• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.39-48
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• 2024

In this paper, we introduce an extended GARCH model designed to address asymmetric leverage effects. The variance in the standard GARCH model is composed of past conditional variances and past squared residuals. However, it is not possible to model asymmetric leverage effects with squared residuals alone, so in this paper, we propose a new extended GARCH model to explain the leverage effects using the Yeo-Johnson transformation which adjusts transformation parameter to make asymmetric data more normal or symmetric. We utilize the reverse properties of Yeo-Johnson transformation to model asymmetric volatility. We investigate the characteristics of the proposed model and parameter estimation. We also explore how to derive forecasts and forecast intervals in the proposed model. We compare it with standard GARCH and other extended GARCH models that model asymmetric leverage effects through empirical data analysis.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.221-230
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• 2016

This paper investigates volatilities of stock returns based on high frequency data from stock market. Incorporating the price duration as one of the factors in volatility, we employ the autoregressive conditional duration (ACD) model for the price duration in addition to the GARCH model to analyze stock volatilities. A combined ACD-GARCH model is analyzed in which a double-threshold is introduced to accommodate asymmetric features on stock volatilities.

• Journal of Intelligence and Information Systems
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• v.23 no.2
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• pp.107-122
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• 2017

Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.41-47
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• 2010

In this paper, we show the performance evaluation of outlier detection methods based on the GARCH model. We first introduce GARCH model and the methods of outlier detection in the GARCH model. The results of small simulation and the real KOSPI data show the out-performance of the outlier detection method over the traditional method in the GARCH model.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• Quantitative Bio-Science
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• v.37 no.2
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• pp.73-79
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• 2018

As high frequency (HF, for short) time series is now prevalent in the presence of real time big data, volatility computations based on traditional ARCH/GARCH models need to be further developed to suit the high frequency characteristics. This article reviews realized volatilities (RV) and multivariate GARCH (MGARCH) to deal with high frequency volatility computations. As a (functional) infinite dimensional models, the fARCH and fGARCH are introduced to accommodate ultra high frequency (UHF) volatilities. The fARCH and fGARCH models are developed in the recent literature by Hormann et al. [1] and Aue et al. [2], respectively, and our discussions are mainly based on these two key articles. Real data applications to domestic UHF financial time series are illustrated.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.29-43
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• 2012

Financial data such as stock index returns and exchange rates have the properties of heavy tail and asymmetry compared to normal distribution. When we estimate VaR using the GARCH model (with the conditional return distribution of normal) it shows the tendency of the lower estimation and clustering in the losses over the estimated VaR. In this paper, we argue that this problem can be resolved through the adaptation of the unbounded Johnson distribution as that of the condition return. We also compare this model with the GARCH with the conditional return distribution of normal and student-t. Using the losses exceed the ex-ante VaR, estimates, we check the validity of the GARCH models through the failure proportion test and the clustering test. We nd that the GARCH model with conditional return distribution of unbounded Johnson provides an appropriate estimation of the VaR and does not occur the clustering of violations.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.251-260
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• 2017

The option pricing of Black와 Scholes (1973) and Merton (1973) has been widely reported to fail to reflect the time varying volatility of financial time series in many real applications. For example, Duan (1995) proposed GARCH option pricing method through Monte Carlo simulation. However, financial time series is known to follow a fat-tailed and leptokurtic probability distribution, which is not explained by Duan (1995). In this paper, in order to overcome such defects, we proposed the option pricing method based on GARCH models with normal mixture errors. According to the analysis of KOSPI200 option price data, the option pricing based on GARCH models with normal mixture errors outperformed the option pricing based on GARCH models with normal errors in the unstable period with high volatility.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.159-168
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• 2014

The news impact curve(NIC) originally proposed by Engle and Ng (1993) is a graphical representation of volatility for financial time series. The NIC is a simple but a powerful tool for identifying variability of a given time series. It is noted that the NIC is suited to symmetric volatility. Recently a lot of attention has been paid to asymmetric volatility models and therefore asymmetric version of the NIC would be useful in the field of financial time series. In this article, we propose to incorporate LASSO in constructing asymmetric NICs based on asymmetric GARCH models. In particular, bilinear GARCH models are considered and illustrated via KOSDAQ data.

• International Commerce and Information Review
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• v.12 no.1
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• pp.99-121
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• 2010

This paper reviews the categories and properties of risk measures, analyzes the classes and structural equations of volatility forecasting models, and presents the practical methodologies and their expansion methods of estimating and forecasting the volatilities of exchange rates using Excel spreadsheet modeling. We apply the GARCH(1,1) model to the Korean won(KRW) denominated daily and monthly exchange rates of USD, JPY, EUR, GBP, CAD and CNY during the periods from January 4, 1998 to December 31, 2009, make the estimates of long-run variances in the returns of exchange rate calculated as the step-by-step change rate, and test the adequacy of estimated GARCH(1,1) model using the Box-Pierce-Ljung statistics Q and chi-square test-statistics. We demonstrate the adequacy of GARCH(1,1) model in estimating and forecasting the volatility of exchange rates in the monthly series except the semi-variance GARCH(1,1) applied to KRW/JPY100 rate. But we reject the adequacy of GARCH(1,1) model in estimating and forecasting the volatility of exchange rates in the daily series because of the very high Box-Pierce-Ljung statistics in the respective time lags resulting to the self-autocorrelation. In conclusion, the GARCH(1,1) model provides for the easy and helpful tools to forecast the exchange rate volatilities and may become the powerful methodology to overcome the application difficulties with the spreadsheet modeling.