• 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.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.915-925
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• 2007

Multivariate GARCH has been useful to model dynamic relationships between volatilities arising from each component series of multivariate time series. Methodologies including EWMA(Exponentially weighted moving-average model), DVEC(Diagonal VEC model), BEKK and CCC(Constant conditional correlation model) models are comparatively reviewed for bivariate time series. In addition, these models are applied to evaluate VaR(Value at Risk) and to construct joint prediction region. To illustrate, bivariate stock prices data consisting of Samsung Electronics and LG Electronics are analysed.

• 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.27 no.7
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• pp.1219-1228
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• 2014

Constant conditional correlation (CCC) is frequently employed for parsimony in the field of multivariate GARCH time series. An extended-CCC (ECCC) model is further developed in order to allow interactions between multivariate volatilities. The paper introduces both CCC model and ECCC model to the domestic financial time series. The CCC and ECCC models are fitted and then compared with each other through various multivatiate time series.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.667-675
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• 2018

When a financial time series consists of daily (closing) returns, traditional volatility models such as autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) are useful to figure out daily volatilities. With high frequency returns in a day, one may adopt various multivariate GARCH techniques (MGARCH) (Tsay, Multivariate Time Series Analysis With R and Financial Application, John Wiley, 2014) to obtain intraday volatilities as long as the high frequency is moderate. When it comes to the ultra high frequency (UHF) case (e.g., one minute prices are available everyday), a new model needs to be developed to suit UHF time series in order to figure out continuous time intraday-volatilities. Aue et al. (Journal of Time Series Analysis, 38, 3-21; 2017) proposed functional GARCH (fGARCH) to analyze functional volatilities based on UHF data. This article introduces fGARCH to the readers and illustrates how to estimate fGARCH equations using UHF data of KOSPI and Hyundai motor company.

• The Journal of Asian Finance, Economics and Business
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• v.4 no.4
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• pp.27-37
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• 2017

This study examines the behaviour of staple food price using Multivariate BEKK-GARCH Model. Understanding of staple food price behaviour is important for determining the unpredictability of staple food market and also for policy making. In this paper, we focus on the commodity prices of sugar, rice, soybean and wheat to examine the volatility behaviour of those commodities. The empirical results show that the own-volatility spillover are relatively significant for all food prices. The own-volatility spillover effect for sugar price is relatively large compared with the volatility spillover of other staple food commodities. The findings also highlight that the price volatility of wheat increases during food crisis more than it does when the condition is stable. Also, the own-volatility of rice and wheat in the period of the food crisis is significant and higher compared to the period before food crisis indicates that the past own-volatility effects during food crisis are relatively more difficult to predict because of the uncertainty and high price volatility. Policy recommendations that can be proposed based on the findings are: (1) a better trade agreement in food commodity trade, (2) lower the dependence on wheat importation in Indonesia, and (3) reliable system to minimize food price volatility risks.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.825-835
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• 2008

Multivariate GARCH(MGARCH) has been useful in financial studies and econometrics for modeling volatilities and correlations between components of multivariate time series. An obvious drawback lies in that the number of parameters increases rapidly with the number of variables involved. This thesis tries to resolve the problem by using dimension reduction technique. We briefly review both factor models for dimension reduction and the MGARCH models including EWMA (Exponentially weighted moving-average model), DVEC(Diagonal VEC model), BEKK and CCC(Constant conditional correlation model). We create meaningful portfolios obtained after reducing dimension through statistical factor models and fundamental factor models and in turn these portfolios are applied to MGARCH. In addition, we compare portfolios by assessing MSE, MAD(Mean absolute deviation) and VaR(Value at Risk). Various financial time series are analyzed for illustration.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.1013-1024
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• 2015

We compare the performance of two representative estimation methods for the dynamic conditional correlation (DCC) GARCH model. The first method is the pairwise estimation which exploits partial information from the paired series, irrespective to the time series dimension. The second is the multi-dimensional estimation that uses full information of the time series. As a simulation for the comparison, we generate a multivariate time series similar to those observed in real markets and construct a DCC GARCH model. As an empirical example, we constitute various portfolios using real KOSPI 200 sector indices and estimate volatility and VaR of the portfolios. Through the estimated dynamic correlations from the simulation and the estimated volatility and value at risk (VaR) of the portfolios, we evaluate the performance of the estimations. We observe that the multi-dimensional estimation tends to be superior to pairwise estimation; in addition, relatively-uncorrelated series can improve the performance of the multi-dimensional estimation.

• Environmental and Resource Economics Review
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• v.11 no.3
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• pp.397-414
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• 2002

This paper presents an empirical analysis of exchange rate volatility, petroleum's import price and industrial production on petroleum imports. The GARCH framework is used to measure the exchange rate volatility. One of the most appealing features of the GARCH model is that it captures the volatility clustering phenomenon. We found one long-run relationship between petroleum imports, import price, industrial production, and exchange rate volatility using Johansen's multivariate cointegration methodology. Since there exists a cointegrating vector, therefore, we employ an error correction model to examine the short-run dynamic linkage, finding that the exchange rate volatility performs a key role in the short-run. This paper also apply impulse-response functions to provide the dynamic responses of energy consumption to the exchange rate volatility. The results show that the response of energy consumption to exchange rate volatility declines at the first month and dies out very quickly.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.199-226
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• 2009

We examine the intertemporal relation between risk and return in the Korean stock market and foreign exchange market based on the two factor ICAPM framework. The standard GARCH model and the GJR(1993) model are employed to estimate conditional variances of the stock returns and foreign exchange rates. The covariance between the rates of stock returns and changes in the exchange rates are estimated by the constant conditional correlation model of Bollerslev(1990) and the dynamic conditional correlation model of Engle(2002). The multivariate GARCH in mean model and quasi-maximum likelihood estimation method, consequently, are applied to investigate riskreturn relation jointly. We find that the estimated coefficient of relative risk aversion is negative and statistically significant in the post-financial crisis sample period in the Korean stock market. We also show that the expected stock returns are negatively related to the dynamic covariance with foreign exchange rates. Both estimated parameters of conditional variance and covariance in the foreign exchange market, however, are not statistically significant. The GJR model is better than the standard GARCH model to estimate the conditional variances. In addition, the dynamic conditional correlation model has higher explanatory power than the constant correlation model. The empirical results of this study suggest following two points to investors and risk managers in hedging and diversifying strategies for their portfolios in the Korean stock market: first, the variability of foreign exchange rates should be considered, and second, time-varying correlation between stock returns and changes in foreign exchange rates supposed to be considered.