MODELING EXCHANGE RATE VOLATILITY USING ARCH AND GARCH FRAMEWORKS: A COMPARATIVE THEORETICAL REVIEW

This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which implies that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the UK foreign exchange market experienced a similar pattern of volatility shifts and suffered smaller but longer volatility than the Korean one. The volatility shifts are estimated using a Markov switching GARCH model and a Bayesian method is suggested.Keywords: Bayesian Inference, Markov Switching GARCH Models, Exchange Rate Volatility, Credit CrisisJEL classification: C11, C22, F31(ProQuest: ... denotes formulae omitted.)1. INTRODUCTIONThe Korean foreign exchange market has experienced two crises during the last two decades, as shown in Figure 1. The exchange rate was managed by the government before the Asian financial crisis in 1997-8. The Korean currency, or the won, depreciated sharply during the crisis and showed a trend of appreciating during the next decade. The foreign exchange market suffered from another foreign capital flight during the global credit crisis in 2008-9. Contrary to the case of the 1997-8 crisis, the 2008-9 credit crisis stemmed from the developed economies. However, the credit crisis led many developing countries, including South Korea, to an economic or financial crisis. Many policies were implemented to stabilize the financial and foreign exchange markets in Korea. The Bank of Korea has swiftly lowered the policy rate from 5.25% to 2% for 4 months since October 2008. The government announced the Financial Market Stabilization Measures, which included government warrants of the foreign currency debt of the commercial banks and provision of dollar liquidity to them, on October 19, 2008. The Bank of Korea has also made a 30-billion US dollar swap arrangement with the Federal Reserve on October 30, 2008 and other deals with the People's Bank of China and the Bank of Japan on December 12, 2008. From October 2008 to February 2009, it provided around 30-billion dollar liquidity to financial institutions which had difficulties in overseas fund raising.This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis and investigates what determined the volatility. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which suggests that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the dollar-pound exchange rate experienced a similar pattern of volatility shifts to that of the won-dollar exchange rate. But, the UK foreign exchange market suffered smaller but longer volatility than the Korean one.Since the Autoregressive Conditional Heteroskedastic (ARCH) model was suggested by Engle (1982), the conditional heteroskedastic models have been updated and developed to analyze the volatility of the financial markets. Researchers, including Bollerslev (1986), generalized the ARCH model to GARCH (generalized ARCH) and its variants, such as IGARCH, GARCH-M, and EGARCH. The models are known to describe well the many features of volatility, such as volatility clustering and the leverage effect.1 However, as Schwert (1990) and Engle and Mustaffa (1992) show, the GARCH models imply too much persistence in the conditional variance. To overcome this shortcoming, Cai (1994) and Hamilton and Susmel (1994) incorporate the Markov switching component into the ARCH model. Gray (1996) and Dueker (1997) generalize their model to Markov switching GARCH (hereafter, MS-GARCH) models. …

An important development in the modelling of exchange rate volatility is the use of artificial neural networks (ANN) to create enhanced generalised autoregressive conditional heteroskedasticity (GARCH) models. Conventional GARCH models are good at capturing the clustering of volatility in financial time series, but they have trouble understanding complex linkages and non-linear patterns in the data. This paper aims to investigate the hybrid approach in modelling exchange rate volatility of two currency pairs: South African Rand against Brazilian Real (ZAR/REAL) and South African Rand against Chinese Yuan (ZAR/YUAN) using monthly observations over the period of January 1996-March 2024. The paper introduced ANN as an additional factor to both symmetric and asymmetric GARCH models that capture most common stylised facts about exchange rate volatility and leverage effects. The GARCH (1,1)-ANN, EGARCH (1,1)-ANN, and GJR-GARCH (1,1)-ANN models were used, and their performance was assessed using mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results revealed that the EGARCH (1,1)-ANN model had the best overall performance when compared to the other hybrid models based on all three evaluation measures for both the currency pairs’ data. The paper recommends further similar studies to predict future exchange rate trends and also incorporating other nonlinear methods.

Uncertainty is often associated with travel-time prediction. Traditional point prediction methods only provide point values that are unable to offer enough information on the reliability of prediction results. The recent development of statistical volatility models has given us an effective way to capture uncertainties in data. Generalized autoregressive conditional heteroskedasticity (GARCH) models have been widely used in transportation systems as a way to account for this uncertainty by providing more accurate prediction intervals. However, a GARCH model arguably does not consider the trend and seasonality in data. If there is a trend or seasonality, the performance of the GARCH model may be affected. In the context of travel-time prediction, this paper proposes two component GARCH models that are able to model trend and seasonal components through decomposition. The travel-time data obtained along a freeway corridor in Houston, TX, USA, were used to empirically test the performance of the proposed models. The study results indicate that the proposed models perform well when capturing uncertainties associated with travel-time prediction.

This current study explores the application of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to forecast and model crude oil price volatility. Crude oil is a vital commodity whose price fluctuations significantly impact global economies, energy markets, and strategic decisions of both National Oil Companies (NOCs) and International Oil Corporations (IOCs). Using the GARCH(1,1) and GARCH(1,2) models, this study evaluates the effectiveness of these models in capturing the dynamic nature of oil price volatility. The findings indicate that while both models fit the data well, the GARCH(1,1) model is preferred due to its parsimonious nature and comparable forecast accuracy. Despite including an additional lag in the GARCH(1,2) model, it did not significantly outperform the GARCH(1,1) model in predictive performance. The study further analyzes the residuals and autocorrelation characteristics, highlighting the potential for model refinement. The study underscores the importance of selecting an appropriate model complexity, incorporating external factors, and exploring advanced methodologies to enhance forecast accuracy. These insights are critical for developing effective risk management strategies and informing policy decisions in volatile crude oil markets.

This paper collects a total of 541 groups of the RMB exchange rate to build the model of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) for forecasting of RMB exchange rate against US dollar. The empirical results show that the GARCH models can fit the series well and the prediction effects of both the GARCH (1, 1) model and the GARCH-M model are good.

This paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back‐propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p‐value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p‐value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p‐value of MCS of the best model estimated by this method is higher than the p‐value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p‐value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.

Steel structures such as transmission towers may have cracks and other damages during the service period. When the structure vibrates, the cracks will open and close, which makes the structure have nonlinear characteristics of variant stiffness. In order to identify this type of nonlinear damage, a time-domain damage identification method based on the residual deviation distance (RDD) of the autoregressive conditional heteroskedasticity (ARCH) model is proposed. First, the basic theory of the ARCH model is introduced, and the methods of model order determination and parameter estimation are given. Then, the time-domain nonlinear damage characteristics are analyzed, and the second-order variance (SOV) index based on the ARCH model is introduced. Considering that both the ARCH model coefficient and the RDD contain nonlinear information, a conversion index is constructed using the Euclidean distance (ED) of the ARCH model coefficients before and after the damage. On this basis, an RDD conversion index is further proposed to improve the identification accuracy. Finally, a three-storey frame experiment and a complex transmission tower model experiment are used to verify the effectiveness of the proposed method. The experimental results show that the proposed RDD conversion index can better identify the location of structural damage, and the identification results of the RDD conversion index are obviously better than those of the SOV conversion index and the ED conversion index.

Volatility plays an important role in financial markets and has held the attention of academics and practitioners. Using Generalized autoregressive conditional heteroscedasticity (GARCH) is one of the effective perspective for forecasting volatility. This study focused on comparing GARCH (P, Q) model with GJR-GARCH (P, Q) model and EGARCH (P, Q) model to make prediction more reliable and accurate. The results suggested that both GARCH (P, Q) model and GJR-GARCH (P, Q) model are good choices for forecasting volatility in financial market, especially for describing heteroscedastic time series. GARCH models are consistent with various forms of efficient market theory. These theories state that asset returns observed in the past cannot improve the forecasts of asset returns in the future.

GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models are new statistical methods that are used especially in economic time series. There is a consensus that speech signals exhibit variance that changes through time. GARCH models are a popular choice to model these changing variances. In this chapter, we propose three methods for VAD, which are based on GARCH models. In the first method, heteroscedasticity will be modeled by GARCH process and hard detection is the result of comparing a Multiple Observation Likelihood Ratio Test (MOLRT) with a threshold function. In the second method, no distinct probability functions are assumed for speech and noise distributions and no LRT is employed. We will show that VAD is related to the parameter constancy test in GARCH process. For testing parameter constancy in GARCH models, the algorithm of the Cramer-von Mises (CVM) test is described. In the last method, the process of outlier detection in GARCH model is presented and the motivation for using it and its relation with VAD are discussed.

For the limitations of vibration signals caused by non-stationary autoregressive (AR) model which can not effectively describe the signal characteristics, it is presented a fault diagnosis based on autoregressive conditional heteroskedasticity (ARCH) model. This method firstly uses ARCH model to fit various fault signals and regard the proceeds of the model parameters as the characteristics of fault diagnosis, using RBF neural network classification as fault diagnosis method. The experimental results verify the feasibility and effectiveness of the ARCH model, and at the same time it makes the comparison with the method based on same AR model and another modified method based on AR model. The results show that the method has significantly improvements in the diagnosis rate.

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.

This article develops a leverage trend Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model by incorporating asymmetric trend of returns of the exponential autoregressive and asymmetric volatility of GARCH models to study the asymmetric effects. Using in-sample daily data of Taiex over the period 4 January 1980 to 25 August 1997 and postsample daily data over the period 26 August 1997 to 10 September 2007, the evidence reveals that a curvaceous risk–return relationship and both asymmetric volatility and asymmetric trend of returns are significant in Taiex. The episode of asymmetric trend of returns is that the positive information creates a higher return trend than the negative information of the same amount, while similarly to most studies, the evidence of asymmetric volatility appears that the negative information makes a higher volatility than the positive information of the same size. Most remarkably, we evidence that the volatility asymmetry effect is a conservative trading factor and the return trend asymmetry effect is an active trading factor. In comparison of post-sample performance using rolling-window technique, the leverage trend GARCH model indeed outperforms the other three models with single asymmetry adjusted or without asymmetry adjusted, while the asymmetry nonadjusted model performs the worst. It implies that the return trend asymmetry (active trading) and the volatility asymmetry effects (conservative trading) tend to compensate, but not offset each other.

This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both cases, the limiting distributions of the log empirical likelihood ratio statistics are established. These two statistics can be used to test for unit roots under the GARCH framework. Finite-sample performances are assessed through simulations for GARCH models with unit roots.This research was supported in part by Hong Kong Research grants Council Grants CUHK4043/02P and HKUST6273/03H. The authors thank two referees and the Co-Editor, Bruce Hansen, for insightful and helpful comments about the relationship between QMLE and MELE, which led to substantial improvement of the presentation. Computational assistance from Jerry Wong and Chun-Yip Yau is also gratefully acknowledged.

Stock price data at State Gas Company is defined as the time-series data comprising varying volatility and heteroscedasticity. One of the best models used to solve the problem of heteroscedasticity is the GARCH (generalized autoregressive conditional heteroscedasticity) model. Therefore, this study aims to build the most suitable model for predicting the 186 days before and 176 days after the Covid-19 pandemic, as well as to provide recommendations to reduce the impact of daily stock price movements. Data were obtained by examining the daily stock price data in Indonesian National Gas Companies from 2019 to 2020. The study also discusses the Event Window, with the best model identified as AR (1) -GARCH (1,1). The result showed that an error of less than 0.0015 is AR (1) - GARCH (1,1), provided the best model for price forecasting of Indonesian National Gas Companies.Keywords: Stock Price, Heteroscedasticity, GARCH Model, Event WindowJEL Classifications: C5, O42, Q4, Q47DOI: https://doi.org/10.32479/ijeep.10999

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