• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.243-257
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• 2017

In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.5
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• pp.613-619
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• 2005

Indigenous Yakutian cattle' adaptation to the hardest subarctic conditions makes them a valuable genetic resource for cattle breeding in the Siberian area. Since early last century, crossbreeding between native Yakutian cattle and imported Simmental and Kholmogory breeds has been widely adopted. In this study, variations at 22 polymorphic microsatellite loci in 5 populations of Yakutian, Kholmogory, Simmental, Yakutian-Kholmogory and Yakutian-Simmental cattle were analysed to estimate the genetic contribution of Yakutian cattle to the two hybrid populations. Three statistical approaches were used: the weighted least-squares (WLS) method which considers all allele frequencies; a recently developed implementation of a Markov chain Monte Carlo (MCMC) method called likelihood-based estimation of admixture (LEA); and a model-based Bayesian admixture analysis method (STRUCTURE). At population-level admixture analyses, the estimate based on the LEA was consistent with that obtained by the WLS method. Both methods showed that the genetic contribution of the indigenous Yakutian cattle in Yakutian-Kholmogory was small (9.6% by the LEA and 14.2% by the WLS method). In the Yakutian-Simmental population, the genetic contribution of the indigenous Yakutian cattle was considerably higher (62.8% by the LEA and 56.9% by the WLS method). Individual-level admixture analyses using STRUCTURE proved to be more informative than the multidimensional scaling analysis (MDSA) based on individual-based genetic distances. Of the 9 Yakutian-Simmental animals studied, 8 showed admixed origin, whereas of the 14 studied Yakutian-Kholmogory animals only 2 showed Yakutian ancestry (>5%). The mean posterior distributions of individual admixture coefficient (q) varied greatly among the samples in both hybrid populations. This study revealed a minor existing contribution of the Yakutian cattle in the Yakutian-Kholmogory hybrid population, but in the Yakutian-Simmental hybrid population, a major genetic contribution of the Yakutian cattle was seen. The results reflect the different crossbreeding patterns used in the development of the two hybrid populations. Additionally, molecular evidence for differences among individual admixture proportions was seen in both hybrid populations, resulting from the stochastic process in crossing over generations.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.241-251
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• 2007

The observed spectra from Odaesan earthquake were fitted to a point-source spectral model to evaluate the source spectrum and spatial features of the modelling error. The source spectrum was calculated by removing from the observed spectra the path and site dependent responses (Yun, 2007) that were previously revealed through an inversion process applied to a large accumulated spectral dataset. The stress drop parameter of one-corner Brune's ${\omega}^2$ source model fitted to the estimated source spectrum was well predicted by the scaling relation between magnitude and stress drop developed by Yun et al. (2006). In particular, the estimated spectrum was quite comparable to the two-corner source model that was empirically developed for recent moderate earthquakes occurring around the Korean Peninsula, which indicates that Odaesan earthquake is one of typical moderate earthquakes representative of Korean Peninsula. Other features of the observed spectra from Odaesan earthquake were also evaluated based on the commonly treated random error between the observed data and the estimated point-source spectral model. Radiation pattern of the error according to azimuth angle was found to be similar to the theoretical estimate. It was also observed that the spatial distribution of the errors was correlated with the geological map and the $Q_0$ map which are indicatives of seismic boundaries.

• Journal of Korea Water Resources Association
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• v.42 no.3
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• pp.213-225
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• 2009

A stationary Markov chain model is a stochastic process with the Markov property. Having the Markov property means that, given the present state, future states are independent of the past states. The Markov chain model has been widely used for water resources design as a main tool. A main assumption of the stationary Markov model is that statistical properties remain the same for all times. Hence, the stationary Markov chain model basically can not consider the changes of mean or variance. In this regard, a primary objective of this study is to develop a model which is able to make use of exogenous variables. The regression based link functions are employed to dynamically update model parameters given the exogenous variables, and the model parameters are estimated by canonical correlation analysis. The proposed model is applied to daily rainfall series at Seoul station having 46 years data from 1961 to 2006. The model shows a capability to reproduce daily and seasonal characteristics simultaneously. Therefore, the proposed model can be used as a short or mid-term prediction tool if elaborate GCM forecasts are used as a predictor. Also, the nonstationary Markov chain model can be applied to climate change studies if GCM based climate change scenarios are provided as inputs.

• Journal of Korea Water Resources Association
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• v.45 no.12
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• pp.1321-1330
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• 2012

In this study, the daily inflow at the basin of Chungju dam is predicted using wavelet-artificial neural network for nonlinear model. Time series generally consists of a linear combination of trend, periodicity and stochastic component. However, when framing time series model through these data, trend and periodicity component have to be removed. Wavelet transform which is denoising technique is applied to remove nonlinear dynamic noise such as trend and periodicity included in hydrometeorological data and simple noise that arises in the measurement process. The wavelet-artificial neural network (WANN) using data applied wavelet transform as input variable and the artificial neural network (ANN) using only raw data are compared. As a results, coefficient of determination and the slope through linear regression show that WANN is higher than ANN by 0.031 and 0.0115 respectively. And RMSE and RRMSE of WANN are smaller than those of ANN by 37.388 and 0.099 respectively. Therefore, WANN model applied in this study shows more accurate results than ANN and application of denoising technique through wavelet transforms is expected that more accurate predictions than the use of raw data with noise.

• Progress in Medical Physics
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• v.14 no.4
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• pp.211-217
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• 2003

The Principal component analysis (PCA) is a well-known data analysis method that is useful in linear feature extraction and data compression. The PCA is a linear transformation that applies an orthogonal rotation to the original data, so as to maximize the retained variance. PCA is a classical technique for obtaining an optimal overall mapping of linearly dependent patterns of correlation between variables (e.g. neurons). PCA provides, in the mean-squared error sense, an optimal linear mapping of the signals which are spread across a group of variables. These signals are concentrated into the first few components, while the noise, i.e. variance which is uncorrelated across variables, is sequestered in the remaining components. PCA has been used extensively to resolve temporal patterns in neurophysiological recordings. Because the retinal signal is stochastic process, PCA can be used to identify the retinal spikes. With excised rabbit eye, retina was isolated. A piece of retina was attached with the ganglion cell side to the surface of the microelectrode array (MEA). The MEA consisted of glass plate with 60 substrate integrated and insulated golden connection lanes terminating in an 8${\times}$8 array (spacing 200 $\mu$m, electrode diameter 30 $\mu$m) in the center of the plate. The MEA 60 system was used for the recording of retinal ganglion cell activity. The action potentials of each channel were sorted by off­line analysis tool. Spikes were detected with a threshold criterion and sorted according to their principal component composition. The first (PC1) and second principal component values (PC2) were calculated using all the waveforms of the each channel and all n time points in the waveform, where several clusters could be separated clearly in two dimension. We verified that PCA-based waveform detection was effective as an initial approach for spike sorting method.

• Korean Journal of Agricultural and Forest Meteorology
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• v.14 no.3
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• pp.124-131
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• 2012

This study was carried out to evaluate a possible change in freeze risk for 'Changhowon Hwangdo' peach buds in three major peach growing areas under the future climate projected by RCP8.5 emission scenario. Mean values of the monthly temperature data for the present decade (2000s) and the future decades (2020s, 2050s, 2080s) were extracted for farm lands in Icheon, Chungju, and Yeongcheon-Gyeongsan region at 1km resolution and 30 sets of daily temperature data were generated randomly by a stochastic process for each decade. The daily data were used to calculate a thermal time-based dormancy depth index which is closely related to the cold tolerance of peach buds. Combined with daily minimum temperature, dormancy depth can be used to estimate the potential risk of freezing damage on peach buds. When the freeze risk was calculated daily for the winter period (from 1 November to 15 March) in the present decade, Icheon and Chungju regions had high values across the whole period, but Yeongcheon-Gyeongsan regions had low values from mid-December to the end of January. In the future decades, the frequency of freezing damage would be reduced in all 3 regions and the reduction rate could be as high as 75 to 90% by 2080's. However, the severe class risk (over 80% damage) will not disappear in the future and most occurrences will be limited to December to early January according to the calculation. This phenomenon might be explained by shortened cold hardiness period caused by winter warming as well as sudden cold waves resulting from the higher inter-annual climate variability projected by the RCP8.5 scenario.

• Proceedings of the Korea Society for Simulation Conference
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• 1996.05a
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• pp.1-3
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• 1996

시뮬레이션 기법을 이용한 시스템의 분석에 있어서 실험의 자동화는 현재 많은 연구와 개발이 진행 중인 분야이다. 컴퓨터와 정보통신 시스템에 대한 시뮬레이션의 예를 들어 보면, 수많은 모델을 대한 시뮬레이션을 수행할 경우 자동화된 실험의 제어가 요구되고 있다. 시뮬레이션 수행회수, 수행길이, 데이터 수집방법 등과 관련하여 시뮬레이션 실험방법이 자동화가 되지 않으면, 시뮬레이션 실험에 필요한 시간과 인적 자원이 상당히 커지게 되며 출력데이터에 대한 분석에 있어서도 어려움이 따르게 된다. 시뮬레이션 실험방법을 자동화하면서 효율적인 시뮬레이션 출력분석을 위해서는 시뮬레이션을 수행하는 경우에 항상 발생하는 초기편의 (initial bias)를 제거하는 문제가 선결되어야 한다. 시뮬레이션 출력분석에 사용되는 데이터들이 초기편의를 반영하지 않는 안정상태에서 수집된 것이어야만 실제 시스템에 대한 올바른 해석이 가능하다. 실제로 시뮬레이션 출력분석과 관련하여 가장 중요하면서도 어려운 문제는 시뮬레이션의 출력데이터가 이루는 추계적 과정 (stochastic process)의 안정상태 평균과 이 평균에 대한 신뢰구간(confidence interval: c. i.)을 구하는 것이다. 한 신뢰구간에 포함되어 있는 정보는 의사결정자에게 얼마나 정확하게 평균을 추정할 구 있는지 알려 준다. 그러나, 신뢰구간을 구성하는 일은 하나의 시뮬레이션으로부터 얻어진 출력데이터가 일반적으로 비정체상태(nonstationary)이고 자동상관(autocorrelated)되어 있기 때문에, 전통적인 통계적인 기법을 직접적으로 이용할 수 없다. 이러한 문제를 해결하기 위해 시뮬레이션 출력데이터 분석기법이 사용된다.본 논문에서는 초기편의를 제거하기 위해서 필요한 출력데이터의 제거시점을 찾는 새로운 기법으로, 유클리드 거리(Euclidean distance: ED)를 이용한 방법과 현재 패턴 분류(pattern classification) 문제에 널리 사용 중인 역전파 신경망(backpropagation neural networks: BNN) 알고리듬을 이용하는 방법을 제시한다. 이 기법들은 대다수의 기존의 기법과는 달리 시험수행(pilot run)이 필요 없으며, 시뮬레이션의 단일수행(single run) 중에 제거시점을 결정할 수 있다. 제거시점과 관련된 기존 연구는 다음과 같다. 콘웨이방법은 현재의 데이터가 이후 데이터의 최대값이나 최소값이 아니면 이 데이터를 제거시점으로 결정하는데, 알고기듬 구조상 온라인으로 제거시점 결정이 불가능하다. 콘웨이방법이 알고리듬의 성격상 온라인이 불가능한 반면, 수정콘웨이방법 (Modified Conway Rule: MCR)은 현재의 데이터가 이전 데이터와 비교했을 때 최대값이나 최소값이 아닌 경우 현재의 데이터를 제거시점으로 결정하기 때문에 온라인이 가능하다. 평균교차방법(Crossings-of-the-Mean Rule: CMR)은 누적평균을 이용하면서 이 평균을 중심으로 관측치가 위에서 아래로, 또는 아래서 위로 교차하는 회수로 결정한다. 이 기법을 사용하려면 교차회수를 결정해야 하는데, 일반적으로 결정된 교차회수가 시스템에 상관없이 일반적으로 적용가능하지 않다는 문제점이 있다. 누적평균방법(Cumulative-Mean Rule: CMR2)은 여러 번의 시험수행을 통해서 얻어진 출력데이터에 대한 총누적평균(grand cumulative mean)을 그래프로 그린 다음, 안정상태인 점을 육안으로 결정한다. 이 방법은 여러 번의 시뮬레이션을 수행에서 얻어진 데이터들의 평균들에 대한 누적평균을 사용하기 매문에 온라인 제거시점 결정이 불가능하며, 작업자가 그래프를 보고 임의로 결정해야 하는 단점이 있다. Welch방법(Welch's Method: WM)은 브라운 브리지(Brownian bridge) 통계량()을 사용하는데, n이 무한에 가까워질 때, 이 브라운 브리지 분포(Brownian bridge distribution)에 수렴하는 성질을 이용한다. 시뮬레이션 출력데이터를 가지고 배치를 구성한 후 하나의 배치를 표본으로 사용한다. 이 기법은 알고리듬이 복잡하고, 값을 추정해야 하는 단점이 있다. Law-Kelton방법(Law-Kelton's Method: LKM)은 회귀 (regression)이론에 기초하는데, 시뮬레이션이 종료된 후 누적평균데이터에 대해서 회귀직선을 적합(fitting)시킨다. 회귀직선의 기울기가 0이라는 귀무가설이 채택되면 그 시점을 제거시점으로 결정한다. 일단 시뮬레이션이 종료된 다음, 데이터가 모아진 순서의 반대 순서로 데이터를 이용하기 때문에 온라인이 불가능하다. Welch절차(Welch's Procedure: WP)는 5회이상의 시뮬레이션수행을 통해 수집한 데이터의 이동평균을 이용해서 시각적으로 제거시점을 결정해야 하며, 반복제거방법을 사용해야 하기 때문에 온라인 제거시점의 결정이 불가능하다. 또한, 한번에 이동할 데이터의 크기(window size)를 결정해야 한다. 지금까지 알아 본 것처럼, 기존의 방법들은 시뮬레이션의 단일 수행 중의 온라인 제거시점 결정의 관점에서는 미약한 면이 있다. 또한, 현재의 시뮬레이션 상용소프트웨어는 작업자로 하여금 제거시점을 임의로 결정하도록 하기 때문에, 실험중인 시스템에 대해서 정확하고도 정량적으로 제거시점을 결정할 수 없게 되어 있다. 사용자가 임의로 제거시점을 결정하게 되면, 초기편의 문제를 효과적으로 해결하기 어려울 뿐만 아니라, 필요 이상으로 너무 많은 양을 제거하거나 초기편의를 해결하지 못할 만큼 너무 적은 양을 제거할 가능성이 커지게 된다. 또한, 기존의 방법들의 대부분은 제거시점을 찾기 위해서 시험수행이 필요하다. 즉, 안정상태 시점만을 찾기 위한 시뮬레이션 수행이 필요하며, 이렇게 사용된 시뮬레이션은 출력분석에 사용되지 않기 때문에 시간적인 손실이 크게 된다.