• Title/Summary/Keyword: Archimedean Copula

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VaR Estimation with Multiple Copula Functions (다차원 Copula 함수를 이용한 VaR 추정)

  • Hong, Chong-Sun;Lee, Won-Yong
    • 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.

Archimedean Copula for bivariate Frequency Analysis (이변량 빈도해석을 위한 Archimedean Copula)

  • Sung, Jang-Hyun;Baek, Hee-Jeong;Kwon, Won-Tae;Kim, Young-Oh
    • Proceedings of the Korea Water Resources Association Conference
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    • 2010.05a
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    • pp.600-604
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    • 2010
  • 수문설계 인자인 확률홍수량 산정시 짧은 홍수량 자료 길이로 인해 홍수량을 직접 이용하기 보다는 강우자료와 강우-유출모형에 의존하고 있는 현시점에서 무엇보다 중요한 것은 신뢰할 만한 확률강우량이 산정되어야 한다는 것이다. 하지만 지금까지의 강우빈도해석(rainfall frequency analysis)은 강도(intensity), 지속기간(duration), 깊이(depth) 사이의 연관성은 고려하지 않은 단편적인 방법론에 그치고 있다. 즉, 강우를 표현하는 인자들 간 독립(independency)이라는 가정을 거친 후, 간단한 단변량(univariate) 강우빈도분포(rainfall frequency distribution)로 확률강우량을 산정하고 있다는 것이다. 간단한 모형에 따른 이점은 있으나 최근의 강우 형태는 매우 복잡한 양상을 띠고 있어, 단변량 강우빈도분포로 이를 대표하기에는 무리가 따른다. 따라서 본 연구에서는 강우빈도해석의 인자가 독립적이며 정규분포(normal distribution)라 가정하지 않고, 세 개의 주변 분포(marginal distribution)의 형태가 같지 않다는 점, 또한 가정하지 않는 방법론 중, 그 가치를 널리 인정받고 있는 Archimedean Copula (AC)에 대한 연구를 수행하였다. AC를 이용하여 강도, 지속기간, 깊이 사이의 종속성 중, 두 가지 변량을 고려한 이변량(bivariate) 강우빈도해석을 수행하였고 그 효용성을 검토해 보았다.

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A copula based bias correction method of climate data

  • Gyamfi Kwame Adutwum;Eun-Sung Chung
    • Proceedings of the Korea Water Resources Association Conference
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    • 2023.05a
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    • pp.160-160
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    • 2023
  • Generally, Global Climate Models (GCM) cannot be used directly due to their inherent error arising from over or under-estimation of climate variables compared to the observed data. Several bias correction methods have been devised to solve this problem. Most of the traditional bias correction methods are one dimensional as they bias correct the climate variables separately. One such method is the Quantile Mapping method which builds a transfer function based on the statistical differences between the GCM and observed variables. Laux et al. introduced a copula-based method that bias corrects simulated climate data by employing not one but two different climate variables simultaneously and essentially extends the traditional one dimensional method into two dimensions. but it has some limitations. This study uses objective functions to address specifically, the limitations of Laux's methods on the Quantile Mapping method. The objective functions used were the observed rank correlation function, the observed moment function and the observed likelihood function. To illustrate the performance of this method, it is applied to ten GCMs for 20 stations in South Korea. The marginal distributions used were the Weibull, Gamma, Lognormal, Logistic and the Gumbel distributions. The tested copula family include most Archimedean copula families. Five performance metrics are used to evaluate the efficiency of this method, the Mean Square Error, Root Mean Square Error, Kolmogorov-Smirnov test, Percent Bias, Nash-Sutcliffe Efficiency and the Kullback Leibler Divergence. The results showed a significant improvement of Laux's method especially when maximizing the observed rank correlation function and when maximizing a combination of the observed rank correlation and observed moments functions for all GCMs in the validation period.

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VaR Estimation of Multivariate Distribution Using Copula Functions (Copula 함수를 이용한 이변량분포의 VaR 추정)

  • Hong, Chong-Sun;Lee, Jae-Hyung
    • 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.

Prediction of steel corrosion in magnesium cement concrete based on two dimensional Copula function

  • Feng, Qiong;Qiao, Hongxia;Wang, Penghui;Gong, Wei
    • Computers and Concrete
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    • v.21 no.2
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    • pp.181-187
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    • 2018
  • In order to solve the life prediction problem of damaged coating steel bar in magnesium cement concrete, this study tries to establish the marginal distribution function by using the corrosion current density as a single degradation factor. Representing the degree of steel corrosion, the corrosion current density were tested in electrochemical workstation. Then based on the Copula function, the joint distribution function of the damaged coating was established. Therefore, it is indicated that the corrosion current density of the bare steel and coated steel bar can be used as the boundary element to establish the marginal distribution function. By using the Frank-Copula function of Copula Archimedean function family, the joint distribution function of the damaged coating steel bar was successfully established. Finally, the life of the damaged coating steel bar has been lost in 7320d. As a new method for the corrosion of steel bar under the multi-dimensional factors, the two-dimensional Copula function has certain practical significance by putting forward some new ideas.

ON SOME APPLICATIONS OF THE ARCHIMEDEAN COPULAS IN THE PROOFS OF THE ALMOST SURE CENTRAL LIMIT THEOREMS FOR CERTAIN ORDER STATISTICS

  • Dudzinski, Marcin;Furmanczyk, Konrad
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.839-874
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    • 2017
  • Our goal is to establish and prove the almost sure central limit theorems for some order statistics $\{M_n^{(k)}\}$, $k=1,2,{\ldots}$, formed by stochastic processes ($X_1,X_2,{\ldots},X_n$), $n{\in}N$, the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima $\{M_n\}$, the second class of the presented results and proofs applies for sequences of the second largest maxima $\{M_n^{(2)}\}$ and the third (and the last) part of our investigations is devoted to the proofs of the almost sure central limit theorems for the k-th largest maxima $\{M_n^{(k)}\}$ in general. The assumptions imposed in the first two of the mentioned groups of claims significantly differ from the conditions used in the last - the most general - case.

Analysis of extreme wind speed and precipitation using copula (코플라함수를 이용한 극단치 강풍과 강수 분석)

  • Kwon, Taeyong;Yoon, Sanghoo
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.4
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    • pp.797-810
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    • 2017
  • The Korean peninsula is exposed to typhoons every year. Typhoons cause huge socioeconomic damage because tropical cyclones tend to occur with strong winds and heavy precipitation. In order to understand the complex dependence structure between strong winds and heavy precipitation, the copula links a set of univariate distributions to a multivariate distribution and has been actively studied in the field of hydrology. In this study, we carried out analysis using data of wind speed and precipitation collected from the weather stations in Busan and Jeju. Log-Normal, Gamma, and Weibull distributions were considered to explain marginal distributions of the copula. Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling test statistics were employed for testing the goodness-of-fit of marginal distribution. Observed pseudo data were calculated through inverse transformation method for establishing the copula. Elliptical, archimedean, and extreme copula were considered to explain the dependence structure between strong winds and heavy precipitation. In selecting the best copula, we employed the Cramer-von-Mises test and cross-validation. In Busan, precipitation according to average wind speed followed t copula and precipitation just as maximum wind speed adopted Clayton copula. In Jeju, precipitation according to maximum wind speed complied Normal copula and average wind speed as stated in precipitation followed Frank copula and maximum wind speed according to precipitation observed Husler-Reiss copula.

Construction of Bivariate Probability Distribution with Nonstationary GEV/Gumbel Marginal Distributions for Rainfall Data (비정상성 GEV/Gumbel 주변분포를 이용한 강우자료 이변량 확률분포형 구축)

  • Joo, Kyungwon;Choi, Soyung;Kim, Hanbeen;Heo, Jun-Haeng
    • Proceedings of the Korea Water Resources Association Conference
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    • 2016.05a
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    • pp.41-41
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    • 2016
  • 최근 다변량 확률모형을 이용한 빈도해석이 수문자료 등에 적용되면서 다양하게 연구되고 있으며 다변량 확률모형 중 copula 모형은 주변분포형에 대한 제약이 없어 여러 분야에 걸쳐 활발히 연구되고 있다. 강우자료는 기존 일변량 빈도해석을 수행하기 위하여 사용하던 block maxima 방법 대신 최소무강우시간(inter event time)을 통하여 강우사상을 추출하여 표본으로 사용한다. 또한 기후변화로 인한 강우량의 변화등에 대응하기 위하여 비정상성 Generalized Extreme Value(GEV)와 Gumbel 등의 확률분포형에 대한 연구도 많은 부분 이루어져 있다. 본 연구에서는, Archimedean copula 모형을 이용하여 이변량 확률모형을 구축하면서 여기에 사용되는 주변분포형에 정상성/비정상성 분포형을 적용하였다. 모형의 매개변수는 inference function for margin 방법을 이용하였으며 주변분포형으로는 정상성/비정상성 GEV, Gumbel 모형을 적용하였다. 결과로 정상성/비정상성 경향을 나타내는 지점을 구분하고 각 지점에 대한 정상성/비정상성 주변분포형을 적용한 이변량 확률분포형을 구하였다.

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Future drought risk assessment under CMIP6 GCMs scenarios

  • Thi, Huong-Nguyen;Kim, Jin-Guk;Fabian, Pamela Sofia;Kang, Dong-Won;Kwon, Hyun-Han
    • 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.

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Storm Surge Analysis using Archimedean Copulas (Copulas에 기반한 우리나라 동해안 폭풍해일 분석)

  • Hwang, Jeongwoo;Kwon, Hyun-Han
    • Proceedings of the Korea Water Resources Association Conference
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    • 2017.05a
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    • pp.421-421
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    • 2017
  • In order to secure the safety of coastal areas from the continuous storm surge in Korea, it is important to predict the wave movement and properties accurately during the storm event. To improve the accuracy of the storm simulation, and to quantify coastal risks from the storm event, the dependencies between wave height, wave period, and storm duration should be analyzed. In this study, therefore, copulas were used to develop multivariate statistical models of sea storms. A case study of the east coast of Korea was conducted, and the dependencies between wave height, wave period, water level, storm duration and storm interarrival time were investigated using Kendall's tau correlation coefficient. As a result of the study, only wave height, wave period, and storm duration appeared to be correlated.

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