• The Korean Journal of Applied Statistics
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• v.33 no.3
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• pp.297-308
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• 2020

We focus on the functional autoregressive conditional heteroscedasticity (fARCH) modelling to analyze intraday volatilities based on high frequency financial time series. Multivariate volatility models are investigated to approximate fARCH(1). A formula of multi-step ahead volatilities for fARCH(1) model is derived. As an application, in implementing fARCH(1), a choice of appropriate time interval for the intraday return is discussed. High frequency KOSPI data analysis is conducted to illustrate the main contributions of the article.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.667-675
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• 2018

When a financial time series consists of daily (closing) returns, traditional volatility models such as autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) are useful to figure out daily volatilities. With high frequency returns in a day, one may adopt various multivariate GARCH techniques (MGARCH) (Tsay, Multivariate Time Series Analysis With R and Financial Application, John Wiley, 2014) to obtain intraday volatilities as long as the high frequency is moderate. When it comes to the ultra high frequency (UHF) case (e.g., one minute prices are available everyday), a new model needs to be developed to suit UHF time series in order to figure out continuous time intraday-volatilities. Aue et al. (Journal of Time Series Analysis, 38, 3-21; 2017) proposed functional GARCH (fGARCH) to analyze functional volatilities based on UHF data. This article introduces fGARCH to the readers and illustrates how to estimate fGARCH equations using UHF data of KOSPI and Hyundai motor company.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.885-893
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• 2015

It is important to improve the forecasting accuracy of one-year-ahead seasonal factors in order to produce seasonally adjusted series of the following year. In this paper, seasonal factors of 8 monthly Korean economic time series are examined and forecast based on the functional principal component regression. One-year-ahead forecasts of seasonal factors from the functional principal component regression are compared with other forecasting methods based on mean absolute error (MAE) and mean absolute percentage error (MAPE). Forecasting seasonal factors via the functional principal component regression performs better than other comparable methods.

• Journal of Intelligence and Information Systems
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• v.23 no.2
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• pp.107-122
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• 2017

Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.313-313
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• 2020

여름철 발생하는 집중호우는 해안지역 및 하천유역의 저지대에 상습적인 침수를 유발하며, 도시지역은 높은 불투수율로 인해 추가적인 침수 피해가 발생하는 경우가 많다. 본 연구에서는 폭함수를 통해 하천망의 공간적인 특성을 함수형태로 나타내어 유역의 수문분석에 이용하는 폭함수 단위도법(WFIUH, Width Function Instantaneous Unit Hydrograph)을 소개하고, 적용성을 검토하기 위하여 실제 유역 및 강우 사상에 적용해보았다. WFIUH는 기존의 집중형 수문모형과 다르게 매개변수를 물리적으로 결정할 수 있으며, 유역특성과 시공간적 변동성을 수문곡선 산정에 반영할 수 있는 장점이 있다. WFIUH의 적용성을 검토하기 위하여 2003년 한반도에 심각한 침수피해를 입힌 태풍 매미로 인해 발생한 강우사상과 그로인해 큰 피해가 있었던 마산 지역의 남천, 삼호천 일부 유역을 대상으로 강우-유출 분석을 실시하였다. 분석결과 범용 수문모형인 HEC-HMS와 비교 시 유사한 결과를 보이며, 실제 관측치와도 유사한 결과를 보이는 것으로 나타났다. 또한 강우의 이동을 반영하여 강우의 이동이 수문곡선과 첨두유량에 미치는 영향을 비교분석 하였다.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.218-227
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• 1992

전통적인 비김분석이 기업의 이익계획이나 의사결정에 간단하면서도 유용한 방법이긴 하지만, 소득함수나 비용함수를 선형함수로 가정함으로써 현실성이 결여된 점과 기업에서 경제성평가의 대상이 되는 투자대안들이 다기간이거나 장기인 사업들이 대부분인데도 단기간의 분석으로 제한된 점이 이 분석의 유용성을 크게 떨어뜨리고 있다. 이 논문은 장기적인 사업에서 일반적인 비용이나 수익의 변동성을 고려하여 전통적인 비김분석을 다기간의 사업에도 적용할 수 있도록 한다.

• Journal of the Korea Society for Simulation
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• v.20 no.2
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• pp.1-10
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• 2011

In queueing network analysis, arrival processes are usually modeled as renewal processes by matching mean and variance. The renewal approximation simplifies the analysis and provides reasonably good estimate for the performance measures of the queueing systems under moderate conditions. However, high variability in arrival process or in service process requires more sophisticated approximation procedures for the variability parameter of departure/arrival processes. In this paper, we propose an heuristic approach to refine Whitt's variability function with the k-interval squared coefficient of variation also known as the index of dispersion for intervals(IDI). Regression analysis is used to establish an empirical relationships between the IDI of arrival process and the IDI of departure process of a queueing system.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.983-991
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• 2017

High frequency time series are now prevalent in financial data. However, models need to be further developed to suit high frequency time series that account for intraday volatilities since traditional volatility models such as ARCH and GARCH are concerned only with daily volatilities. Due to $H{\ddot{o}}rmann$ et al. (2013), functional ARCH abbreviated as fARCH is proposed to analyze intraday volatilities based on high frequency time series. This article introduces fARCH to readers that illustrate intraday volatility configuration on the KOSPI and the Hyundai motor company based on the data with one minute high frequency.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.171-171
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• 2017

강우의 시간분포는 다양한 시간규모에 걸쳐 프랙털 또는 멀티프랙털 특성을 가지고 있음이 알려졌다. 기존의 연구는 주로 시간단위 이상의 프랙털 특성에 관한 것이었다. 실제로 극한 홍수를 가져오는 집중호우는 짧은 시간 규모에서 발생함에도, 이것에 대해서는 관측 자료가 제한되어 극소수의 실험적 연구만 가능했다. 본 연구에서는 기상청에서 제공한 고해상도(1분 단위) ASOS(Automated Synoptic Observation System) 자료를 이용하여, 강우 사상 안에서의 프랙털 특성을 분석해보았다. 대부분의 사상에서 단일 멱함수보다는 2개의 멱함수로 나누어지는 것이 밝혀졌으며, 나뉘는 시간 규모(T*)는 $3{\times}10$ 분으로 파악되었다. 이 시간 규모는 한 단위의 집중호우를 가져올 수 있는 구름크기의 물리적 상한과 관련이 있는 것으로 보인다. T*보다 작은 시간 규모에서의 멱함수 지수는 그 이후의 값보다 대체로 작은 것으로 나타났다. 이는 호우가 집중되는 기간의 변동성이, 강수가 물리적 한계에 도달한 이후보다 훨씬 작기 때문으로 보인다. 구체적인 멱함수의 지수는 강수의 발생과정과도 관련이 있을 것으로 추정된다.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.431-445
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• 2006

In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.