Generalized Autoregressive Conditional Heteroskedasticity Model Research Articles

Analysing volatility patterns in emerging markets: symmetric or asymmetric models?

PurposeInvestors aim for returns when investing in stocks, making return volatility a crucial concern. This study compares symmetric and asymmetric GARCH models to forecast volatility in emerging nations like the G4 countries. Accurate volatility forecasting is vital for investors to make well-informed investment decisions, forming the core purpose of this study.Design/methodology/approachFrom January 1993 to May 2021, the study spans four periods, focusing on the global economic crisis of 2008, the Russian crisis of 2015 and the COVID-19 pandemic. Standard generalized autoregressive conditional heteroscedasticity (GARCH), exponential GARCH (E-GARCH) and Glosten-Jagannathan-Runkle GARCH models were employed to analyse the data. Robustness was assessed using the Akaike information criterion, Schwarz information criterion and maximum log-likelihood criteria.FindingsThe study's findings show that the E-GARCH model is the best model for forecasting volatility in emerging nations. This is because the E-GARCH model is able to capture the asymmetric effects of positive and negative shocks on volatility.Originality/valueThis unique study compares symmetric and asymmetric GARCH models for forecasting volatility in emerging nations, a novel approach not explored in prior research. The insights gained can aid investors in constructing more effective risk-adjusted international portfolios, offering a better understanding of stock market volatility to inform strategic investment decisions.

Empirical Analysis of SSE 50 Index Volatility Based on GARCH Model

Volatility is an important index for measuring the risk in the financial market. The research on the volatility of the financial market is the basis of risk prevention and asset pricing. The volatility of the market is predicted by using financial time series analysis and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. This paper uses the 5 min closing price of the Shanghai 50 index from January 2021 to December 2021 as the small sample data, and the daily closing price of the Shanghai 50 index from January 2012 to December 2020 as the large sample data. The large sample data of SSE 50 index are divided into five sample groups with different interval lengths, and GARCH models are established to empirically analyze the volatility of its return. The “realized” volatility method is used to process the small sample data of the Shanghai Stock Exchange 50 index, and the estimated value of volatility is obtained as the substitute for the real value. The predicted value of five groups of data is compared with the real value, and the influence of sample size on the predicted value is analyzed. The results show that GARCH’s estimation coefficient is very significant and has the expected characteristics, which verifies the existence of persistent volatility aggregation, and the daily return fluctuation of the closing price of the Shanghai 50 index is largely affected by the news about volatility and lagging volatility in the previous period. This result shows that the daily return of the Shanghai Stock Exchange 50 index has sustained high volatility, the investment risk of the Shanghai stock market increases, and the regulatory authorities should take appropriate measures to prevent systemic risks.

A time series modeling approach for damage monitoring of concrete dam under seismic effects

In order to improve the applicability of time series models for the diagnosis of concrete dam damage under seismic loading, this paper proposes a diagnostic method for structural damage by combining linear time series modeling and non-linear modeling of model residuals. Starting from the linear structural dynamic response transmissibility function, the expressions of the generalized Auto-Regressive with eXtra inputs (GARX) model for the dynamic response under stationary excitation conditions were derived. The GARX model with dynamic coefficients was extended to model the dynamic response under seismic loading and the generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) model was used to nonlinearly model the model residuals. To track the coefficients of the GARX model, an adaptive least squares recursion method based on fuzzy forgetting factor was studied. The damage indicator of Minkowski distance based on the GARCH model coefficients was proposed. Finally, the effectiveness of the diagnostic methods of the GARX and GARCH models was verified by a numerical calculation of the non-linear damage to a dam. The results showed that GARX can effectively describe the input-output relationship of the dam in the absence of damage. After damage occurs, the GARCH model and the improved Minkowski distance index for the model residuals of GARX can effectively characterize the non-linear damage evolution of the dam.

Performance of the Realized-GARCH Model against Other GARCH Types in Predicting Cryptocurrency Volatility

Cryptocurrencies have increasingly attracted the attention of several players interested in crypto assets. Their rapid growth and dynamic nature require robust methods for modeling their volatility. The Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) model is a well-known mathematical tool for predicting volatility. Nonetheless, the Realized-GARCH model has been particularly under-explored in the literature involving cryptocurrency volatility. This study emphasizes an investigation on the performance of the Realized-GARCH against a range of GARCH-based models to predict the volatility of five prominent cryptocurrency assets. Our analyses have been performed in both in-sample and out-of-sample cases. The results indicate that while distinct GARCH models can produce satisfactory in-sample fits, the Realized-GARCH model outperforms its counterparts in out of-sample forecasting. This paper contributes to the existing literature, since it better reveals the predictability performance of Realized-GARCH model when compared to other GARCH-types analyzed when an out-of-sample case is considered.

GARCH Models and Distributions Comparison for Nonlinear Time Series with Volatilities

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is extensively used for handling volatilities. However, with numerous extensions to the standard GARCH model, selecting the most suitable model for forecasting price volatilities becomes challenging. This study aims to examine the performance of different GARCH models in forecasting crude oil price volatilities using West Texas Intermediate (WTI) data. The models considered are the standard GARCH, Integrated GARCH (IGARCH), Exponential GARCH (EGARCH), and Golsten, Jagannathan, and Runkle GARCH (GJR-GARCH), each with normal distribution, Student’s t-distribution, and Generalized Error Distribution (GED). To evaluate the performance of each model, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used as the model selection criteria, along with forecast accuracy measures such as absolute error, root mean squared error (RMSE), and mean absolute error (MAE). Post-estimation tests, including the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test and the Ljung-Box test, are conducted to ensure the adequacy of all models. The results reveal that all GARCH models are suitable for modeling the data, as indicated by statistically significant estimated parameters and satisfactory post-estimation outcomes. However, the EGARCH (1, 1) model, particularly with Student’s t-distribution, outperforms other models in both data fitting and accurate forecasting of nonlinear time series.

ESG Volatility Prediction Using GARCH and LSTM Models

Abstract This study aims to predict the ESG (environmental, social, and governance) return volatility based on ESG index data from 26 October 2017 and 31 March 2023 in the case of India. In this study, we utilized GARCH (Generalized Autoregressive Conditional Heteroskedasticity) and LSTM (Long Short-Term Memory) models for forecasting the return of ESG volatility and to evaluate the model’s suitability for prediction. The study’s findings demonstrate the GARCH effect inside the ESG return volatility data, indicating the occurrence of volatility in response to market fluctuations. This study provides insight concerning the suitability of models for volatility predictions. Moreover, based on the analysis of the return volatility of the ESG index, the GARCH model is more appropriate than the LSTM model.

A comparative study of error distributions in the GARCH model through a Monte Carlo simulation approach

Financial time series data are known to exhibit volatility clustering, which implies that the volatility of financial returns tends to persist over time. This phenomenon has significant implications for risk management and financial decision-making. To capture this volatility clustering effect, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is widely used. Through a Monte Carlo simulation experiment, the performance GARCH-type model with five different error distribution specifications were compared. The study found that the Skewed Generalized Error Distribution (SGED) was the most efficient and consistent distribution for modelling financial time series. The SGED outperformed the Normal, Student's t, GED, and skewed Student's t distributions in terms of goodness-of-fit, MSE, MAE and different sample sizes. The study suggests that the SGED may be more suitable for modelling financial time series with a GARCH-type specification in general contexts.

COVID-19 Pandemic and Indices Volatility: Evidence from GARCH Models

This study examines the impact of volatility on the returns of nine National Stock Exchange (NSE) indices before, during, and after the COVID-19 pandemic. The study employed generalized autoregressive conditional heteroskedasticity (GARCH) modelling to analyse investor risk and the impact of volatility on returns. The study makes several contributions to the existing literature. First, it uses advanced volatility forecasting models, such as ARCH and GARCH, to improve volatility estimates and anticipate future volatility. Second, it enhances the analysis of index return volatility. The study found that the COVID-19 period outperformed the pre-COVID-19 and overall periods. Since the Nifty Realty Index is the most volatile, Nifty Bank, Metal, and Information Technology (IT) investors reaped greater returns during COVID-19 than before. The study provides a comprehensive review of the volatility and risk of nine NSE indices. Volatility forecasting techniques can help investors to understand index volatility and mitigate risk while navigating these dynamic indices.

Sustainable economic performance and natural resource price volatility in the post-covid-pandemic: Evidence using GARCH models in Chinese context

Recent research demands the influence of COVID-19 on every field of life. Plenty of research work investigated the influence of the volatility of natural resources on economic advancements during COVID-19, though, the impact of the pandemic still persists in the post-pandemic era. Therefore, the current research aims to explore the connectedness of the volatility of oil prices and sustainable economic development during the era after the pandemic. The slump in prices of oil during the pandemic is subject to major concerns in the era after the pandemic. Although this connection is explored by recent researchers, current research work underwrites the prevailing literature by inspecting the connection between oil price volatility and sustainable economic performance during and post COVID-pandemic in China over the period comprising January 2020 to April 2023. The study employs the ordinary least squares regression (OLS), generalized Autoregressive conditional heteroskedasticity (GARCH) (1,1), and Threshold GARCH econometric models to explore the connection between the said constructs. The outcomes infer that the volatility of oil prices is negatively associated with the sustainable economic performance in China during Post COVID-pandemic. The research infers that the vulnerability of the oil prices is more during and after the pandemic eras in China. On the basis of the results, this research work recommends introducing technological innovations, and protective trials to avoid the impact of pandemics on the connection between natural resource volatility and sustainable economic performance.

The Volatility Assessment of CO2 Emissions in Uzbekistan: ARCH/GARCH Models

The study is pioneer to investigate the volatility of CO2 emissions in Uzbekistan. To this end, ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models are used spanning the period 1925-2021 for the annual data of CO2 emissions. The results indicate that ARCH model is more adequate that GARCH model in the volatility assessment. Furthermore, it is found that the volatility of CO2 emissions in Uzbekistan is very high. The policymakers have to consider the high volatility of CO2 emissions in the environmental policy measures dedicated to reduce carbon dioxide emissions.

Risk Analysis of the Chinese Financial Market with the Application of a Novel Hybrid Volatility Prediction Model

This paper endeavors to enhance the prediction of volatility in financial markets by developing a novel hybrid model that integrates generalized autoregressive conditional heteroskedasticity (GARCH) models and long short-term memory (LSTM) neural networks. Using high-frequency data, we first estimate realized volatility as a robust measure of volatility. We then feed the outputs of multiple GARCH models into an LSTM network, creating a hybrid model that leverages the strengths of both approaches. The predicted volatility from the hybrid model is used to generate trading strategy signals, which are subsequently used to build an investment strategy. Empirical analysis using the China Securities Index 300 (CSI300) dataset demonstrates that the hybrid model significantly improves value-at-risk (VaR) prediction performance compared to traditional GARCH models. This study’s findings have broad implications for risk management in financial markets, suggesting that hybrid models incorporating mathematical models and economic mechanisms can enhance derivative pricing, portfolio risk management, hedging transactions, and systemic risk early-warning systems.

Is the Evergrande crisis spilling beyond China?

This study investigates whether Evergrande transmits shocks to regional and global equity markets using the vector autoregressive (VAR), asymmetric dynamic conditional correlation (ADCC), and exponential generalised autoregressive conditional heteroskedasticity (EGARCH) models. The results show that Evergrande has caused notable and enduring shocks to both domestic and foreign equities markets. The spillover test further supports the idea that the Evergrande crisis has spread to important markets. The findings have practical implications for regulators, sovereign wealth managers, institutional and retail investors, and policymakers trying to come up with ways to deal with external shocks.

Forecasting the Volatility of Real Residential Property Prices in Malaysia: A Comparison of Garch Models

Abstract The presence of volatility in residential property market prices helps investors generate substantial profit while also causing fear among investors since high volatility implies a high return with a high risk. In a financial time series, volatility refers to the degree to which the residential property market price increases or decreases during a particular period. The present study aims to forecast the volatility returns of real residential property prices (RRPP) in Malaysia using three different families of generalized autoregressive conditional heteroskedasticity (GARCH) models. The study compared the standard GARCH, EGARCH, and GJR-GARCH models to determine which model offers a better volatility forecasting ability. The results revealed that the GJR-GARCH (1,1) model is the most suitable to forecast the volatility of the Malaysian RRPP index based on the goodness-of-fit metric. Finally, the volatility forecast using the rolling window shows that the volatility of the quarterly index decreased in the third quarter (Q3) of 2021 and stabilized at the beginning of the first quarter (Q1) of 2023. Therefore, the best time to start investing in the purchase of real residential property in Malaysia would be the first quarter of 2023. The findings of this study can help Malaysian policymakers, developers, and investors understand the high and low volatility periods in the prices of residential properties to make better investment decisions.

Comparison Of Artificial Neural Network Backpropagation and Garch Methods In Predicting Stock Price (Case Study: Indosat Shares 2012 – 2022)

Abstract: One of the problems encountered in the forecasting process is the problem of heteroscedasticity. Heteroscedasticity occurs a lot, especially in stock data. Pt Share Price Indosat (tbk) from March 6 2012 – January 18 2022 has fluctuated from time to time, so the variance is heteroscedasticity. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Artificial Neural Network Backpropagation (ANNBP) are methods that can be used on data with heteroscedasticity. The aim of this research is to obtain models and forecasting results from GARCH and ANN Backpropagation. In this study, the two models were compared based on the smallest MAPE value. This study uses daily data on the closing of Indosat shares. Forecasting is done on Indosat stock closing data, the total data is 2453 data divided into two parts, namely 80% training data totaling 1962 data and 20% training data totaling 491 data. Forecasting results from the GARCH model obtained a MAPE value of 11.04%, and the ANN Backpropagation model with 7 input layers, 20 hidden layers, obtained a MAPE value of 7.01%. Thus, the best model for predicting Indosat's share price in this study is the backpropagation model.

Volatilitas Imbal Hasil Saham dan Kaitannya dengan Harga Minyak Dunia (Pendekatan Model ARCH/GARCH dan VAR)

Volatility generally refers to the amount of uncertainty or risk associated with changes in a security's value. The value of a security can potentially spread over a wider range of values if it has higher volatility. This study aims to analyze the volatility of stock returns and the growth of world oil prices. The stock that the author analyzes in this scientific article is PT Pakuwon Jati Tbk. by using daily time series data from January 2 2019 to December 14 2020. The model used in this study is Autoregressive Conditional Heteroskedasticity (ARCH)/Generalized Autoregressive Conditional Heteroskedasticity (GARCH), to understand clustering volatility behavior, and Vector Autoregression ( VAR) to determine the dynamic behavior between stock returns and world oil price growth. The results of the study show that stock returns and growth in world oil prices have clustering volatility in both variables. The results of the GARCH model, on the LPwon variable, indicate that when the return variable is not influenced by any variable, the tendency for stock returns tends to decrease, in contrast to the lnbrent variable, which tends to always increase.

Predicting the returns of the US real estate investment trust market: evidence from the group method of data handling neural network

PurposeThe Group Method of Data Handling (GMDH) neural network has demonstrated good performance in data mining, prediction, and optimization. Scholars have used it to forecast stock and real estate investment trust (REIT) returns in some countries and region, but not in the United States (US) REIT market. The primary goal of this study is to predict the US REIT market using GMDH and then compare its accuracy with that derived from the traditional prediction method.Design/methodology/approachTo forecast the return on the US REIT index, this study used the GMDH neural network and the generalized autoregressive conditional heteroscedasticity (GARCH) model. In this test, the training samples, testing samples, and kernel functions of the GMDH model are controlled to investigate their impact on the accuracy of the machine learning approach. Corresponding experiments were performed using the GARCH model, and the accuracies of these two approaches were compared.FindingsCompared with GARCH, GMDH’s accuracy is much higher, indicating that the machine learning approach can provide a highly accurate prediction of REIT prices. The size of the training samples and the kernel functions in the GMDH model affect the accuracy of the prediction results. In particular, the kernel function has a significant impact on prediction accuracy. The linear and linear covariance kernel functions are simple to train and yield accurate predictions, whereas the quadratic function is difficult to train. Even with small training samples, GMDH can outperform GARCH in prediction accuracy.Research limitations/implicationsAlthough GMDH shows good performance in predicting the US REIT return, it is still a black-box model, and the algorithm is difficult for financial analysts to develop and customize. The data used in this study come from the US REIT market, which is the world’s largest and most liquid market.Social implicationsThis research shows that the GMDH model outperforms the GARCH model in forecasting REIT returns. Hence, investors can use the machine learning approach to make more accurate predictions of the target REITs’ returns and thus better investment decisions. Future investors and researchers may use GMDH to forecast the performance of REITs in other markets.Originality/valueThis is the first study to apply the GMDH neural network to the US REIT market and determine the impact of the two factors on its performance. For example, this research first discusses the impact of kernel functions on the US REIT market using the GMDH neural network. It also includes short-term daily prediction returns that were not previously considered, making it a valuable reference for financial industry analysts.

Reverse gamma correction based GARCH model for underwater image dehazing and detail exposure

Underwater imaging poses significant challenges as water alters the behavior of light in comparison to air or vacuum. Therefore, it is crucial to effectively utilize the unique characteristics of unclear edges in hazy underwater images to achieve high-performance results in real-time applications. In this paper, we exploit such features as edges and visual perception in underwater haze images. To achieve this, we estimate the true transmission of the image by enhancing the visibility of discontinuous edges using the reverse gamma correction based on the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The parameters of the GARCH model are defined by the local and global pixel dynamics in adjacent neighborhoods, which improves the color orientation of the image while preserving image details. Additionally, we perform deseasoning to separate pixels while maintaining the natural contours of interactions between them. By considering the volatility of the RGB color channels, we predict the variance of the pixels based on the difference of the deseasoned pixels, which improves pixel intensity and allows for scene depth estimation. While estimating gamma correction and global ambient light, we deseasonalize image pixels based on their colors, enhancing the color of the final dehazed images. Using the greedy algorithm with a Convolutional Neural Network (CNN), our proposed method outperforms commonly used state-of-the-art methods.

The Effectiveness of the Huber's Weight on Dispersion and Tuning Constant: A Simulation Study

Dispersion measurement and tuning constants are critical aspects of a model's robustness and efficiency. However, in the presence of outliers, the standard deviation is not a reliable measure of dispersion in Huber's weight. This research aimed to assess the efficacy of the Huber weight function in terms of dispersion measurement and tuning constant. The simulation study was conducted on a hybrid of the autoregressive (AR) model and the generalized autoregressive conditional heteroscedasticity (GARCH) model with 10% and 20% additive outlier contamination. In the simulation analysis, three dispersion measurements were compared: median absolute deviation (MAD), interquartile range (IQR), and IQR/3, with two tuning constant values (1.345 and 1.5). The numerical simulation results showed that during contamination with 10% and 20% additive outliers, the IQR/3 outperformed the MAD and IQR. Our findings also showed that IQR/3 is a potentially more robust dispersion measurement in Huber's weight. The tuning constant of 1.5 revealed a decrease in resistance to outliers and increased efficiency. The proposed IQR/3 model with a constant tuning value (h) of 1.5 outperformed the AR(1)-GARCH(1,2) model while minimising the effect of additive outliers.

A new hybrid PM[Formula: see text] volatility forecasting model based on EMD and machine learning algorithms.

In recent years, the frequent occurrence of air pollution incidents has seriously affected people's health and life. Therefore, PM[Formula: see text], as the main pollutant, is an important research object of air pollution at present. Effectively improving the prediction accuracy of PM[Formula: see text] volatility makes the PM[Formula: see text] prediction content perfect, which is an important aspect of PM[Formula: see text] concentration research. The volatility series has an inherent complex function law, which drives the volatility movement. When machine learning algorithms such as LSTM (Long Short-Term Memory Network) and SVM (Support Vector Machine) are used for volatility analysis, a high-order nonlinear form is used to fit the functional law of the volatility series, but the time-frequency information of the volatility has not been utilized. Based on EMD (Empirical Mode Decomposition) technique, GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) model and machine learning algorithms, a new hybrid PM[Formula: see text] volatility prediction model is proposed in this study. This model realizes time-frequency characteristic extraction of volatility series through EMD technology, and integrates residual and historical volatility information through GARCH model. The simulation results of the proposed model are verified by comparing the samples of 54 cities in North China with the benchmark models. The experimental results in Beijing showed that MAE (mean absolute deviation) of hybrid-LSTM decreased from 0.00875 to 0.00718 compared with LSTM, and hybrid-SVM based on the basic model SVM also significantly improved generalization ability, and its IA (index of agreement) improved from 0.846707 to 0.96595, showing the best performance. The experimental results show that the hybrid model is superior to other considered models in terms of prediction accuracy and stability, which verifies that the hybrid system modeling method is suitable for PM[Formula: see text] volatility analysis.

Recurrent neural network architecture for forecasting banana prices in Gujarat, India.

The forecasting of horticulture commodity prices, such as bananas, has wide-ranging impacts on farmers, traders and end-users. The considerable volatility in horticultural commodities pricing estimates has allowed farmers to exploit various local marketplaces for profitable sales of their farm produce. Despite the demonstrated efficacy of machine learning models as a suitable substitute for conventional statistical approaches, their application for price forecasting in the context of Indian horticulture remains an area of contention. Past attempts to forecast agricultural commodity prices have relied on a wide variety of statistical models, each of which comes with its own set of limitations. Although machine learning models have emerged as formidable alternatives to more conventional statistical methods, there is still reluctance to use them for the purpose of predicting prices in India. In the present investigation, we have analysed and compared the efficacy of a variety of statistical and machine learning models in order to get accurate price forecast. Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average model (SARIMA), Autoregressive Conditional Heteroscedasticity model (ARCH), Generalized Autoregressive Conditional Heteroscedasticity model (GARCH), Artificial Neural Network (ANN) and Recurrent Neural Network (RNN) were fitted to generate reliable predictions of prices of banana in Gujarat, India from January 2009 to December 2019. Empirical comparisons have been made between the predictive accuracy of different machine learning (ML) models and the typical stochastic model and it is observed that ML approaches, especially RNN, surpassed all other models in the majority of situations. Mean Absolute Percent Error (MAPE), Root Mean Square Error (RMSE), symmetric mean absolute percentage error (SMAPE), mean absolute scaled error (MASE) and mean directional accuracy (MDA) are used to illustrate the superiority of the models and RNN resulted least in terms of all error accuracy measures. RNN outperforms other models in this study for predicting accurate prices when compared to various statistical and machine learning techniques. The accuracy of other methodologies like ARIMA, SARIMA, ARCH GARCH, and ANN falls short of expectations.