024 to October 31, 2025, obtained through the CryptoCompare API. The methodological framework includes data preprocessing, log-return transformation, stationarity analysis using the Augmented Dickey–Fuller test, detection of heteroskedasticity via the ARCH–LM test, and estimation of several ARCH and GARCH model specifications. The results show that ETH/USD returns are stationary, non-normally distributed, and exhibit clear volatility clustering. Among the ARCH models, only ARCH(1) adequately captures short-term fluctuations, while ARCH(2) provides no additional benefit. In contrast, GARCH models demonstrate superior performance in capturing both short-term shocks and long-term persistence. Based on AIC, BIC, and log-likelihood values, GARCH(1,2) emerges as the best-performing model, offering the highest flexibility in representing Ethereum’s persistent and reactive volatility patterns. These findings confirm that ETH/USD volatility is predictable and can be modeled statistically. Future research may incorporate asymmetric GARCH extensions or external explanatory variables to improve predictive performance.

An increase in inflation volatility implies higher uncertainty about future prices. As a result, producers and consumers can be affected by the increased inflation volatility, because it increases the uncertainty and the risk in the market. Thus, inflation volatility attracts the attention of researchers to find a suitable model which can predict the future conditions of the market. This study aims to fit appropriate ARMA-GARCH family models for food and non-food inflation rate of from the period January 1971 through June 2020. Since the main objective of the study is identifying an appropriate model for inflation series, the null and alternative hypotheses are defined in comparison of the two types of models. H0: The symmetric GARCH models better capture inflation volatility of Ethiopia. H1: The asymmetric GARCH models better capture inflation volatility of Ethiopia. The ARMA-GARCH family models were applied to capture the stylized facts of financial time series such us leptokurtic, volatility clustering and leverage effects. The mean model results show that, an ARMA (1, 2) and ARIMA (0, 1, 1) models are identified as the best fitted model for food and non-food inflation, respectively. From the estimation results of volatility model, an asymmetric TGARCH (1, 1) model with Student's t- distributional assumptions of the residual is the best model for non-food inflation. Thus, modeling of information, news of events is very significant determinants of volatility and GARCH family models are appropriate for the given series (monthly food-inflation volatility) of Ethiopia under the study period considered.

Malaysia is one of the largest producers of natural rubber in the world. Among the various types of natural rubber which contribute to the country’s agricultural sector is the Standard Malaysian Rubber Grade 20 (S.M.R 20). Since 2008, the rubber price has received attention of investors and Malaysia Rubber Board due to price fluctuation. The price of rubber is characterized by the existence of heavy tails and volatility clustering. These properties play a significant impact on parameter estimation and forecasting performance resulting from S.M.R 20 rubber price data. The approach used in modeling S.M.R 20 rubber price data, is Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The aims of this paper are to find the best ARMA-GARCH model by using different specifications structures and to forecast the daily price for 20 days ahead. There are 20 models produced from different specifications in ARMA(R,M) dan GARCH(p,q) models. In this study, 1953 daily price data of S.M.R 20 are taken into consideration. The validity comparison of diagnostic checking and forecasting performance are based on AIC, AICC, SBC, HQC, MSE, RMSE and MAPE. The results reveals that ARMA(1,0)-GARCH(1,2) model is the best volatility modeling in S.M.R 20 rubber price. Based on the implications of the results, the scope of the future research directions has been widen.

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. …

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

Nut consumption and risk of cardiovascular disease events and all-cause mortality: A systematic review and dose-response meta-analysis of prospective cohort studies.

Increasing environmental consciousness among various stakeholders of financial markets has led to the introduction of GREENEX and CARBONEX indices by Bombay Stock Exchange (BSE). This study is an attempt to analyse the impact of macro-economic variables, namely growth rate (GDP), inflation (WPI) and exchange rate (FOREX) on both the sustainability indices. The paper also attempts to find the presence of volatility clustering in the sustainability indices of India. The cointegration amongst the macro-economic variables and sustainability indices is tested through auto-regressive distributive lag (ARDL) Approach and significant results are achieved for both the indices. The volatility clustering for GREENEX and CARBONEX is tested through GARCH (1, 1) model and significant volatility clustering is established for both the indices. These significant relationships highlight that the macro-economic variables have a significant and crucial impact on sustainability of the Indian economy. Any measure taken to improve the growth rate, exchange rate, or inflation shall significantly facilitate sustainability in the Indian economy, further reducing the volatility in stock market and economy.

Background:Employing a developmental psychopathology framework, we tested the utility of the hormesis model in examining the strengthening of children and youth through limited levels of adversity in relation to internalizing and externalizing outcomes within a brain-by-development context.Methods:Analyzing data from the Adolescent Brain and Cognitive Development study (N = 11,878), we formed latent factors of threat, deprivation, and unpredictability. We examined linear and nonlinear associations between adversity dimensions and youth psychopathology symptoms and how change of resting-state functional connectivity (rsFC) in the default mode network (DMN) from Time 1 to Time 5 moderates these associations.Results:A cubic association was found between threat and youth internalizing problems; low-to-moderate family conflict levels reduced these problems. Deprivation also displayed a cubic relation with youth externalizing problems, with moderate deprivation levels associated with fewer problems. Unpredictability linearly increased both problem types. Change in DMN rsFC significantly moderated the cubic link between threat levels and internalizing problems, with declining DMN rsFC levels from Time 1 to Time 5 facilitating hormesis. Hormetic effects peaked earlier, emphasizing the importance of sensitive periods and developmental timing of outcomes related to earlier experiences.Conclusions:Strengthening through limited environmental adversity is crucial for developing human resilience. Understanding this process requires considering both linear and nonlinear adversity-psychopathology associations. Testing individual differences by brain and developmental context will inform preventive intervention programming.