Auswahl der wissenschaftlichen Literatur zum Thema „Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH)“

Time series data is a type of data that is often used to estimate future values. Long memory phenomenon often occurs in time series data. Long memory is a condition that shows a strong correlation between observations even though they are quite far away. This phenomenon can be overcome by modeling time series data using the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. This model is characterized by a fractional difference value. ARFIMA (Autoregressive Fractional Integrated Moving Average) model assumes that the residuals are normally distributed, mutually independent, and homogeneous. However, usually in financial data, the residual variants are not constant. This can be overcome by modeling variants. Standard equipment that can be used to model variants is the ARCH / GARCH (Auto Regressive Conditional Heteroscedasticity / Generalized Auto Regressive Conditional Heteroscedasticity) model. Another phenomenon that often occurs in GARCH models is the leverage effect on the residuals of the model. EGARCH (Exponential General Auto Regessive Conditional Heteroscedasticity) is a development of the GARCH model that is appropriate for data that has an leverage effect. The implementation of this model is by modeling financial data, so this study takes 136 monthly data on rice prices in Semarang City from January 2009 to April 2020. The purpose of this study is to create a long memory data forecasting model using the Exponential method. Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). The best model obtained is ARFIMA (1, d, 1) EGARCH (1,1) which is capable of forecasting with a MAPE value of 3.37%.Keyword : Rice price, forecasting , long memory, leverage effect, GARCH, EGARCH

Purpose This paper aims to analyse the volatility of the fixed income market from 11 countries (Brazil, Russia, India, China, South Africa, Argentina, Chile, Mexico, USA, Germany and Japan) from January 2000 to December 2011 by examining the interbank interest rates from each market. Design/methodology/approach To the volatility of interest rates returns, the study used models of auto-regressive conditional heteroscedasticity, autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), exponential generalized autoregressive conditional heteroscedasticity (EGARCH), threshold generalized autoregressive conditional heteroscedasticity (TGARCH) and periodic generalized autoregressive conditional heteroscedasticity (PGARCH), and a combination of these with autoregressive integrated moving average (ARIMA) models, checking which of these processes were more efficient in capturing volatility of interest rates of each of the sample countries. Findings The results suggest that for most markets, studied volatility is best modelled by asymmetric GARCH processes – in this case the EGARCH – demonstrating that bad news leads to a higher increase in the volatility of these markets than good news. In addition, the causes of increased volatility seem to be more associated with events occurring internally in each country, as changes in macroeconomic policies, than the overall external events. Originality/value It is expected that this study has contributed to a better understanding of the volatility of interest rates and the main factors affecting this market.

Two economic models, i.e. auto-regressive and moving average model (ARMA) and generalized auto-regressive conditional heteroscedasticity model (GARCH), are adopted to assess the conditions of structures and to detect structural nonlinear damage based on time series analysis in this study. To improve the reliability of the method for nonlinear damage detection, a new damage sensitive feature (DSF) for the ARMA-GARCH model is defined as a ratio of the standard deviation of the variance time series of ARMA-GARCH model residual errors in test condition to ones in reference condition. Compared to the traditional DSF defined as the ratio between the deviations of ARMA-GARCH model residual error in two conditions, the successful outcomes of the new DSF can give obvious explanation for the current states of structures and can detect the nonlinear damage exactly, which enhance the worth of structural health monitoring as well as condition-based maintenance in practical applications. This method is finally verified by a series of experimental data of three-story building structure made in Los Alamos National Laboratory USA.

Crude oil is one of the most important energy commodities for various sectors. Changes in crude oil prices will have an impact on oil-related sectors, and even on the stock price index. Therefore, the prediction of crude oil prices needs to be done to avoid the future prices of these non-renewable natural resources to increase dramatically. In this paper, the prediction of crude oil prices is carried out using the Auto-Regressive Integrated Moving Average (ARIMA) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) models. The data used for forecasting are Indonesian Crude Price (ICP) crude oil data for the period January 2005 to November 2012. The results show that the data analyzed follows the ARIMA(1,2,1)-GARCH(0,3) model, and the crude oil price forecast for December 2012 is 105.5528 USD per barrel. The prediction results of crude oil prices are expected to be important information for all sectors related to crude oil.

In this paper, a hybrid ARIMA-GARCH model is proposed to model and predict the equity returns for three US benchmark indices: Dow Transportation, S&P 500 and VIX. Equity returns are univariate time series data sets, one of the methods to predict them is using the Auto-Regressive Integrated Moving Average (ARIMA) models. Despite the fact that the ARIMA models are powerful and flexible, they are not be able to handle the volatility and nonlinearity that are present in the time series data. However, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are designed to capture volatility clustering behavior in time series. In this paper, we provide motivations and descriptions of the hybrid ARIMA-GARCH model. A complete data analysis procedure that involves a series of hypothesis testings and a model fitting procedure using the Akaike Information Criterion (AIC) is provided in this paper as well. Simulation results of out of sample predictions are also provided in this paper as a reference.

Financial economists believe that the arbitrage forces in the market are the main reason of market efficiency and these forces are the fundamental concept of efficient market hypothesis (EMH). During last few years, various theoretical and empirical evidences have been presented to support the work of financial modeling for the markets with less than rational investors whose trading strategies are based on psychological factors like mood and emotions. Weather condition is among the substantial factors affecting investors’ mood and emotions. Present study investigates the impact of temperature on stock market returns in emerging economy of Pakistan. Using the daily temperature records and stock market indices of Karachi and Islamabad, the study has employed auto regressive (AR) – generalized autoregressive conditional heteroscedasticity (GARCH) model from 2006 to 2010. Based on AR (1)-GARCH (1, 1) estimation the study has found that weather temperatures of both Karachi and Islamabad are negatively related with Karachi Stock Exchange (KSE) and Islamabad Stock Exchange (ISE) index returns, respectively.

It is well-known that financial time series exhibits changing variance and this can have important consequences in formulating economic or financial decisions. In much recent evidence shows that volatility of financial assets is not constant, but rather that relatively volatile periods alternate with more tranquil ones. Thus, there are many opportunities to obtain forecasts of this time-varying risk. The paper presents the modelling volatility of the Kuala Lumpur Composite Index (KLCI) using SV and GARCH models. Thus, the aim of this study is to model the KLCI stock market using two models; Stochastic Volatility (SV) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH). This study employs an SV model with Bayesian approach and Markov Chain Monte Carlo (MCMC) sampler; and GARCH model with MLE estimator. The best model will be used to forecast the future volatility of stock returns. The study involves 971 daily observations of KLCI Closing price index, from 2 January 2008 to 10 November 2016, excluding public holidays. SV model is found to be the best based on the lowest RMSE and MAE values.

This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.

AbstractThe paper aims to find what determines the choice of companies listed on the Warsaw Stock Exchange (WSE) between public debt (corporate bonds) and private debt (bank loans). For this purpose, we estimate logistic regression models and panel models of corporate borrowing determinants to compare the impact of enterprise characteristics on financing with the use of corporate bonds or bank loans. In this study, we are interested in explanatory variables that explain the role of transparency measured by the level of information disclosure; and a risk proxy of the variability of operational cash flows and investment risk (retrieved from generalised auto-regressive conditional heteroscedasticity [GARCH] models estimated on companies’ stocks [shares] trading on the WSE).

Several intelligent data mining approaches, including neural networks, have been widely employed by academics during the last decade. In today's rapidly evolving economy, stock market data prediction and analysis play a significant role. Several non-linear models like neural network, generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional heteroscedasticity (ARCH) as well as linear models like Auto-Regressive Integrated Moving Average (ARIMA), Moving Average (MA) and Auto Regressive (AR) may be used for stock forecasting. The deep learning architectures inclusive of Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), Recurrent Neural Networks (RNN), Multilayer Perceptron (MLP) and Support Vector Machine (SVM) are used in this paper for stock price prediction of an organization by using the previously available stock prices. The National Stock Exchange (NSE) of India dataset is used for training the model with day-wise closing price. Data prediction is performed for a few sample companies selected on a random basis. Based on the comparison results, it is evident that the existing models are outperformed by CNN. The network can also perform stock predictions for other stock markets despite being trained with single market data as a common inner dynamics that has been shared between certain stock markets. When compared to the existing linear models, the neural network model outperforms them in a significant manner, which can be observed from the comparison results.

This study has applied a geographical perspective with the ambition of evaluating the presence of the Sell in May effect, January effect and monthly anomalies in the Nordic stock markets. In extension the study examines the relationship between corporate size and the returns of calendar anomalies. The study has conducted statistical tests based on Newey-West regressions as well as a Generalized Auto-Regressive Conditional Heteroscedasticity model. The findings suggest that the Sell in May and January are present in the Nordic region and partially abide by theory and results of previous research. The findings suggest that the Sell in May and January effect are independent, however, tendencies when the January effect has a considerable influence on the Sell in May effect are also evident. Additionally, the “April Effect” is an unexpected outlier with positive excess returns that was identified through this study.

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Em consequência da evolução da internet, causada por mudanças de paradigma como a Internet das coisas, por exemplo, surgem novas demandas tecnológicas por conta do crescimento do número de dispositivos conectados. Um dos novos desafios que vieram junto a esta demanda é gerenciar esta rede em expansão, de maneira a garantir conectividade aos dispositivos que a integram. Um dos aspectos que merecem atenção no gerenciamento da rede é o provisionamento da largura de banda, que deve ser realizado de maneira a evitar o desperdício de banda, sem por outro lado comprometer a conectividade ao restringi-la demais. No entanto, balancear esta equação não é uma tarefa simples, pois o tráfego de dados na rede é bastante complexo e exibe componentes, como a volatilidade, que tornam difícil a sua modelagem. Já há algum tempo, estudos são publicados apresentando a utilização de ferramentas de análise de séries temporais para prever a vazão de dados em redes de computadores, e entre as técnicas aplicadas com mais sucesso estão os modelos ARMA, GARCH e RNA. Embora estas técnicas tenham sido discutidas como alternativa para modelar dados de tráfego de redes, pouco material está disponível sobre a comparação de suas acurácias, de maneira que neste estudo foi proposta uma avaliação das acurácias dos modelos ARIMA, GARCH e RNA. Esta avaliação foi realizada em cenários configurados em diferentes granularidades de tempo e para múltiplos horizontes de previsão. Para cada um destes cenários foram ajustados modelos ARIMA, GARCH e RNA, e a validação das métricas de acurácia das previsões obtidas se deu através do Rolling Forecast Horizon. Os resultados obtidos mostraram que a RNA exibiu melhor acurácia em grande parte dos cenários propostos, chegando a exibir RMSE até 32% menor que as previsões geradas pelos modelos ARIMA e GARCH. No entanto, na presença de alta volatilidade, o GARCH conseguiu apresentar as previsões com melhor desempenho, exibindo RMSE até 29% menores que os outros modelos estudados. Os resultados deste trabalho servem de auxílio para a área de gerenciamento de redes, em especial a tarefa de provisionamento de largura de banda de tráfego, pois trazem mais informações sobre os desempenhos dos modelos ARIMA, GARCH e RNA ao gerar previsões para este tipo de tráfego.
The Internet evolution, caused by paradigm changes as the Internet of Things, fosters technological advances to cope with the rising number of connected devices. One of the new challenges that appeared with this new reality is the management of such expanding networks, assuring connectivity to every device within them. One of the major aspects of network management is bandwidth provisioning, which must be performed in a way to avoid bandwidth wasting, but without compromising connectivity by restricting it too much. Balancing such an equation is not a simple task, as network data traffic is very complex and presents property features, such as volatility, that turns its modeling rather difficult. It has been some time since research is published with the use of temporal analysis tools to predict data throughput in computer networks, among them, the most successful techniques employ the ARMA, GARCH and ANN models. Although these approaches have been discussed as alternatives do network data traffic modeling, there is little literature available concerning their accuracy, which motivated this work to perform an accuracy evaluation of the ARIMA, GARCH and ANN models. This evaluation was conducted in scenarios configured with different time granularities and for multiple forecast horizons. For each scenario, ARIMA, GARCH and ANN models were set, and the accuracy metrics evaluation was performed with a Rolling Forecast Horizon. Results show that ANN yielded better accuracy in most proposed scenarios, having a RMSE up to 32% lower than the forecasts generated by the ARIMA and GARCH models. However, when there is a high volatility, GARCH provided better forecasts, with a RMSE up to 29% lower than its counterparts. The results from this work provide a useful assistance to network management, especially to bandwidth provisioning, by shedding light on the accuracy presented by the ARIMA, GARCH and ANN models when generating forecasts for this type of traffic.

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.

In this paper, we have examined 4 models for Great Salt Lake level forecasting: ARMA (Auto-Regression and Moving Average), ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity). Through our empirical data analysis where we divide the time series in two parts (first 2000 measurement points in Part-1 and the rest is Part-2), we found that for Part-2 data, FIGARCH offers best performance indicating that conditional heteroscedasticity should be included in time series with high volatility.

Great Salt Lake (GSL) is the largest salt lake in the western hemisphere, the fourth-largest terminal lake in the world. The elevation of Great Salt Lake has critical effect on the people who live nearby and their properties. It is crucial to build an exact model of GSL elevation time series in order to predict the GSL elevation precisely. Although some models, such as FARIMA or ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity), have been built to characterize the variation of Great Salt Lake elevation, these models can not characterize it perfectly. Therefore, it became a key point to build a more appropriate model of GSL elevation time series. In this paper a new model based on fractional autoregressive integrated moving average (ARFIMA) with Stable innovations is applied to analyze the data and predict the future levels. From the analysis we can see that the new model can characterize GSL elevation time series more accurately. The new model will be beneficial to predict GSL elevation more precisely.