• Journal of Information Technology Applications and Management
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• v.25 no.4
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• pp.157-169
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• 2018

The purpose of this study was to examine the volatility of bitcoin, diagnose if bitcoin are a systematic risk asset, and evaluate their effectiveness by estimating market beta representing systematic risk using GARCH (Generalized Auto Regressive Conditional Heteroskedastieity) model. First, the empirical results showed that the market beta of Bitcoin using the OLS model was estimated at 0.7745. Second, using GARCH (1, 2) model, the market beta of Bitcoin was estimated to be significant, and the effects of ARCH and GARCH were found to be significant over time, resulting in conditional volatility. Third, the estimated market beta of the GARCH (1, 2), AR (1)-GARCH (1), and MA (1)-GARCH (1, 2) models were also less than 1 at 0.8819, 0.8835, and 0.8775 respectively, showing that there is no systematic risk. Finally, in terms of efficiency, GARCH model was more efficient because the standard error of a market beta was less than that of the OLS model. Among the GARCH models, the MA (1)-GARCH (1, 2) model considering non-simultaneous transactions was estimated to be the most appropriate model.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.697-707
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• 2017

In this paper, we propose a modified GARCH(p, q)-X model which is obtained by adding the exogenous variables to the modified GARCH(p, q) process. Some limiting properties are shown under various stationary and nonstationary exogenous processes which are generated by another process independent of the noise process. The proposed model extends the GARCH(1, 1)-X model studied by Han (2015) to various GARCH(p, q)-type models such as GJR GARCH, asymptotic power GARCH and VGARCH combined with exogenous process. In comparison with GARCH(1, 1)-X, we expect that many stylized facts including long memory property of the financial time series can be explained effectively by modified GARCH(p, q) model combined with proper additional covariate.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.517-525
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• 2011

This paper shows the performance evaluation of a robust estimator based on the GARCH model. We first introduce the method of a robust estimate in the GARCH model and the method of an outlier detection in the GARCH model. The results of the real internet traffic data show the out-performance of the robust estimator over the outlier detection method in the GARCH model. In addition, the method of the robust estimate is less complex than the method of the outlier detection method in the GARCH model.

• 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.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.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.429-442
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• 2015

Volatility forecasting in financial markets is an important issue because it is directly related to the profit of return. The volatility is generally modeled as time-varying conditional heteroskedasticity. A generalized autoregressive conditional heteroskedastic (GARCH) model is often used for modeling; however, it is not suitable to reflect structural changes (such as a financial crisis or debt crisis) into the volatility. As a remedy, we introduce the Markov regime switching GARCH (MRS-GARCH) model. For the empirical example, we analyze and forecast the volatility of the daily Korea Composite Stock Price Index (KOSPI) data from January 4, 2000 to October 30, 2014. The result shows that the regime of low volatility persists with a leverage effect. We also observe that the performance of MRS-GARCH is superior to other GARCH models for in-sample fitting; in addition, it is also superior to other models for long-term forecasting in out-of-sample fitting. The MRS-GARCH model can be a good alternative to GARCH-type models because it can reflect financial market structural changes into modeling and volatility forecasting.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1333-1343
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• 2014

Hansen and Lund (2005) documented that a univariate GARCH(1,1) model is no worse than other sophisticated GARCH models in terms of prediction errors such as MSPE and MAE. Here, we extend Hansen and Lund (2005) by considering multivariate GARCH models and incorporating risk management measures such as VaR and fail percentage. Our Monte Carlo simulations study shows that multivariate GARCH(1,1) model also performs well compared to asymmetric GARCH models. However, we suggest that actual model selection should be done with care in light of risk management. It is applied to the realized volatilities of KOSPI, NASDAQ and HANG SENG index for recent 10 years.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.1037-1044
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• 2008

In this paper, we show the performance of the power transformation GARCH(PGARCH) model to analyze the internet traffic data. The long memory property which is the typical characteristic of internet traffic data can be explained by the PGARCH model rather than the linear GARCH model. Small simulation and the analysis of the real internet traffic show the out-performance of the PARCH MODEL over the linear GARCH one.

• 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.

• 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.