• 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.

• 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.

• 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.

• 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.

• 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.

• Knowledge Management Research
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• v.22 no.2
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• pp.247-268
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• 2021

Investors mainly use PER and PBR among financial ratios for valuation and investment decision-making. I conduct an analysis of two basic financial ratios from a statistical perspective. Financial ratios contain key accounting numbers which reflect firm fundamentals and are useful for valuation or risk analysis such as enterprise credit evaluation and default prediction. The distribution of financial data tends to be extremely heavy-tailed, and PER and PBR show exceedingly high level of kurtosis and their extreme cases often contain significant information on financial risk. In this respect, Extreme Value Theory is required to fit its right tail more precisely. I introduce not only GPD but exGPD. GPD is conventionally preferred model in Extreme Value Theory and exGPD is log-transformed distribution of GPD. exGPD has recently proposed as an alternative of GPD(Lee and Kim, 2019). First, I conduct a simulation for comparing performances of the two distributions using the goodness of fit measures and the estimation of 90-99% percentiles. I also conduct an empirical analysis of Information Technology firms in Korea. Finally, exGPD shows better performance especially for PBR, suggesting that exGPD could be an alternative for GPD for the analysis of financial ratios.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• Journal of Environmental Policy
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• v.13 no.1
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• pp.69-93
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• 2014

The aim of this research was to develop a climate change vulnerability index at the district level (Si, Gun, Gu) with respect to the health care sector in Korea. The climate change vulnerability index was esimated based on the four major causes of climate-related illnesses : vector, flood, heat waves, and air pollution/allergies. The vulnerability assessment framework consists of six layers, all of which are based on the IPCC vulnerability concepts (exposure, sensitivity, and adaptive capacity) and the pathway of direct and indirect impacts of climate change modulators on health. We collected proxy variables based on the conceptual framework of climate change vulnerability. Data were standardized using the min-max normalization method. We applied the analytic hierarchy process (AHP) weight and aggregated the variables using the non-compensatory multi-criteria approach. To verify the index, sensitivity analysis was conducted by using another aggregation method (geometric transformation method, which was applied to the index of multiple deprivation in the UK) and weight, calculated by the Budget Allocation method. The results showed that it would be possible to identify the vulnerable areas by applying the developed climate change vulnerability assessment index. The climate change vulnerability index could then be used as a valuable tool in setting climate change adaptation policies in the health care sector.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.33 no.5
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• pp.448-454
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• 2000

This study was to examine the physicochemical characteristics of coagulation reaction between ignited oyster shell powder (IOSP) and red tide organisms (RTO), and its feasibility, in developing a technology for the removal of RTO bloom in coastal sea,IOSP was made from oyster shell and its physicochemical characteristics were examined for particle size distribution, surface characteristic by scanning electron microscope, zeta potential, and alkalinity and pH variations in sea water. Two kinds of RTO that were used in this study, Cylindrotheca closterium and Skeletonema costatum, were sampled in Masan bay and were cultured in laboratory. Coagulation experiments were conducted using various c(Incentrations of IOSP, RTO, and a jar tester. The supernatant and RTO culture solution were analyzed for pH, alkalinity, RTO cell number, IOSP showed positive zeta potentials of $11.1{\~}50.1\;mV\;at\;pH\;6.2{\~}12.7$, A positive zeta potential of IOSP slowly decreased with decreasing pNa 4,0 to 2,0. When pNa reached zero, the zeta potential approached zero, When a pMg value was decreased, the positive zeta potential of IOSP increased until pMg 3.0 and decreased below pMg 3.0. IOSP showed 4.8 mV of positive zeta potential while RTO showed -9.2 mV of negative zeta potential in sea water. A positive-negative EDL (electrical double-layer) interaction occurred between $Mg(OH)_2$ adsorption layer of IOSP and RTO in sea water so that EDL attractive force always worked between them. Hence, their coagulation reaction occurred at primary minimum on which an extreme attractive force acted because of charge neutralization by $Mg(OH)_2$ adsorption layer of IOSP. As a result, the coagulation reaction was rapidly processed and was irreversible according to DLVO (Deriaguin-Landau-Verwey-Overbeek) theory. Removal rates of RTO were exponentially increased with increasing both IOSP concentration and G-value. The removal rates were steeply increased until 50 mg/l of IOSP and reached $100{\%}\;at\;400\;mg/l$ of IOSP. Removal rates of RTO were $70.5,\;70.5,\;81.7,\;85.3{\%}$ for G-values of $1,\;6,\;29,\;139\;sec^(-1)$at IOSP 100 mg/l, respectively. This indicated that mixing (i.e., collision among particles) was very important for a coagulation reaction.