• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.261-270
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• 2009

Current financial crisis triggered by shaky U.S. banking system adds to the emphasis on the importance of the volatility in controlling and understanding financial time series data. The ARCH and GARCH models have been useful in analyzing economic time series volatilities. In particular, multivariate GARCH(MGARCH, for short) provides both volatilities and conditional correlations between several time series and these are in turn applied to computations of hedge-ratio and VaR. In this short article, we try to assess various MGARCH models with respect to the back-testing performances in VaR study. To this end, 14 korean stock prices are analyzed and it is found that MGARCH outperforms rolling window, and BEKK and CCC are relatively conservative in back-testing performance.

• 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.

• 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.

• Geosystem Engineering
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• v.21 no.6
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• pp.297-308
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• 2018

In this paper, we investigate the differences between LNG price of South Korea and Japan. Although S. Korean and Japanese LNG markets have similar structures, there are some differences in the price formation. From DCC-MGARCH, we confirm that Japan LNG price have less persistence of disturbance on time than S. Korean LNG price. The conditional correlation also shows linkage effects between LNG prices and impacts of S-curve and DS-curve. Moreover, ARDL estimation result shows that there is co-integration in all models and that impacts of Fukushima accident and LNG volumes are responsible for the increase in Japanese LNG price. Also, adjustment speed of error correction term shows that Japan's deviation from long-run equilibrium disappears faster than S. Korea does, indicating relatively strong Japanese linkage between LNG price and oil price.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.11
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• pp.117-126
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• 2020

This paper is aimed to explore the co-movement capital market in Southeast Asia and analysis the correlation of conventional and Islamic Index in the regional and global equity. This research become necessary to represent the risk on the capital market and measure market performance, as investor considers the volatility before investing. The time series daily data use from April 2012 to April 2020 both conventional and Islamic stock index in Malaysia and Indonesia. This paper examines the dynamics of conditional volatilities and correlations between those markets by using Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH). Our result shows that conventional or composite index in Malaysia less volatile than Islamic, but on the other hand, both drive correlation movement. The other output captures that Islamic Index in Indonesian capital market more gradual volatilities than the Composite Index that tends to be low in risk so that investors intend to keep the shares. Generally, the result shows a correlation in each country for conventional and the Islamic index. However, Internationally Indonesia and Malaysia composite and Islamic is low correlated. Regionally Indonesia's indices movement looks to be more correlated and it's similar to Malaysian Capital Market counterparts. In the global market distress condition, the diversification portfolio between Indonesia and Malaysia does not give many benefits.

• 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.

• The Journal of Asian Finance, Economics and Business
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• v.9 no.5
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• pp.1-9
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• 2022

The study examines stock prices (LOGKSE) and exchange rate (LOGPK)-Pakistani Rupee vis-à-vis US Dollar- interactions in Pakistan. This study employs a multivariate VAR-GARCH model using monthly data from January 2012 to October 2020. The results of the Johansen cointegration test show that there is no relationship between Foreign Exchange Market and Stock Market in the long run. In the short-run, stock exchange returns are affected slightly negatively by the changes in the foreign exchange market, but the foreign exchange market does not seem to be affected by the ups and downs of the stock exchange. The VAR model and Granger Causality show that both markets are strongly influenced by their own lagged values rather than by the lagged values of one another and show weak or no correlation between the two markets. Volatility persistence is observed in both the stock and foreign exchange markets, implying that shocks and past period volatility are major drivers of future volatility in both markets. Thus greater uncertainties today will induce panic and consequently generate higher volatility in the future period. This phenomenon has been observed many times on Pakistan Stock Exchange especially. The results have important implications for local international investors in portfolio diversification decisions and risk hedging strategies.

• 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.