Generalized Autoregressive Conditional Heteroskedasticity Model Research Articles

Comparative Performance of Arima and Garch Models in Modelling and Forecasting Volatility of Kuala Lumpur Composite Index

Time series is a set of observations in sequence over time. Time series modelling is used to create an applicable model that defines the necessary arrangement of the series by study the previous information of a time series. The past information of a time series is used to generate forecast value for the series. It is well acknowledged that a time series are regularly affected with outliers. Outliers may impact the forecasting where the tendency in parameter estimates created by extreme observation will reduce its effectiveness because the optimum predictor for an Autoregressive Integrated Moving Average (ARIMA) model is determined by its parameters. Thus, the occurrence of extreme observations might have a huge effect on predictions value. Therefore, Generalized Autoregressive Conditional Heteroskedastic (GARCH) model has been used to compare the result obtain from ARIMA model. This study used ARIMA and GARCH to compare the best model for forecasting Kuala Lumpur Composite Index (KLCI) when the outlier exists. The best models of ARIMA and GARCH were evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). It can be concluded that GARCH model performed better compared to Box-Jenkins ARIMA in forecasting KLCI.

Portfolio Rebalancing with GARCH Model at Jarvis Balanced Fund

With high inflation economy, investors must find another way to minimize their risk, but also maximize their return of the portfolio. Various instruments used for finding the most suitable amount of portfolio allocation. Single instruments, such as stocks, bonds, and time deposits is chosen by investors to secure their assets from inflation. The other investors chose mutual funds to grow their investments. One of the solutions to find the portfolio allocation is to rebalance the portfolio. In other perspectives, time-series model will help investors to predict the volatility that will happen in the future. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model is used for finding volatility and generalized it from the ARCH Model. With GARCH Model, the total amount of residual and GARCH has to be less than 1. Either way, it will be categorized as a volatile asset. From the top 5 balanced fund in 2021, Jarvis Balanced Fund is one of the best-balanced funds with return of 55.85%/year. Using Jarvis Balanced Fund (JBF) portfolio from 2021 prospectus as the sample of this research, it is concluded that JBF has to reduce the number of stocks and increase the risk-free assets to prevent volatility that happen in the portfolio. Following with the macro economy of high-inflation economy era.

Interest rate, foreign exchange and stock performance in a dual banking industry: evidence from Saudi Arabia

PurposeThis study aims to extend the literature by extensively investigating the impact of foreign exchange and interest rate changes on the returns and volatility of bank stocks in Saudi Arabia, which is the largest dual banking industry.Design/methodology/approachThis study employs the generalized autoregressive conditional heteroscedasticity (GARCH) model on stock returns of four fully Islamic Saudi banks and eight conventional Saudi banks.FindingsThe results showed that the foreign exchange rate return has a positive impact on Saudi conventional bank returns, while it has an adverse impact on Saudi Islamic bank returns. Moreover, a higher interest rate return has a positive impact on Saudi bank stock returns implying that the assets side is more sensitive to changes in interest rates than the liability side. Finally, higher foreign exchange and interest rates volatility increases the volatility of Saudi bank returns, where the former has the largest significant impact. Therefore, Saudi regulators should pay more attention to the risk management of their banks because this could threaten the stability of their financial system.Originality/valueTo the best knowledge of the author, this is the first study that tries to extensively analyze the joint impact of foreign exchange and interest rates on bank stock returns and volatility in Saudi Arabia by applying the GARCH model. The study uses a long data set from 2010 to 2019 that includes all Saudi banks and employs four measures of interest rates to increase the robustness of the results.

Testing for parameter change epochs in GARCH time series

Summary We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against the alternative that there is an ‘abnormal’ period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process. Simulations in the Appendix show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e., the Bitcoin returns.

Факторы доходности Ethereum как платформы для создания децентрализованных приложений

By now, cryptocurrencies have almost become a part of the modern financial asset space, but the cryptocurrency market itself is not homogeneous, and individual cryptocurrencies can differ significantly in their properties and functions. For example, the cryptocurrency Ether is second in capitalization after Bitcoin, but the Ethereum and Bitcoin blockchains differ significantly in their properties and functions. In particular, Ethereum is the most popular digital platform for creating decentralized applications (dApps). The purpose of this work is to try to answer the question "Does the market take into account the features of the Ethereum blockchain in the price dynamics of the Ether cryptocurrency?" This question is also directly related to the search for potential fundamental factors that can explain the price dynamics of Ether. The main econometric method used in the study is generalized autoregressive conditional heteroskedasticity (GARCH) models. Having evaluated about 15 thousand different specifications of GARCH models, where various Ethereum blockchain usage metrics were used as explanatory variables, we obtained the results that Ethereum network usage metrics do not significantly correlate with Ether cryptocurrency returns. Moreover, these metrics are also unable to explain the relative strengthening/weakening of Ether relative to Bitcoin. Thus, we conclude that despite the presence of a number of special functional properties of the Ethereum blockchain, the price dynamics of the Ether cryptocurrency does not reflect them.

Assessing the accuracy of exponentially weighted moving average models for Value-at-Risk and Expected Shortfall of crypto portfolios

A plethora of academic papers on generalized autoregressive conditional heteroscedasticity (GARCH) models for bitcoin and other cryptocurrencies have been published in academic journals. Yet few, if indeed any, of these are employed by practitioners. Previous academic studies produce results that are fragmented, confusing and conflicting, so there is no commercial incentive to drive an expensive implementation of complex multivariate GARCH models, which anyway would commonly require more data for calibration than are available in the history of most cryptocurrencies, at least at the daily frequency. Consequently, this paper assesses the forecasting accuracy of simple parametric RiskMetrics type volatility and covariance models, with a focus on ad hoc parameter choice instead of a data-intensive calibration procedure. We provide extensive backtests of hourly and daily Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts that are regarded as best practice in the industry and commonly used for regulatory approval. Our results demonstrate that much simpler models in the exponentially weighted moving average (EWMA) class are just as accurate as GARCH models for VaR and ES forecasting, provided they capture an asymmetric volatility response and a heavy-tailed returns distribution. Moreover, on ranking each model's variance and covariance forecasts using average scores generated from proper univariate and multivariate scoring rules, there is no evidence of superior performance of variance and covariance forecasts generated by GARCH models, using either daily or hourly data.

Penerapan Metode Generalized Auto-Regressive Conditional Heteroscedasticity untuk Peramalan Harga Minyak Mentah Dunia

Crude oil is one of the commodities that are needed in various fields. World crude oil prices that continue to fluctuate, of course, have a big influence on the country's economy. Crude oil price data collected is time series or the collection process is carried out from time to time with monthly periods. Therefore, we need a system that can forecast future world crude oil prices which are expected to be taken into consideration by the government for decision making. One method that can be used to predict world crude oil prices is ARIMA (Auto-Regressive Integrated Moving Average) and GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) model. After modeling, it is proven that the world crude oil price data for the period January 2002 to June 2022 has a heteroscedasticity effect that cannot be overcome if only using the ARIMA model. The results of data processing show that the ARIMA (0,1,2) followed by the ARCH (2) is the best model with a MAPE value of 5,32%. The accuracy values obtained are classifield as very good for forecasting world crude oil prices.

How the effective reproductive number impacts global stock markets

AbstractThe pandemic caused by the novel coronavirus COVID‐19 has impact the economies of countries across the world. In a short period of time, researchers have begun to analyse the effect of the pandemic on global stock markets. Although the most known measurements of COVID‐19 are the number of new cases and deaths, there are more robust indicators. In particular, the effective reproductive number is one of the most important indicators to analyse the pandemic which indicates the degree to which the spread is under control. In this paper, we assess the impact that the Effective Reproductive Number (Rt) has on 26 countries around the world (32 stock market indexes) comparing the performance of various forms of Generalized AutoRegressive Conditional Heteroskedasticity models. The results demonstrate that of the 32 stock markets analysed, 37.5% had a negative effect with respect to Rt and only in 12.5% of the cases was the effect of the variation of Rt positive. This implies that in more than a third of the stock markets analysed as the pandemic progressed uncontrolled the result was a decrease in the value of the market index. The 11 of the 26 countries analysed had a negative and significant effect (Brazil, Germany, Indonesia, Israel, Italy, Japan, Russia, South Korea, Sweden, Taiwan, and United States). Findings suggest that the Effective Reproductive Number volatility had a significant impact on 10 of the 26 countries analysed (38.5%) (Australia, Brazil, Canada, China, India, Italy, Mexico, Russia, Singapore and United Kingdom).

Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models

This paper aims to make a comparison between range-based and return-based volatility models. For this purpose, we compare the Conditional Autoregressive Range (CARR) type and Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models with different innovation distributions and the Exponential Weighted Moving Average (EWMA) model with fixed and estimated lambda parameters. The out-of-sample forecasts obtained from the volatility processes are compared according to the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Heteroskedastic Root Mean Square Error (HRMSE), and Heteroskedastic Mean Absolute Error (HMAE) statistics. We use the USD-TRY exchange rate data for real-life applications since estimating the volatility of forex helps to determine prices for goods and services to avoid the uncertainty created by exchange rate shocks in developing countries such as Turkiye. Although MAE and RMSE show Gumbel CARR and Weibull CARR have the minimum error statistics, respectively, the HMAE and HRMSE statistics indicate that among the range-based models, the EWMA model, in which the lambda parameter is estimated, performs better. Furthermore, we find that Exponential CARR according to RMSE and MAE statistics, and Weibull CARR according to HMAE and HRMSE statistics appear as the return-based volatility models with minimum error.

The Economics of Cryptocurrencies: Finance in Digital Era

Global economic markets are encountering apprehensions and susceptibilities after the pandemic of COVID-19. Investment patterns are becoming restrained because of uncertain global scenarios and reduced GDP worldwide. World economies are moving towards digital era and investors are becoming more open towards the newest forms of investments. Due to the uncertain scenarios, investors globally are looking forward to some lucrative forms of investments and cryptocurrencies are the ray of hope for global investors. The present study is attempt to explore the changing dynamics of cryptocurrencies with the market uncertainties. Volatility of five cryptocurrencies, namely Bitcoin, Ethereum, XRP, Chainlink and Bitcoin Cash are analysed using the Generalised AutoRegressive Conditional Heteroskedasticity Model. Results showed that the investors preferred taking cautious decisions and invested more in famous bitcoin rather than other cryptocurrencies.

Forecasting Bitcoin Volatility Using Hybrid GARCH Models with Machine Learning

The time series movements of Bitcoin prices are commonly characterized as highly nonlinear and volatile in nature across economic periods, when compared to the characteristics of traditional asset classes, such as equities and commodities. From a risk management perspective, such behaviors pose challenges, given the difficulty in quantifying and modeling Bitcoin’s price volatility. In this study, we propose hybrid analytical techniques that combine the strengths of the non-stationary properties of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models with the nonlinear modeling capabilities of deep learning algorithms, such as Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Bidirectional LSTM (BiLSTM) algorithms with single, double, and triple layer network architectures to forecast Bitcoin’s realized price volatility. Our findings, both in-sample and out-of-sample, show that such hybrid models can generate accurate forecasts of Bitcoin’s price volatility.

Volatility Prediction via Hybrid LSTM Models with GARCH Type Parameters

Since the establishment of financial models for risk prediction, the measurement of volatility at risky market has improved, and its significance has also grown. For high-frequency financial data, the degree of investment risk, which has always been the focus of attention, is measured by the variance of residual sequence obtained following model regression. By integrating the long short-term memory (LSTM) model with multiple generalized autoregressive conditional heteroscedasticity (GARCH) models, a new hybrid LSTM model is used to predict stock price volatility. In this paper, three GARCH models are used, and the model that can best fit the data is determined.

Interaction Between Spot and Future Currency Market of India: Empirical Evidence

The study empirically analyses the interdependence and price discovery mechanism between the spot and futures (S&F) prices of the Indian Foreign Exchange Market. Daily closing prices of S&F currency pairs were collected from February 2010 to March 2021. Before investigating causality, the descriptive statistical test and unit root test (augmented Dickey–Fuller) are used to test the stationarity of data. An error correction model examines the long- and short-run relationship between S&F market currency pairs. The currency returned series stationarity at I(1) identified the presence of heteroscedasticity and found the absence of the Autoregressive Conditional Heteroskedasticity effect. To avoid the possible ignorance of the long-run relationship between S&F and to confirm the trustworthiness of regression at levels, the cointegration technique was employed under Johansen’s technique. The existence of cointegration at levels provides power to use Vector Error Correction Models, considering the level and difference in the estimation process. There is a long-run equilibrium relationship between spot rates and future rates, with a bidirectional causal association among currency S&F prices of all the currency pairs. Additionally, the futures market tends to regulate any new data quicker than the spot market. It suggests that spot price is led by future price, thus contributing substantially to the price-discovery process. The Generalized Autoregressive Conditional Heteroskedasticity models establish persistence in volatility, and the bad news gives rise to more volatility as compared to good news.

Capital‐flow volatility in emerging markets: A panel GARCH approach

AbstractThis study analyzes the role of push–pull factors on the level, volatility and comovement of capital flows in emerging markets (EMs). Taking the commonality of capital flows into account, we employ the panel Generalized Autoregressive Conditional Heteroscedasticity model developed by Cermeño and Grier for 16 EMs. This method not only accounts for country‐specific heterogeneity and cross‐section dependence but also allows the examination of the sources of the level, volatility and comovement of capital flows in a single step. The results show that domestic factors explain two‐thirds of the variation in net capital‐flow volatility. While both global and domestic factors, with the prominent ones being global risks and domestic economic growth, influence the comovement, their impacts somewhat vary by the types of capital flows.

Modeling and Forecasting Cryptocurrency Returns and Volatility: An Application of GARCH Models

The future of e-money is crypocurrencies, it is the decentralize digital and virtual currency that is secured by cryptography. It has become increasingly popular in recent years attracting the attention of the individual, investor, media, academia and governments worldwide. This study aims to model and forecast the volatilities and returns of three top cryptocurrencies, namely; Bitcoin, Ethereum and Binance Coin. The data utilized in the study was extracted from the higher market capitalization at 31st December, 2021 and the data for the period starting from 9th November, 2017 to 31st December 2021. The Generalised Autoregressive conditional heteroscedasticity (GARCH) type models with several distributions were fitted to the three cryptocurrencies dataset with their performances assessed using some model criteria. The result shows that the mean of all the returns are positive indicating the fact that the price of this three crptocurrencies increase throughout the period of study. The ARCH-LM test shows that there is no ARCH effect in volatility of Bitcoin and Ethereum but present in Binance Coin. The GARCH model was fitted on Binance Coin, the AIC and log L shows that the CGARCH is the best model for Binance Coin. Automatic forecasting was perform based on the selected ARIMA (2,0,1), ARIMA (0,1,2) and the random walk model which has the lowest AIC for ETH-USD, BNB-USD and BTC-USD respectively. This finding could aid investors in determining a cryptocurrency's unique risk-reward characteristics. The study contributes to a better deployment of investor’s resources and prediction of the future prices the three cryptocurrencies.

A Garlic-Price-Prediction Approach Based on Combined LSTM and GARCH-Family Model

The frequent and sharp fluctuations in garlic prices seriously affect the sustainable development of the garlic industry. Accurate prediction of garlic prices can facilitate correct evaluation and scientific decision making by garlic practitioners, thereby avoiding market risks and promoting the healthy development of the garlic industry. To improve the prediction accuracy of garlic prices, this paper proposes a garlic-price-prediction method based on a combination of long short-term memory (LSTM) and multiple generalized autoregressive conditional heteroskedasticity (GARCH)-family models for the nonstationary and nonlinear characteristics of garlic-price series. Firstly, we obtain volatility characteristic information such as the volatility aggregation of garlic-price series by constructing GARCH-family models. Then, we leverage the LSTM model to learn the complex nonlinear relationships between the garlic-price series and the volatility characteristic information of the series, and predict the garlic price. We applied the proposed model to a real-world garlic dataset. The experimental results show that the prediction performance of the combined LSTM and GARCH-family model containing volatility characteristic information of garlic price is generally better than those of the separate models. The combined LSTM model incorporating GARCH and PGARCH models (LSTM-GP) had the best performance in predicting garlic price in terms of evaluation indexes, such as mean absolute error, root mean-square error, and mean absolute percentage error. The combined model of LSTM-GARCH provides the best results in garlic price prediction and can provide support for garlic price prediction.

Modelling and forecasting COVID-19 stock returns using asymmetric GARCH-ICAPM with mixture and heavy-tailed distributions

ABSTRACT COVID-19 pandemic is an extreme event that created turmoil in stock markets around the world. This unexpected circumstance poses a critical question of whether the prevailing models can help predict the plummets of indices, hence the returns. In this study, we aim to analyse and forecast the daily stock returns using various generalized autoregressive conditional heteroscedastic (GARCH) models with intertemporal capital asset pricing structure and innovation following (1) a mixture of generalized Pareto and Gaussian distributions and (2) generalized error distribution that can capture extreme events. We also employ the parallel griddy Gibbs (GG) sampling, which is a Markov chain Monte Carlo method, to facilitate parameter estimation. Our simulation study shows that the GG estimation method outperforms the benchmark quasi-maximum likelihood estimation method. We then proceed to the empirical study of seven stock markets where the results from the in-sample period before the COVID-19 pandemic justify the use of the proposed GARCH models. The out-of-sample forecasts during the early COVID-19 period also show satisfactory results.

A market sentiment indicator, behaviourally grounded, for the analysis and forecast of volatility and bubbles

PurposeThis work aims at designing an indicator for detecting and forecasting price volatility and speculative bubbles in three markets dealing with agricultural and soft commodities, i.e. Intercontinental Exchange Futures market Europe, (IFEU), Intercontinental Exchange Futures market United States (IFUS) and Chicago Board of Trade (CBOT). This indicator, designed as a demand/supply odds ratio, intends to overcome the subjectivity limits embedded in sentiment indexes as the Bull and Bears ratio by the Bank of America Merrill Lynch.Design/methodology/approachData evidence allows for the parameter estimation of a Jacobi diffusion process that models the demand share and leads the forecast of speculative bubbles and realised volatility. Validation of outcomes is obtained through the dynamic regression with autoregressive integrated moving average (ARIMA) error. Results are discussed in comparison with those from the traditional generalized autoregressive conditional heteroskedasticity (GARCH) models. The database is retrieved from Thomson Reuters DataStream (nearby futures daily frequency).FindingsThe empirical analysis shows that the indicator succeeds in capturing the trend of the observed volatility in the future at medium and long-time horizons. A comparison of simulations results with those obtained with the traditional GARCH models, usually adopted in forecasting the volatility trend, confirms that the indicator is able to replicate the trend also providing turning points, i.e. additional information completely neglected by the GARCH analysis.Originality/valueThe authors' commodity demand as discrete-time process is capable of replicating the observed trend in a continuous-time framework, as well as turning points. This process is suited for estimating behavioural parameters of the agents, i.e. long-term mean, speed of mean reversion and herding behaviour. These parameters are used in the forecast of speculative bubbles and realised volatility.

Enhanced data fidelity after ground roll attenuation using conditional standard deviation clustering obtained from the GARCH model

ABSTRACT The main purpose of this research is to evaluate the effectiveness of coherent noise clustering in reconstructing leaked signals after conventional noise attenuation filters. We use Generalised Auto Regressive Conditional Heteroskedasticity (GARCH) model. We apply clustering, conditional variance, and conditional standard deviation analysis to synthetic and experimental seismic field data. The conditional variance and conditional standard deviation of coherent noises that are attenuated by the Ormsby and f-k filter are calculated. Each cluster is labelled using the two-dimensional average clustering method and then leaked signals are reconstructed from the initially filtered data to improve the signal-to-noise ratio. Results show that the proposed method mostly reconstructs the leaked signals after conventional filters.

Forecasting the exchange rate of Nigerian Naira to United State’ Dollar using ARIMA-GARCH Model

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).