• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.443-455
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• 2017

In this paper, we study ARCH(${\infty}$) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for $L_2$-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(${\infty}$) models are proved.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.495-504
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• 2001

In this paper we consider the (generalized) autoregressive model with conditional heteroscedasticity (ARCH/GARCH models). We willing give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.

• Journal of Intelligence and Information Systems
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• v.16 no.2
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• pp.19-32
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• 2010

Volatility plays a central role in both academic and practical applications, especially in pricing financial derivative products and trading volatility strategies. This study presents a novel mechanism based on generalized autoregressive conditional heteroskedasticity (GARCH) models that is able to enhance the performance of intelligent volatility trading systems by predicting Korean stock market volatility more accurately. In particular, we embedded the concept of the volatility asymmetry documented widely in the literature into our model. The newly developed Korean stock market volatility index of KOSPI 200, VKOSPI, is used as a volatility proxy. It is the price of a linear portfolio of the KOSPI 200 index options and measures the effect of the expectations of dealers and option traders on stock market volatility for 30 calendar days. The KOSPI 200 index options market started in 1997 and has become the most actively traded market in the world. Its trading volume is more than 10 million contracts a day and records the highest of all the stock index option markets. Therefore, analyzing the VKOSPI has great importance in understanding volatility inherent in option prices and can afford some trading ideas for futures and option dealers. Use of the VKOSPI as volatility proxy avoids statistical estimation problems associated with other measures of volatility since the VKOSPI is model-free expected volatility of market participants calculated directly from the transacted option prices. This study estimates the symmetric and asymmetric GARCH models for the KOSPI 200 index from January 2003 to December 2006 by the maximum likelihood procedure. Asymmetric GARCH models include GJR-GARCH model of Glosten, Jagannathan and Runke, exponential GARCH model of Nelson and power autoregressive conditional heteroskedasticity (ARCH) of Ding, Granger and Engle. Symmetric GARCH model indicates basic GARCH (1, 1). Tomorrow's forecasted value and change direction of stock market volatility are obtained by recursive GARCH specifications from January 2007 to December 2009 and are compared with the VKOSPI. Empirical results indicate that negative unanticipated returns increase volatility more than positive return shocks of equal magnitude decrease volatility, indicating the existence of volatility asymmetry in the Korean stock market. The point value and change direction of tomorrow VKOSPI are estimated and forecasted by GARCH models. Volatility trading system is developed using the forecasted change direction of the VKOSPI, that is, if tomorrow VKOSPI is expected to rise, a long straddle or strangle position is established. A short straddle or strangle position is taken if VKOSPI is expected to fall tomorrow. Total profit is calculated as the cumulative sum of the VKOSPI percentage change. If forecasted direction is correct, the absolute value of the VKOSPI percentage changes is added to trading profit. It is subtracted from the trading profit if forecasted direction is not correct. For the in-sample period, the power ARCH model best fits in a statistical metric, Mean Squared Prediction Error (MSPE), and the exponential GARCH model shows the highest Mean Correct Prediction (MCP). The power ARCH model best fits also for the out-of-sample period and provides the highest probability for the VKOSPI change direction tomorrow. Generally, the power ARCH model shows the best fit for the VKOSPI. All the GARCH models provide trading profits for volatility trading system and the exponential GARCH model shows the best performance, annual profit of 197.56%, during the in-sample period. The GARCH models present trading profits during the out-of-sample period except for the exponential GARCH model. During the out-of-sample period, the power ARCH model shows the largest annual trading profit of 38%. The volatility clustering and asymmetry found in this research are the reflection of volatility non-linearity. This further suggests that combining the asymmetric GARCH models and artificial neural networks can significantly enhance the performance of the suggested volatility trading system, since artificial neural networks have been shown to effectively model nonlinear relationships.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.11-16
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• 2007

Since the seminal work of Engle (1982), many researchers and practitioners have developed ARCH-type models to deal with volatility modelling, which, for instance, is crucial to perform the task of derivative pricing, measuring risk, and risk hedging. In this paper, we base the GARCH(1,1) model to analyze the KOSPI200 data, and perform the CUSUM test for detecting parameter changes in the GARCH model. It is shown that the data suffers from a parameter change.

• Korea Real Estate Review
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• v.27 no.3
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• pp.41-50
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• 2017

Previous studies, especially that by Lee (2014), showed how time series volatility models can be applied to the house price series. As the regional housing market trends, however, have shown significant differences of late, analysis with national data may have limited practical implications. This study applied volatility models in analyzing and forecasting regional house prices. The estimation of the AR(1)-ARCH(1), AR(1)-GARCH(1,1), and AR(1)-EGARCH(1,1,1) models confirmed the ARCH and/or GARCH effects in the regional house price series. The RMSEs of out-of-sample forecasts were then compared to identify the best-fitting model for each region. The monthly rates of house price changes in the second half of 2017 were then presented as an example of how the results of this study can be applied in practice.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.217-224
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• 2003

The volatility in the financial data is usually measured by conditional variance. Two main streams for gauging conditional variance are stochastic volatility (SV) model and autoregressive type approach (GARCH). This article is conducting comparative study between SV and GARCH through the Korean Stock Prices Index (KOSPI) data. It is seen that SV model is slightly better than GARCH(1,1) in analyzing KOSPI data.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.183-200
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• 2007

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.