• Title/Summary/Keyword: 극단값이론

### Extreme Quantile Estimation of Losses in KRW/USD Exchange Rate (원/달러 환율 투자 손실률에 대한 극단분위수 추정)

• Yun, Seok-Hoon
• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.803-812
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• 2009
• The application of extreme value theory to financial data is a fairly recent innovation. The classical annual maximum method is to fit the generalized extreme value distribution to the annual maxima of a data series. An alterative modern method, the so-called threshold method, is to fit the generalized Pareto distribution to the excesses over a high threshold from the data series. A more substantial variant is to take the point-process viewpoint of high-level exceedances. That is, the exceedance times and excess values of a high threshold are viewed as a two-dimensional point process whose limiting form is a non-homogeneous Poisson process. In this paper, we apply the two-dimensional non-homogeneous Poisson process model to daily losses, daily negative log-returns, in the data series of KBW/USD exchange rate, collected from January 4th, 1982 until December 31 st, 2008. The main question is how to estimate extreme quantiles of losses such as the 10-year or 50-year return level.

### Estimation of VaR Using Extreme Losses, and Back-Testing: Case Study (극단 손실값들을 이용한 VaR의 추정과 사후검정: 사례분석)

• Seo, Sung-Hyo;Kim, Sung-Gon
• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.219-234
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• 2010
• In index investing according to KOSPI, we estimate Value at Risk(VaR) from the extreme losses of the daily returns which are obtained from KOSPI. To this end, we apply Block Maxima(BM) model which is one of the useful models in the extreme value theory. We also estimate the extremal index to consider the dependency in the occurrence of extreme losses. From the back-testing based on the failure rate method, we can see that the model is adaptable for the VaR estimation. We also compare this model with the GARCH model which is commonly used for the VaR estimation. Back-testing says that there is no meaningful difference between the two models if we assume that the conditional returns follow the t-distribution. However, the estimated VaR based on GARCH model is sensitive to the extreme losses occurred near the epoch of estimation, while that on BM model is not. Thus, estimating the VaR based on GARCH model is preferred for the short-term prediction. However, for the long-term prediction, BM model is better.

### Analysis of Extreme Values of Daily Percentage Increases and Decreases in Crude Oil Spot Prices (국제현물원유가의 일일 상승 및 하락율의 극단값 분석)

• Yun, Seok-Hoon
• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.835-844
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• 2010
• Tools for statistical analysis of extreme values include the classical annual maximum method, the modern threshold method and variants improving the second one. While the annual maximum method is to t th generalized extreme value distribution to the annual maxima of a time series, the threshold method is to the generalized Pareto distribution to the excesses over a high threshold from the series. In this paper we deal with the Poisson-GPD method, a variant of the threshold method with a further assumption that the total number of exceedances follows the Poisson distribution, and apply it to the daily percentage increases and decreases computed from the spot prices of West Texas Intermediate, which were collected from January 4th, 1988 until December 31st, 2009. According to this analysis, the distribution of daily percentage increases as well as decreases turns out to have a heavy tail, unlike the normal distribution, which coincides well with the general phenomenon appearing in the analysis of lots of nowaday nancial data.

### Prediction of recent earthquake magnitudes of Gyeongju and Pohang using historical earthquake data of the Chosun Dynasty (조선시대 역사지진자료를 이용한 경주와 포항의 최근 지진규모 예측)

• Kim, Jun Cheol;Kwon, Sookhee;Jang, Dae-Heung;Rhee, Kun Woo;Kim, Young-Seog;Ha, Il Do
• The Korean Journal of Applied Statistics
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• v.35 no.1
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• pp.119-129
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• 2022
• In this paper, we predict the earthquake magnitudes which were recently occurred in Gyeongju and Pohang, using statistical methods based on historical data. For this purpose, we use the five-year block maximum data of 1392~1771 period, which has a relatively high annual density, among the historical earthquake magnitude data of the Chosun Dynasty. Then, we present the prediction and analysis of earthquake magnitudes for the return level over return period in the Chosun Dynasty using the extreme value theory based on the distribution of generalized extreme values (GEV). We use maximum likelihood estimation (MLE) and L-moments estimation for parameters of GEV distribution. In particular, this study also demonstrates via the goodness-of-fit tests that the GEV distribution can be an appropriate analytical model for these historical earthquake magnitude data.

### A Bayesian Extreme Value Analysis of KOSPI Data (코스피 지수 자료의 베이지안 극단값 분석)

• Yun, Seok-Hoon
• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011
• This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.