• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.809-820
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• 2011

VaR(Value at risk) is a measure of market risk management and needs to be estimated for multiple distributions. In this paper, Copula functions are used to generate distributions of multivariate random variables. The dependence structure of random variables is classified by the exchangeable Copula, fully nested Copula, partially nested Copula. For the earning rate data of four Korean industries, the parameters of the Archimedean Copula functions including Clayton, Gumbel and Frank Copula are estimated by using three kinds of dependence structure. These Copula functions are then fitted to to the data so that corresponding VaR are obtained and explored.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.279-279
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• 2020

최근 copula 모형은 여러 확률변수를 갖는 수문현상에 대해 빈도해석을 수행할 경우 결합확률분포형으로 유용하게 사용되고 있다. 하나의 자료를 확률변수로 사용하는 단변량 빈도해석에 비해 여러 수문자료를 동시에 각각 확률변수로 취하여 결합확률분포형을 추정할 수 있는 다변량 빈도해석은 수문자료의 상관성을 고려하면서 확률분포형을 추정할 수 있다는 장점이 있다. Copula 모형 중 Gumbel copula는 extreme-value 확률분포형으로 극치사상에 적합한 확률분포형이다. 본 연구에서는 Gumbel copula를 이용하여 우리나라 기상청 64개 종관기상관측소의 강우자료로부터 극치 강우사상을 추출하고, 이를 이용하여 빈도해석을 수행하였다. 극치 강우사상은 전체 강우사상 중 각 년도별로 최대강우량을 갖는 연최대강우량사상(annual maximum volume event)을 사용하였다. 각 확률변수의 주변분포형으로는 gamma, Gumbel, generalized extreme value, generalized logistic, Weibull 등 5개 확률분포형을 검토하였으며 각각 적합한 주변분포형을 적용하고 copula 모형의 매개변수는 의사최우도법(maximum pseudo-likelihood method)를 사용하여 추정하였다. 또한 추정된 copula 모형은 Cramer-von Mises 함수와 경험적 copula를 이용하여 적합도 검정을 수행하였다. 이를 통해 극치강우사상에 대하여 Gumbel copula 모형의 적용성을 검토하였으며 추정된 결합확률분포형을 이용하여 빈도별 확률강우사상을 2차원 등치선(contour line)형태로 제시하였다.

• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.523-533
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• 2011

Most nancial preference methods for market risk management are to estimate VaR. In many real cases, it happens to obtain the VaRs of the univariate as well as multivariate distributions based on multivariate data. Copula functions are used to explore the dependence of non-normal random variables and generate the corresponding multivariate distribution functions in this work. We estimate Archimedian Copula functions including Clayton Copula, Gumbel Copula, Frank Copula that are tted to the multivariate earning rate distribution, and then obtain their VaRs. With these Copula functions, we estimate the VaRs of both a certain integrated industry and individual industries. The parameters of three kinds of Copula functions are estimated for an illustrated stock data of two Korean industries to obtain the VaR of the bivariate distribution and those of the corresponding univariate distributions. These VaRs are compared with those obtained from other methods to discuss the accuracy of the estimations.

• Journal of Korea Water Resources Association
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• v.49 no.10
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• pp.823-833
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• 2016

This study developed a trivariate Copula function based drought frequency analysis model to better evaluate the recent 2014~2015 drought event. The bivariate frequency analysis has been routinely used for the drought variables of interest (e.g. drought duration and severity). However, the recent drought patterns showed that the intensity can be regarded as an important factor which is being characterized by short duration and severe intensity. Thus, we used the trivariate Copula function approach to incorporate the trivariate drought characteristics into the drought frequency analysis. It was found that the return periods based on the trivariate frequency analysis are, in general, higher than the existing bivariate frequency analysis. In addition, this study concludes that the increase in drought frequency claimed by the Gumbel copula function has been overestimated compared to the Student t Copula function. In other words, the selection of copula functions is rather sensitive to the estimation of trivariate drought return periods at a given duration, magnitude and intensity.

• Proceedings of the Korean Society for Language and Information Conference
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• 2002.02a
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• pp.36-49
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• 2002

One main complexity of the copula constructions concerns a mismatch between morphology and syntactic constituency: the copula seems to form a morphological unit with the immediately preceding element, whereas in terms of syntax the copula appears to take this as its syntactic complement. In capturing such mismatches, we show that the copula is treated as an independent verb at the level of tectogrammatical structure (or syntax tree), whereas as a bound morpheme at the level of phonogram-matical structure (or domain tree), in terms of Dowty 1992 (or Reape 1994). This paper, adopting the notion of DOMAIN in HPSG, shows that copula constructions are a subtype of compacting-constructions. These constructions compact the domain value of the copula and that of its preceding element together into one domain unit, eventually making it inert to syntactic phenomena such as scrambling, deletion and pro-form substitution. This construction-based approach provides a clean analysis for the formation of the copula construction and related phenomena.

• Geomechanics and Engineering
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• v.36 no.6
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• pp.601-618
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• 2024

The joint probability distribution of uncertain geomechanical parameters of geotechnical strata is a crucial aspect in constructing the reliability functional function for roof structures. However, due to the limited number of on-site exploration and test data samples, it is challenging to conduct a scientifically reliable analysis of roof geotechnical strata. This study proposes a Copula method based on small sample exploration and test data to construct the intensity characteristics of roof geotechnical strata. Firstly, the theory of multidimensional copula is systematically introduced, especially the construction of four-dimensional Gaussian copula. Secondly, data from measurements of 176 groups of geomechanical parameters of roof geotechnical strata in 31 coal mines in China are collected. The goodness of fit and simulation error of the four-dimensional Gaussian Copula constructed using the Pearson method, Kendall method, and Spearman methods are analyzed. Finally, the fitting effects of positive and negative correlation coefficients under different copula functions are discussed respectively. The results demonstrate that the established multidimensional Gaussian Copula joint distribution model can scientifically represent the uncertainty of geomechanical parameters in roof geotechnical strata. It provides an important theoretical basis for the study of reliability functional functions for roof structures. Different construction methods for multidimensional Gaussian Copula yield varying simulation effects. The Kendall method exhibits the best fit in constructing correlations of geotechnical parameters. For the bivariate Copula fitting ability of uncertain parameters in roof geotechnical strata, when the correlation is strong, Gaussian Copula demonstrates the best fit, and other Copula functions also show remarkable fitting ability in the region of fixed correlation parameters. The research results can offer valuable reference for the stability analysis of roof geotechnical engineering.

• Wind and Structures
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• v.25 no.3
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• pp.261-282
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• 2017

The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.

• Journal of Korea Port Economic Association
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• v.35 no.4
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• pp.107-120
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• 2019

Crude oil is a resource that is being used as a raw material in major industries, representing the price of the raw material market. It is also an important element that affects the shipping market in terms of fuel costs for freight vessels. As a result, crude oil and freight rates are closely related. Therefore, from January 2009 to June 2019, this study analyzed the dependency structure between oil price (WTI) and freight rates (BDI, BCI, BPI, BSI, and BHI) using daily data. The main results are summarized as follows. First, according to the copula results, survival Gumbel copula in WTI-BDI, Clayton copula in WTI-BCI, Survival Joe copula in WTI-BPI, Joe copula in WTI-BSI, and survival Gumbel copula in WTI-BHI were selected as the best-fitted model. Second, looking at Kendall's tau correlation, there is a positive correlation between BDI and oil price. Furthermore, freight rate index (BCI, BPI, BSI) and oil price show positive dependencies. In particular, the strongest dependence was found in BCI and oil price returns. However, BHI and oil price show a negative dependency. Third, looking at the tail-dependency structure, a pair between oil price and BDI, BCI showed a lower tail-dependency. The pair between oil price and BSI showed the upper tail-dependency.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.488-488
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• 2015

Intermittent streamflow is common phenomenon in arid and semi-arid regions. To manage water resources of intermittent streamflows, stochactic simulation data is essential; however the seasonally stochastic modeling for intermittent streamflow is a difficult task. In this study, using the periodic Markov chain model, we simulate intermittent monthly streamflow for occurrence and the periodic gamma autoregressive and copula models for amount. The copula models were tested in a previous study for the simulation of yearly streamflow, resulting in successful replication of the key and operational statistics of historical data; however, the copula models have never been tested on a monthly time scale. The intermittent models were applied to the Colorado River system in the present study. A few drawbacks of the PGAR model were identified, such as significant underestimation of minimum values on an aggregated yearly time scale and restrictions of the parameter boundaries. Conversely, the copula models do not present such drawbacks but show feasible reproduction of key and operational statistics. We concluded that the periodic Markov chain based the copula models is a practicable method to simulate intermittent monthly streamflow time series.

• IE interfaces
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• v.24 no.1
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• pp.24-39
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• 2011

In this paper, we study the methodology for the measurement and integration of market risk and credit risk using Copula. We apply the methodology of Rosenberg, and Schuermann(2006) to the assets of pension system. Firstly we estimate dynamics of risk factors and their effects on investment returns, then use the estimated result to simulate future movement of risk factors and distribution of investment returns. Finally we measure integrated risk using integrated return distribution by Copula and simulated future investment return distributions. We found the integrated risk changing with the correlation of risks and investment weights of risks and confirmed the diversification effect of risks. This result is consistent when we use normal Copula and normal marginals, t-Copula and t(3) marginals, and normal Copula and non-parametric marginals. And in the case of non-parametric maginals, larger integrated risk is calculated. It means that use of non-parametric marginals is more conservative.