BACKCASTING BITCOIN VOLATILITY: ARCH AND GARCH APPROACHES

In order to model and forecast exchange rates in both developed and emerging countries, majority of time series analysts have employed various technical and fundamental approaches, the forecast outcome differs depending on the approach chosen or implemented. In this view, this study is about hybridization of Autoregressive Integrated Moving Average (ARIMA) with Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in forecasting exchange rate using monthly data of the Nigerian Naira against the U.S. Dollar for the period of January 2002 to February 2020. The stationarity of the exchange rate series is examined using unit root test of Augmented Dickey Fuller (ADF) test and Kwaitkowski-Philips-Schmidt-Shin (KPSS) which showed that the series is non stationary. To make the exchange rate series stationary, the data was transformed by first differencing and appropriate ARIMA models were obtained using Box-Jenkins method. ARIMA (0,1,1) and ARIMA(0,1,2) models were selected using AIC criteria and the residuals of these models were found to be serially correlated and heteroscedastic; hence the need for the hybridization of ARIMA with GARCH model. Therefore ARIMA models were hybridized with GARCH(1,1) to form ARIMA(0,1,1)-GARCH(1,1) and ARIMA(0,1,2)-GARCH(1,1). The results of forecast performance indicates that the best model is ARIMA(0,1,1)–GARCH(1,1) which has the lowest Root Means Square Error (RMSE) and Mean Absolute Error( MAE).

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.

A company acquiring an ownership through transfer of resources and technical know-how is essential for a sustainable growth and to face competition in the existing industry. The aim is to study the effect of CAGR on Foreign Direct Investment (FDI) inflows into Indian Pharmaceutical sector, secondly to regress the stock prices of top listed Indian Pharmaceutical sector and finally to analyse the Generalised Auto Regressive Conditional Heteroskedasticity (GARCH) effect on the Stock prices of selected Pharmaceutical sector. The research methodology applied is descriptive, analytical and univariate analysis. Time series tool of Auto Regressive Integrated Moving Averages (ARIMA) and GARCH is applied for generating the output and the major findings from the study is Apollo Hospitals Enterprise Limited, Cipla Ltd and Dr. Reddy’s Laboratories Limited Lab are stationary and optimum model as per information criteria is at ARIMA, (1, 1, 0) for Apollo Hospitals Enterprise Limited and ARIMA (0, 1, 1) for Cipla Limited and Dr. Reddy’s Laboratories Limited Lab.

Global commodity markets, particularly crude oil markets, are inherently characterized by pronounced price volatility driven by geopolitical tensions, macroeconomic shocks, financial speculation, and structural changes in energy demand and supply.Accurately modeling and forecasting such volatility is essential for policymakers, investors, and risk managers seeking to design effective stabilization, hedging, and investment strategies.This study provides a comprehensive empirical investigation of oil price volatility by applying three prominent members of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family-namely the standard GARCH, Threshold GARCH (TGARCH), and Exponential GARCH (EGARCH) models-to monthly West Texas Intermediate (WTI) crude oil prices over the period from January 2008 to June 2024.The selected timeframe captures multiple episodes of extreme market turbulence, including the global financial crisis, oil price collapses, the COVID-19 pandemic, and recent geopolitical disruptions.The analysis proceeds through a structured econometric methodology, beginning with the transformation of price levels into return series, followed by stationarity testing, descriptive statistical analysis, and volatility modeling.Empirical results reveal strong volatility clustering and persistence in WTI oil returns, confirming the suitability of GARCH-type models for capturing oil price dynamics.While asymmetric specifications (TGARCH and EGARCH) provide valuable insights into the differential effects of positive and negative shocks, the findings indicate that the GARCH(1,1) model offers the most 207 -www.imcra.az.org,

This study aimed to explore the impact of Ramadan on chicken meats in East Java. The ARCH/GARCH model is used in this study to assess whether or not beef has a price. Next, the GARCH model is used to analyze the effects of price volatility and fluctuations in Ramadan on the price of chicken meat in East Java. The ARCH-LM test's findings show that price volatility impacts changes in chicken meat prices. Then, the estimation results for the GARCH (1,1) model show that the volatility from the previous period and the variation in East Java from yesterday affect changes in chicken meat prices. GARCH (1,1) model displays.

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.

PurposeThe goal of the study is to offer important insights into the dynamics of the cryptocurrency market by analyzing pricing data for Bitcoin. Using quantitative analytic methods, the study makes use of a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and an Autoregressive Integrated Moving Average (ARIMA). The study looks at how predictable Bitcoin price swings and market volatility will be between 2021 and 2023.Design/methodology/approachThe data used in this study are the daily closing prices of Bitcoin from Jan 17th, 2021 to Dec 17th, 2023, which corresponds to a total of 1065 observations. The estimation process is run using 3 years of data (2021–2023), while the remaining (Jan 1st 2024 to Jan 17th 2024) is used for forecasting. The ARIMA-GARCH method is a robust framework for forecasting time series data with non-seasonal components. The model was selected based on the Akaike Information Criteria corrected (AICc) minimum values and maximum log-likelihood. Model adequacy was checked using plots of residuals and the Ljung–Box test.FindingsUsing the Box–Jenkins method, various AR and MA lags were tested to determine the most optimal lags. ARIMA (12,1,12) is the most appropriate model obtained from the various models using AIC. As financial time series, such as Bitcoin returns, can be volatile, an attempt is made to model this volatility using GARCH (1,1).Originality/valueThe study used partially processed secondary data to fit for time series analysis using the ARIMA (12,1,12)-GARCH(1,1) model and hence reliable and conclusive results.

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

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.

Crude oil is an important energy commodity to mankind. The fluctuation of crude oil prices has affected many related sectors and stock market indices. Hence, forecasting the crude oil prices is essential to avoid the future prices of the non-renewable natural resources to raise sky-rocket. In this study, daily West Texas Intermediate (WTI) crude oil prices data is obtained from Energy Information Administration (EIA) from 2nd January 1986 to 30th September 2009. This study uses the Box-Jenkins methodology and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) approach in analyzing the crude oil prices. ARIMA(1,2,1) and GARCH(1,1) are found to be the appropriate models under model identification, parameter estimation, diagnostic checking and forecasting future prices. In this study, the analyses are done with the aid of EViews software where the potential of this software in forecasting daily crude oil prices time series data is explored. Finally, using several measures, comparison performances between ARIMA(1, 2, 1) and GARCH(1,1) models are made. GARCH(1,1) is found to be a better model than ARIMA(1, 2, 1) model. Based on the study, it is concluded that ARIMA(1,2,1) model is able to produce good forecast based on a description of history patterns in crude oil prices. However, the GARCH(1,1) is the better model for daily crude oil prices due to its ability to capture the volatility by the non-constant of conditional variance.

This study explores the Nifty Pharma Index, focusing on the key drivers of growth and market behavior within the pharmaceutical sector. The research leverages six years of daily market data to examine trends, volatility, and the factors influencing the market performance of the index. Through a combination of econometric techniques, including Augmented Dickey-Fuller (ADF) tests, autocorrelation analysis, and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) and ARIMA (AutoRegressive Integrated Moving Average) models, the paper provides a detailed understanding of the Nifty Pharma Index's dynamic market behavior. The findings offer valuable insights for investors, policymakers, and market analysts, highlighting the volatility patterns and forecasting future price movements in the pharmaceutical sector.

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.

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. …