• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.571-575
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• 2010

Drought is a natural hazard with different properties that are usually dependent to each other. Therefore, a multivariate model is often used for drought frequency analysis. The Copula based bivariate drought severity and duration frequency analysis is applied in the current study in order to show the effect of tail behavior of drought severity and duration on the selection of a copula function for drought bivariate frequency analysis. Four copula functions, namely Clayton, Gumbel, Frank and Gaussian, were fitted to drought data of four stations in Iran and Canada in different climate regions. The drought data are calculated based on standardized precipitation index time series. The performance of different copula functions is evaluated by estimating drought bivariate return periods in two cases, [$D{\geq}d$ and $S{\geq}s$] and [$D{\geq}d$ or $S{\geq}s$]. The bivariate return period analysis indicates the behavior of the tail of the copula functions on the selection of the best bivariate model for drought analysis.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.445-459
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• 2014

This paper investigates the dependence structure of Korean financial markets (stock, foreign exchange (FX) rates and bond) using copula-GARCH and dynamic conditional correlation (DCC) models. We examine GJR-GARCH with skewed elliptical distributions and four copulas (Gaussian, Student's t, Clayton and Gumbel) to model dependence among returns, and then employ DCC model to describe system-wide correlation dynamics. We analyze the daily returns of KOSPI, FX (WON/USD) and KRX bond index (Gross Price Index) from $2^{nd}$ May 2006 to $30^{th}$ June 2014 with 2,063 observations. Empirical result shows that there is significant asymmetry and fat-tail of individual return, and strong tail-dependence among returns, especially between KOSPI and FX returns, during the 2008 Global Financial Crisis period. Focused only on recent 30 months, we find that the correlation between stock and bond markets shows dramatic increase, and system-wide correlation wanders around zero, which possibly indicates market tranquility from a systemic perspective.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• Journal of Korea Port Economic Association
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• v.36 no.4
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• pp.93-106
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• 2020

Trade is an important economic activity. In particular, since the establishment of the World Trade Organization (WTO), the scope of trade has been expanding due to events such as the entry of China into the WTO in 2001, the establishment of a multilateral trading system, mitigation and integration of trade barriers, and the establishment of the free trade agreement (FTA). Despite the expansion of the trade market, however, extreme events such as the 2008 global financial crisis, the 2016 Brexit, and the 2018 US-China trade war have had a direct negative impact on the trade market. Therefore, the present this study analyzed the dependence structure between the international shipping freight rate index, a variable representing trade activities, and the trade uncertainty between the US and China. The following is a summary of the analysis results. First, the US-Chinese trade policy uncertainty and international shipping freight rate index presented a Frank copula and rotated Clayton copula 270° distribution, respectively, showing the same distribution structure for each country. Second, the Kendall's tau correlation revealed a negative dependence between the international shipping freight rate index and US-Chinese trade policy uncertainty. The degree of dependence was greater in the combination of uncertainty in China's trade policy and international shipping freight rates. In other words, the dependence of global demand and trade policy uncertainty confirmed that China was stronger than the US. Finally, the tail dependence results revealed that the US-Chinese trade policy uncertainty and international shipping freight rates were independent of each other. This means that extreme events related to the trade policy uncertainty or international shipping rate index were not affected by each other.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.420-420
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• 2015

일반적으로 호우사상의 특성은 강우강도, 지속기간, 총 강우량으로 정량화된다. 주어진 호우 사상에 대한 재현기간은 보통 위 세 개 변량 중 두 개의 변량에 대한 이변량 빈도해석을 통해 결정된다. 따라서 3 가지의 다른 빈도해석이 가능하며, 원칙적으로 이 세 가지 빈도해석 결과는 같아야 한다. 그러나, 문제는 어떤 변량을 선택하느냐에 따라 빈도해석 결과가 달라진다는 점이다. 본 연구에서는 이 문제를 해결하고자 다음과 같은 연구를 수행하였다. 첫 번째로 1961-2010년에 관측된 서울지점 연최대치 호우사상에 대한 이변량 빈도해석을 수행하였다. 이변량 빈도해석은 Frank, Gumbel-Hougaard, Clayton, ali-Mikhail-Haq copula 모형을 이용하여 수행하였으며, 모형의 매개변수는 두 변량의 상관관계를 나타내는 Kendall's tau를 이용하여 추정하였다. 호우사상에 대한 이변량 빈도해석을 수행한 결과, 결과가 일관되지 않고 고려한 두 가지 강우변량에 따라 다르게 나타난 것을 확인하였다. 두 번째로 보편적인 강우강도식을 이용하여 호우사상을 이루는 세변량의 특성을 분석하였다. 본 연구에서 고려한 강우강도식은 Talbot 형, Sherman 형, Japanese 형, Grunsky 형이다. 일반적인 강우강도식에서 지속기간과 강우강도의 관계는 I~t^a와 같이 나타나며, 이 때 a의 범위는 -0.5부터 -1까지 값으로 정해진다. 마지막으로, 호우사상을 이루는 세 변량의 상관관계를 이용하여 가장 적절한 이변량 빈도해석결과를 도출하는 강우 변량의 조합을 결정하였다. 결론적으로, 본 연구에서는 지속기간과 강우강도를 copula 모형을 이용한 이변량 빈도 해석의 가장 적절한 것으로 판단되었다.

• Journal of Korea Water Resources Association
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• v.47 no.2
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• pp.171-182
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• 2014

The objective of this study is to evaluate the utilization of bivariate joint drought index in South Korea. In order to develop the bivariate joint drought index, in this study, Clayton copula was used to estimate the joint distribution function and the calibration method was employed for parameter estimation. Precipitation and soil moisture data were selected as input data of bivariate joint drought index for period of 1977~2012. The time series analysis, ROC (Receiver Operating Characteristic) analysis, spatial analysis were used to evaluate the bivariate joint drought index with SPI (Standardized Precipitation Index) and SSI (Standardized Soil moisture Index). As a result, SPI performed better for drought onset and SSI for drought demise. On the other hand the bivariate joint drought index captured both drought onset and demise very well. The ROC score of bivariate joint drought index was higher than that of SPI and SSI, and it also reflected the local drought situations. The bivariate joint drought index overcomes the limitations of existing drought indices and is useful for drought analysis.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.305-305
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• 2022

A better approach for assessing meteorological drought occurrences is increasingly important in mitigating and adapting to the impacts of climate change, as well as strategies for developing early warning systems. The present study defines meteorological droughts as a period with an abnormal precipitation deficit based on monthly precipitation data of 18 gauging stations for the Han River watershed in the past (1974-2015). This study utilizes a Bayesian parameter estimation approach to analyze the effects of climate change on future drought (2025-2065) in the Han River Basin using the Coupled Model Intercomparison Project Phase 6 (CMIP6) with four bias-corrected general circulation models (GCMs) under the Shared Socioeconomic Pathway (SSP)2-4.5 scenario. Given that drought is defined by several dependent variables, the evaluation of this phenomenon should be based on multivariate analysis. Two main characteristics of drought (severity and duration) were extracted from precipitation anomalies in the past and near-future periods using the copula function. Three parameters of the Archimedean family copulas, Frank, Clayton, and Gumbel copula, were selected to fit with drought severity and duration. The results reveal that the lower parts and middle of the Han River basin have faced severe drought conditions in the near future. Also, the bivariate analysis using copula showed that, according to both indicators, the study area would experience droughts with greater severity and duration in the future as compared with the historical period.

• Journal of Korea Water Resources Association
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• v.53 no.12
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• pp.1203-1210
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• 2020

Drought is caused by a combination of various hydrological or meteorological factor, so it is difficult to accurately assess drought event, but various drought indices have been developed to interpret them quantitatively. However, the drought indexes currently being used are calculated from the lack of a single variable, which is a problem that does not accurately determine the drought event caused by complex causes. Shortage of a single variable may not be a drought, but it is judged to be a drought. On the other hand, research on developing indices using unstructured data, which is widely used in big data analysis, is being carried out in other fields and proven to be superior. Therefore, in this study, we intend to calculate the drought index by combining unstructured data (news data) with weather and hydrologic information (rainfall and dam inflow) that are being used for the existing drought index, and to evaluate the utilization of drought interpretation through verification of the calculated drought index. The Clayton Copula function was used to calculate the joint drought index, and the parameter estimation was used by the calibration method. The analysis showed that the drought index, which combines unstructured data, properly expresses the drought period compared to the existing drought index (SPI, SDI). In addition, ROC scores were calculated higher than existing drought indices, making them more useful in drought interpretation. The joint drought index calculated in this study is considered highly useful in that it complements the analytical limits of the existing single variable drought index and provides excellent utilization of the drought index using unstructured data.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.392-392
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• 2012

기후변화로 인해 가뭄 재해는 수자원 관리 및 계획에 큰 부담으로 작용하므로 이에 대한 연구와 대책 마련이 필요하나, 아직까지 가뭄 특성의 정량적인 거동 분석이나 기후변화가 가뭄에 미치는 영향 연구는 아직 미흡하다. 이에 본 논문에서는 가뭄변수 분석을 통해 결합확률을 이용한 가뭄분석이 타당함을 보이고, 코풀라 이론에 의해 결합확률을 이용한 가뭄빈도분석을 수행하고자 하였다. 또한 기후변화가 유역단위의 수문학적인 가뭄에 미치는 영향을 정량적으로 평가하고 예측하고자 하였다. 이를 위하여 가뭄 사상에 대하여 전통적인 방법으로의 빈도분석을 수행하였다. 이를 Clayton 코풀라 함수를 적용하여 가뭄의 결합확률을 고려한 빈도분석을 수행해 기존의 단변량 기반의 빈도분석 방법과 비교 분석 하였다. 또한, 결합확률을 이용하여 가뭄의 재현빈도를 분석하고 이를 이용하여 가뭄의 심도-지속기간-빈도 곡선을 유도하였다. 그리고 기후변화가 가뭄에 미치는 영향을 분석하기 위하여 IPCC의 SRES A1B 시나리오와 KMA RCM 기후모형을 이용하여 미래 가뭄 시계열을 산정하고, 미래 가뭄에 대한 결합확률 빈도해석과 미래 가뭄분석을 수행하였다. 본 연구의 결과에 따르면 가까운 미래에 짧은 지속기간을 가진 심한 가뭄이 다발할 것으로 전망되었다.