Academic literature on the topic 'Generalised AutoRegressive Conditional Heteroscedastic (GARCH)'

Financial time series are defined by their fluctuations, which are characterized by instability or uncertainty, implying that there are periods of volatility followed by periods of relative calm. Therefore, time series analysis requires homogeneity of variance. In this paper, some models used in time series analysis have been studied and applied. Comparison between Autoregressive Moving Average (ARMA) and Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models to identify the efficient model through (MAE, MASE) measures to determine the best forecasting model is studied. The findings show that the models of Generalised Autoregressive Conditional Heteroscedastic are more efficient in forecasting time series of financial. In addition, the GARCH model (1,1) is the best to forecasting exchange rate.

Abstract. In time series data that has a fairly high volatility, it is possible to have an error variance that is not constant (Heteroscedasticity). This is reflected in the square of error that also follows the time series model, for example the autoregressive (AR) model and the expectation of the conditional error square is not constant, the AR model of the square of error is called the Autoregressive Conditional Heteroscedastic (ARCH). The AR model that combines time series data and squared error is called Generalized Autoregressive Conditional Heteroscedastic (GARCH). However, the GARCH model ignores the asymmetric effect on the data. So Nelson (1991) developed the GARCH model to overcome the asymmetric problem with the Exponential GARCH model. The purpose of this study was to determine the symptoms of the EGARCH model and apply the EGARCH model in stock price index data at PT. Bank X in Indonesia. The data used is closing price data for the period January 2019 – December 2021. The results show that the Residual from GARCH(2.0) is used to test the effect of asymmetry. The best model used for forecasting based on the comparison results of MAPE, AIC and SIC values ​​from several other models is the EGARCH(2,1) model. Abstrak. Pada data deret waktu yang memiliki volatilitas cukup tinggi dimungkinkan memiliki varian error menjadi tidak konstan (Heteroskedastisitas). Hal ini tercermin dari kuadrat error yang juga mengikuti model deret waktu, misal model autoregressive (AR) dan ekpektasi kuadrat error bersyarat tidak konstan, model AR dari kuadrat error disebut Autoregressive Conditional Heteroscedastic (ARCH). Model AR yang menggabungkan data deret waktu dan kuadrat error disebut Generalized Autoregressive Conditional Heteroscedastic (GARCH). Namun model GARCH mengabaikan efek asimetris pada data. Sehingga Nelson (1991) mengembangkan model GARCH untuk mengatasi permasalahan asimetris dengan model Exponential GARCH. Tujuan dari penelitian ini adalah untuk mengetahui gejala model EGARCH dan menerapkan model EGARCH pada data indeks harga saham di PT. Bank X di Indonesia. Data yang digunakan merupakan data harga penutupan selama periode Januari 2019 – Desember 2021. Hasilnya menunjukkan bahwa Residual dari GARCH(2,0) dipakai untuk menguji pengaruh asimetri. Model terbaik yang digunakan untuk peramalan berdasarkan hasil perbandingan nilai MAPE, AIC maupun SIC dari beberapa model lainnya ialah model EGARCH(2,1).

Forecasting of the Renewable Energy plays a major role in optimal decision formula for government and industrial sector in Bangladesh. This research is based on time series modeling with special application to solar energy data for Dhaka city. Three families of time series models namely, the autoregressive integrated moving average models, Holt’s linear exponential smoothing, and the autoregressive conditional heteroscedastic (with their extensions to generalized autoregressive conditional heteroscedastic) models were fitted to the data. The goodness of fit is performed via the Akaike information criteria, Schwartz Bayesian criteria. It was established that the generalized autoregressive conditional heteroscedastic model was superior to the autoregressive integrated moving average model and Holt’s linear exponential smoothing because the data was characterized by changing mean and variance.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11486 Dhaka Univ. J. Sci. 60(2): 159-162, 2012 (July)

This study was aimed to build a model for the estimation of national harvested area of rice by incorporating element of variant heterogeneity and the influence of asymmetry factors on time series data using five types of GARCH models, namely: symmetric GARCH, exponential asymmetric GARCH, quadratic asymmetric GARCH, Threshold GARCH, and non-linear asymmetric GARCH. Those models were compared and evaluated, and then the best model was used to predict the accuracy of the national rice harvested area. The results showed that two types of GARCH had significant coefficient, indicating the validity of the model. Those models were symmetric GARCH and quadratic GARCH models. Based on the value of mean absolute percentage error (MAPE) for the twelve month periods ahead, quadratic GARCH model was better than the symmetric GARCH model. Furthermore, based on the value of mean absolute deviation (MAD) and mean square error (MSE), quadratic GARCH model also seemed to be a better model than symmetric GARCH model. The best model can be used to predict the harvested area in the subsequent year.

Rice farming for Indonesia is vital. Rice farming is inseparable from the fact that rice farming is the livelihood of most of the population, while rice is the staple food of almost all Indonesians. The nature of rice that is easy to process and, following the public consumption culture, causes a very high dependence on rice. On the other hand, the price of rice is quite volatile. If the price of rice is soaring high, it can cause changes in the pattern of rice consumption. Some people want a stable supply and rice price, available at all times and evenly distributed and at affordable prices. Because the cost of rice is quite fluctuating, it is necessary to have a model that can be used to predict future rice prices so that the right policies can be implemented. Autoregressive Integrated Moving Average Model Generalized Autoregressive Conditional Heteroscedastic (ARIMA-GARCH) is a useful model for evaluating and predicting price fluctuations. This model's application is implemented in the national average retail rice price data between January 2007 and December 2017. In this study, rice data in the study period was not stationary at the level so that differentiating was carried out in the data. The best model is ARIMA (1,1,2) and Garch model (2,0). In this model, the data has complied with the white noise assumption, and the resulting GARCH model is free from the heteroscedasticity assumption.

In this paper, time series theory is used to modelling monthly inflation data in Albania during the period from January 2000 to December 2016. The autoregressive conditional heteroscedastic (ARCH) and their extensions, generalized autoregressive conditional heteroscedasticity (GARCH)) models are used to better fit the data. The study reveals that the inflation series is stationary, non-normality and has serial correlation. Based on minimum AIC and SIC values the best model turn to be GARCH (1, 1) model with mean equation ARMA (2, 1)x(2, 0)12. Based on the selected model one year of inflation is forecasted (from January 2016 to December 2016).

Abstract Modeling exchange rate volatility became an important topic for research debate starting with 1973, when many countries switched to floating exchange rate system. In this paper, we focus on the EUR/RON exchange rate both as an economic measure and present the implied economic links, and also as a financial investment and analyze its movements and fluctuations through two volatility stochastic processes: the Standard Generalized Autoregressive Conditionally Heteroscedastic Model (GARCH) and the Exponential Generalized Autoregressive Conditionally Heteroscedastic Model (EGARCH). The objective of the conditional variance processes is to capture dependency in the return series of the EUR/RON exchange rate. On this account, analyzing exchange rates could be seen as the input for economic decisions regarding Romanian macroeconomics - the exchange rates being influenced by many factors such as: interest rates, inflation, trading relationships with other countries (imports and exports), or investments - portfolio optimization, risk management, asset pricing. Therefore, we talk about political stability and economic performance of a country that represents a link between the two types of inputs mentioned above and influences both the macroeconomics and the investments. Based on time-varying volatility, we examine implied volatility of daily returns of EUR/RON exchange rate using the standard GARCH model and the asymmetric EGARCH model, whose parameters are estimated through the maximum likelihood method and the error terms follow two distributions (Normal and Student’s t). The empirical results show EGARCH(2,1) with Asymmetric order 2 and Student’s t error terms distribution performs better than all the estimated standard GARCH models (GARCH(1,1), GARCH(1,2), GARCH(2,1) and GARCH(2,2)). This conclusion is supported by the major advantage of the EGARCH model compared to the GARCH model which consists in allowing good and bad news having different impact on the volatility. The EGARCH model is able to model volatility clustering, persistence, as well as the leverage effect.

Abstract This paper studies the quasi-maximum likelihood estimator (QMLE) for the generalized autoregressive conditional heteroscedastic (GARCH) model based on the Laplace (1,1) residuals. The QMLE is proposed to the parameter vector of the GARCH model with the Laplace (1,1) firstly. Under some certain conditions, the strong consistency and asymptotic normality of QMLE are then established. In what follows, a real example with Laplace and normal distribution is analyzed to evaluate the performance of the QMLE and some comparison results on the performance are given. In the end the proofs of some theorem are presented.

This study considers the problem of detecting a change in the conditional variance of time series with time-varying volatilities based on the cumulative sum (CUSUM) of squares test using the residuals from support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) models. To compute the residuals, we first fit SVR-GARCH models with different tuning parameters utilizing a time series of training set. We then obtain the best SVR-GARCH model with the optimal tuning parameters via a time series of the validation set. Subsequently, based on the selected model, we obtain the residuals, as well as the estimates of the conditional volatility and employ these to construct the residual CUSUM of squares test. We conduct Monte Carlo simulation experiments to illustrate its validity with various linear and nonlinear GARCH models. A real data analysis with the S&P 500 index, Korea Composite Stock Price Index (KOSPI), and Korean won/U.S. dollar (KRW/USD) exchange rate datasets is provided to exhibit its scope of application.

During the past several decades, the importance of assessing the risk of GDP growth downturns has increased tremendously. The financial crisis of 2008–2009 and the global lockdown caused by the COVID-19 pandemic demonstrated the vulnerability of the modern economy. As a result, a new framework (Growth-at-Risk) has been developed which allows the estimation of the size of the potential downfall of future GDP growth. However, most of the research focuses on the performance of quantile regression. I apply different approaches to forecasting growth-at-risk, including quantile regression, quantile random forests, and generalised autoregressive conditional heteroscedastic (GARCH) models, using the US economy for the analysis. I find that GARCH-type models perform worse at 5% and 10% coverage levels, but that quantile random forests and quantile regressions seem to have equal predictive ability.

This study investigates the return generating process underlying the South African stock market. The investigation of the return generating process is framed within the Arbitrage Pricing Theory (APT) framework with the APT reinterpreted so as to provide a conceptual framework within which the return generating process can be investigated. In modelling the return generating process, the properties of South African stock returns are taken into consideration and an appropriate econometric framework in the form of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models is applied. Results indicate that the return generating process of South African stock returns is described by innovations in multiple risk factors representative of several risk categories. The multifactor model of the return generating process explains a substantial amount of variation in South African stock returns and the ARCH/GARCH methodology is an appropriate econometric framework for the estimation of models of the return generating process. The APT framework is successfully applied to model and investigate the return generating process of South African stock returns.

This thesis involves a theoretical and empirical examination of issues in financial risk management with a focus on the Australian environment. The primary aim of the thesis is to contribute to the understanding of the use and impact of derivative financial instruments for financial risk management. The majority of published work in this area is from the U.S.A. Therefore, the analysis and results contained in this thesis are of interest to an international audience. The results provide new evidence, in addition to confirmatory evidence, in relation to a number of issues. The thesis is divided into three sections with the conclusions provided in chapter eleven. The thesis is divided into three sections with the conclusions provided in chapter eleven. Following the introduction in chapter one, the first section (chapters two to five)examines issues associated with risk management. Chapter two considers some of the professional standards for the management of risk that have been issued by various professional and regulatory bodies. Chapter three examines different types of derivative contracts and how derivatives may be used. Measuring risk is an essential part of managing it. Financial risk is often difficult to identify from outside the organisation because organisations may hedge any portion of the exposure. Furthermore, financial risk may arise and then cease to exist as contracts are settled in such short periods that there is little evidence outside the firm to allow identification of them. However, there have been attempts to measure exposure to financial risk and these are covered in chapter four. Chapter five examines the theoretical issues associated with hedging financial risk and the potential benefits obtained from hedging. Section two (chapters six and seven) considers the use of derivatives in Australian Commonwealth public sector organisations. Risk management has traditionally been seen within the context of private sector organisations. However, the issue is becoming increasingly relevant and important to public sector entities as governments around the world implement policies that involve corporatisation, devolution of financial responsibility and impose competitive neutrality on their departments and bodies. Australia is no different and in some circles is seen as a world leader in the evolution of a business-orientated public sector. However, the strict translation of private sector theories and practices to the public sector, in which there are fundamental differences, may not be feasible nor desirable. Further, risk management in the public sector may require different practices and methods to achieve the desired outcomes. Chapter six introduces the empirical aspects of the thesis by considering the legal power of Commonwealth organisations in Australia to enter into derivative contracts. Public sector organisations, in particular Commonwealth statutory authorities, do not always have the powers 'of a natural person' afforded to companies governed under Australian corporations law. Such inconsistency is the base for uncertainty and possible additional costs for parties contracting with these organisations. Chapter six concludes with possible solutions to remove the uncertainty with respect to the legal power of Commonwealth organisations to enter derivative contracts. Chapter seven examines the use of derivative contracts in Commonwealth organisations through financial statement analysis and a questionnaire survey. This chapter represents the first public study of derivative use in Commonwealth organisations in Australia. Section three (chapters eight, nine and ten) considers important issues in the efficiency of derivatives markets. Three issues are considered. Chapter eight considers the price and volatility effects surrounding expirations of 90-day Bank Accepted Bill futures contracts. The evidence as presented in chapter eight for the Australian 90-day Bank Accepted Bills market is not sufficient to conclude that there are abnormal price or volatility effects surrounding the expiration of equivalent futures contracts. Hedgers therefore are unlikely to experience higher volatility if contracts are closed out or rolled over on maturity day. Another potential problem when hedging is pricing derivative contracts, such as options. When derivatives, in particular option contracts, are used in risk management the price of the contract must be ascertained. The Black-Scholes option pricing model is commonly used to price options. If the model incorrectly prices options then risk management strategies will be less effective. One bias, which has been identified in studies using overseas data, is the volatility 'smile'. Risk management strategies using options should take account of the effect of this bias. Chapter nine documents the volatility smile in the Australian stock options market. Chapter ten extends chapter nine by considering time varying volatility in option prices. Obtaining estimates of the volatility of the underlying asset price that provide more accurate Black-Scholes option prices is important. Generally, for options already trading, the implied volatility of previous day option prices is found to produce lower pricing errors over a range of different volatility estimates, including those obtained from a Generalised AutoRegressive Conditional Heteroscedastic (GARCH) model. However, if the option is not traded, GARCH estimates provide a better alternative than historical estimates.

The purpose of this study is to put out the impact of volatility of the USD-TRY forex rate on imports to Turkey from Central Asia. The volatility of the USD/TRY exchange rate is analysed with a conditional variance model which is Generalised Autoregressive Conditional Heteroscedastic (GARCH) model and its extensions. The other section of the methodology is an application of Autoregressive Distributed Lag (ARDL) bounds test which is an efficient approach to determine the cointegration, long-term and short-term relations between macroeconomic variables. The exponential GARCH volatility of the exchange rate and the monthly trade data between the years 2005 and 2018 are used in the ARDL bounds test.

This book chapter investigated the place of backtesting approach in financial time series analysis in choosing a reliable Generalized Auto-Regressive Conditional Heteroscedastic (GARCH) Model to analyze stock returns in Nigeria. To achieve this, The chapter used a secondary data that was collected from www.cashcraft.com under stock trend and analysis. Daily stock price was collected on Zenith bank stock price from October 21st 2004 to May 8th 2017. The chapter used nine different GARCH models (standard GARCH (sGARCH), Glosten-Jagannathan-Runkle GARCH (gjrGARCH), Exponential GARCH (Egarch), Integrated GARCH (iGARCH), Asymmetric Power Autoregressive Conditional Heteroskedasticity (ARCH) (apARCH), Threshold GARCH (TGARCH), Non-linear GARCH (NGARCH), Nonlinear (Asymmetric) GARCH (NAGARCH) and The Absolute Value GARCH (AVGARCH) with maximum lag of 2. Most the information criteria for the sGARCH model were not available due to lack of convergence. The lowest information criteria were associated with apARCH (2,2) with Student t-distribution followed by NGARCH(2,1) with skewed student t-distribution. The backtesting result of the apARCH (2,2) was not available while eGARCH(1,1) with Skewed student t-distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student t-distribution passed the backtesting approach. Therefore with the backtesting approach, eGARCH(1,1) with student distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria. This chapter recommended the backtesting approach to selecting reliable GARCH model.

The study examined the asymmetric relationship between exchange rate volatility and macroeconomic performance in Nigeria covering the period between 1986Q1 and 2019Q4. The Non-linear Generalised Autoregressive Distributive Conditional Heteroscedasticity (GARCH) model was employed. The study was motivated as a result of periodic increase in exchange rate of naira to a dollar and instability of macroeconomic variables in the economy. The presence of Autoregressive Distributive Conditional Heteroscedasticity (ARCH) effect established the use of non-linear GARCH models which showed that volatility was persistent over the period of study. Consequently, the result revealed that exchange rate volatility exhibited a positive relationship with trade balance, industrial output and inflation in the study period. Thus, good news prevailed more over bad news in the foreign exchange market. The study therefore recommended that monetary authorities in Nigeria should regulate exchange rate and macroeconomic variables in order to control the general price level in the economy.