• 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 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.

• Management & Information Systems Review
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• v.32 no.3
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• pp.1-23
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• 2013

In this study, we try to investigate the spillover effects of volatility in international tourists arrivals between Korea and US, Japan, China by using the multivariate BEKK model from January 2005 to January 2013. In the results of this study, after the global financial crisis, we found a cointegration relationship and tourist arrivals of Japan were adjusted to recovery in the short term. Also tourists arrivals from China and Japan showed the long-term elasticity. In the conditional mean equation of a BEKK model, there were the spillover effects. And in the conditional variance equation, ARCH(${\epsilon}^2_t$) coefficients showed a strong influence on the arrivals of their own and the spillover effects and the asymmetric effects on the volatility of China and Japan arrivals. In GARCH(${\sigma}^2_t$) coefficients showed the asymmetric effects and the spillover effects of the conditional volatility among source arrivals. Therefore, we examined the asymmetric reaction of one-way or two-way tourist arrivals between source countries and Korea and the spillover effects related to tourists arrivals of source countries to Korea. We has confirmed a causal relationship between some of the tourists arrivals from source countries to korea.

• Management & Information Systems Review
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• v.33 no.1
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• pp.139-155
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• 2014

This study is to examine the linkage of volatility between changes in the stock market of India and other countries through the integration of the world economy. The results were as follows: First, autocorrelation or serial correlation did not exist in the classic RS model, but long-term memory was present in the modified RS model. Second, unit root did not exist in the unit root test for all periods, and the series were a stable explanatory power and a long-term memory with the normal conditions in the ARFIMA model. Third, in the multivariate asymmetric BEKK and VAR model before the financial crisis, it showed that there was a strong influence of the own market of Taiwan and UK in the conditional mean equation, and a strong spillover effect from Japan to India, from Taiwan to China(Korea, US), from US(Japan) to UK in one direction. In the conditional variance equation, GARCH showed a strong spillover effect that indicated the same direction as the result of ARCH coefficient of the market itself. Asymmetric effects in three home markets and between markets existed. Fourth, after the financial crisis, in the conditional mean equation, only the domestic market in Taiwan showed strong influences, and strong spillover effects existed from India to US, from Taiwan to Japan, from Korea to Germany in one direction. In the conditional variance equation, strong spillover effects were the same as the result of the pre-crisis and asymmetric effect in the domestic market in UK was present, and one-way asymmetric effect existed in Germany from Taiwan. Therefore, the results of this study presented the linkage between the volatilities of the stock market of India and other countries through the integration of the world economy, observing and confirming the asymmetric reactions and return(volatility) spillover effects between the stock market of India and other countries.