A Stochastic Generation of Snowfall Data and Probabilistic Snowfall Using Multi-site Markov Chain Model

Se Jin Jeung,Woo Suk Han,Byung Sik Kim 위기관리 이론과 실천 2017 Crisisonomy Vol.13 No.12

본 논문에서는 강원도 주요 기상관측소의 과거 강설자료를 대상으로 자료를 확충하기 위해 Multi site Markov Chain 모형을 이용하여 자료를 추계학적으로 모의 발생하였다. 강원도지역은 태백산맥을 중심으로 영서와 영동으로 나누어져 확연히 구별되는 기상특성을 나타내기 때문에 이를 고려할 수 있는 Multi site 추계학적 모의발생기법이 필요하다. 그러므로 지역의 특성을 고려 할 수 있는Multi site의 공간적 상관성을 반영할 수 있는 추계학적 모의발생기법이 필요하다. 본 논문에서는 먼저 관측 강설량 자료를 이용하여 ACF분석을 통해 자료의 무작위성을 파악하였다. 그리고 다지점 Markov Chain Model을 이용하여 강원도지역(강릉, 속초, 대관령, 춘천, 철원, 원주)지역의 관측자료와 같은 기간의 모의자료를 발생시켰으며, 통계적 분석을 통해 모의 강설량자료를 검토하였다. 검토결과를 근거로 하여 100년의 자료를 모의 발생시켜 확률강설량을 산정하고자 하였다. 그 결과 영서와 영동지역의 확연히 구분되는 기후특성을 나타낼 수 있는 다지점 Markov Chain 모형을 구성하였으며 이를 통해 설계 강설량 산정에 적합함을 확인 할 수 있었다. This paper sought to generate the stochastic simulative snowfall data through a multi-site Markov Chain model, which was constructed from the historical snowfall data collected at major meteorological stations in Gangwon Province in Korea. The need for a multi-site stochastic simulative generation technique was mandated by such a noticeable difference in the weather characteristics between the two regions in Gangwon Province, the Yeongdong and Yongseo regions, divided by the Taebaek Mountain Range. A stochastic simulative generation technique can take into consideration a spatial association of multiple sites. This paper used the Mann–Kendall and autocorrelation function analyses to identify the predisposition and randomness of the data. Then, a multi-site Markov Chain model was used to simulate the data within the period covered by the existing records in Gangwon Province and the simulated data were compared to the actual historical data using a statistical analysis. Based on the comparison, the probabilistic snowfall forecasts were generated for the next 100 years. The multi-site Markov Chain model developed in this paper took into account a sharp distinction between the Yeongdong and Yongseo regions, and was found to be suitable for simulating the snowfall data for architectural purposes.

Markov-Chain Monte Carlo 기법을 이용한 준 분포형 수문모형의 매개변수 및 모형 불확실성 분석

최정현 ( Choi Jeonghyeon ),장수형 ( Jang Suhyung ),김상단 ( Kim Sangdan ) 한국물환경학회(구 한국수질보전학회) 2020 한국물환경학회지 Vol.36 No.5

Hydrological models are based on a combination of parameters that describe the hydrological characteristics and processes within a watershed. For this reason, the model performance and accuracy are highly dependent on the parameters. However, model uncertainties caused by parameters with stochastic characteristics need to be considered. As a follow-up to the study conducted by Choi et al (2020), who developed a relatively simple semi-distributed hydrological model, we propose a tool to estimate the posterior distribution of model parameters using the Metropolis-Hastings algorithm, a type of Markov-Chain Monte Carlo technique, and analyze the uncertainty of model parameters and simulated stream flow. In addition, the uncertainty caused by the parameters of each version is investigated using the lumped and semi-distributed versions of the applied model to the Hapcheon Dam watershed. The results suggest that the uncertainty of the semi-distributed model parameters was relatively higher than that of the lumped model parameters because the spatial variability of input data such as geomorphological and hydrometeorological parameters was inherent to the posterior distribution of the semi-distributed model parameters. Meanwhile, no significant difference existed between the two models in terms of uncertainty of the simulation outputs. The statistical goodness of fit of the simulated stream flows against the observed stream flows showed satisfactory reliability in both the semi-distributed and the lumped models, but the seasonality of the stream flow was reproduced relatively better by the distributed model.

확률적 변동성을 가진 은닉마르코프 모형을 통한 비트코인 가격의 변동성 추정

강태현,황범석 한국통계학회 2023 응용통계연구 Vol.36 No.1

The stochastic volatility (SV) model is one of the main methods of modeling time-varying volatility. In particular, SV model is actively used in estimation and prediction of financial market volatility and option pricing. This paper attempts to model the time-varying volatility of the bitcoin market price using SV model. Hidden Markov model (HMM) is combined with the SV model to capture characteristics of regime switching of the market. The HMM is useful for recognizing patterns of time series to divide the regime of market volatility. This study estimated the volatility of bitcoin by using data from Upbit, a cryptocurrency trading site, and analyzed it by dividing the volatility regime of the market to improve the performance of the SV model. The MCMC technique is used to estimate the parameters of the SV model, and the performance of the model is verified through evaluation criteria such as MAPE and MSE. Stochastic volatility (SV) 모형은 시변 변동성을 모델링하는 주요한 수단 중 하나이며, 특히 금융시장 변동성의 추정 및 예측, 옵션의 가격 결정 등의 분야에서 활발하게 사용되고 있다. 본 논문은 SV 모형을 활용하여 비트코인 시장의 시변 변동성을 모델링하고자 한다. 시장의 변동성은 국면 전환의 특성을 갖고 있다고 알려져 있으며, 시장의 변동 국면을 나누기 위해 시계열의 패턴을 인식하는 작업에 유용한 hidden Markov model (HMM)을 결합하여 사용하고자 한다. 본 연구는 암호화폐 거래 사이트 업비트의 비트코인 데이터를 활용하여 비트코인의 변동성 모형을 추정하였으며 SV 모형의 성능을 높이기 위하여 시장의 변동 국면을 나누어 분석을 진행하였다. MCMC 기법이 SV 모델의 모수를 추정하는 데 사용되며 MAPE, MSE 등의 평가 기준을 통하여 모델의 성능을 확인하고자 한다.

Using predicted cumulative probability distribution of hidden Markov Model for European option pricing

Youngchul Han,Jungwoo Lee,Jeong-Hoon Kim 한국재무학회 2013 한국재무학회 학술대회 Vol.2013 No.11

In this paper, we proposed model for European option pricing using predicted cumulative probability distribution of hidden Markov Model. The Black-Scholes model is based on Gaussian distribution and the model's main shortfall is fat-tail problem. Because of fat-tail problem, the implied volatility surface is shaped skew, smirk or other forms. To correct model's drawback, we extract predicted cumulative distribution using hidden Markov Model and simulate the underlying price paths using Monte Carlo method. In the results, our model re ect current implied volatility surface suciently.

Non-Cooperative Game Joint Hidden Markov Model for Spectrum Allocation in Cognitive Radio Networks

Yan Jiao 한국인터넷방송통신학회 2018 Journal of Advanced Smart Convergence Vol.7 No.1

Spectrum allocation is a key operation in cognitive radio networks (CRNs), where secondary users (SUs) are usually selfish – to achieve itself utility maximization. In view of this context, much prior lit literature proposed spectrum allocation base on non-cooperative game models. However, the most of them proposed non-cooperative game models based on complete information of CRNs. In practical, primary users (PUs) in a dynamic wireless environment with noise uncertainty, shadowing, and fading is difficult to attain a complete information about them. In this paper, we propose a non-cooperative game joint hidden markov model scheme for spectrum allocation in CRNs. Firstly, we propose a new hidden markov model for SUs to predict the sensing results of competitors. Then, we introduce the proposed hidden markov model into the non-cooperative game. That is, it predicts the sensing results of competitors before the non-cooperative game. The simulation results show that the proposed scheme improves the energy efficiency of networks and utilization of SUs.

비정상 마르코프 연쇄모형에 의한 부산권 인구분포 예측 연구

김경수 대한국토·도시계획학회 2004 國土計劃 Vol.39 No.4

The study is pursued by the analysis of the move-in and move-out data of Busan's administrative districts, which shows that the change of address is a primary factor dominating the change in population distribution. The analysis adopts the Markov chain model, which is one of the most popular methods for population analysis home and abroad. In order to overcome the limit of the stationary Markov chain model that takes into account only the size of population of the place to move in and out, this study set up a non-stationary model by adding new factors such as the distance between the move-in and the move-out place, increase of housing in the move-in area, and the areal preference index. In the analysis of this model the correlation coefficient of the predicted result is from 0.01 to 0.999, which means that this non-stationary model has higher predictability than the stationary model.키 워 드 비정상 마르코프 연쇄모형, 부산권, 인구분포 예측Keywords Non- Stationary Markov Chain Model, Busan Metropolitan Areas, Prediction of Population Distribution

HMM근사를 이용한 빠르고 효율적인 확률코퓰러모형 최우추정

김태형,박정민 한국금융학회 2023 금융연구 Vol.37 No.3

The association or interdependence between asset returns plays a crucial role in financial and managerial theories and practices, such as asset pricing, portfolio construction, risk management, and derivative pricing. The Pearson correlation coefficient, a representative measure of linear interdependence under the elliptical distribution, has been widely used in theory and practice. However, after the US financial crisis of 2008, various limitations of the correlation coefficient as a measure of interdependence have been exposed. Since Patton (2006a), The copula function, which has been actively researched in the field of financial econometrics in order to overcome the limitations of the linear measure of interdependence, that is, correlation coefficient. Unlike the linear measure of interdependence, the copula function can capture nonlinear, asymmetric, and tail dependence. Various study results have shown that the interdependence between asset returns, such as time-varying conditional variance and asymmetric behavior, varies over time and with different degrees of asymmetry. To capture such asymmetric time-varying interdependence, various conditional dynamic copula models have been proposed, such as Patton's (2006a) Copula-GARCH model, Creal et al's (2011, 2013) GAS model (generalized autoregressive score models), and Hafner and Manner's (2012) stochastic copula model. In the case of the Copula-GARCH and GAS models, similar to the GARCH models, the dynamic equation of association parameter is a deterministic function of parameters and returns of previous periods. In contrast, the stochastic copula model is a nonlinear, non-normal state space model in which the association parameter is a nonlinear function of a latent state variable as in the stochastic volatility model. As in the maximum likelihood estimation of the volatility model, it is necessary to integrate out unobserved state variables in order to perform maximum likelihood estimation of the Copula model and it is well known that integrating-out of such state variables can be challenging. Efficient Importance Sampling (EIS), proposed by Liesenfeld and Richard (2003) and Richard and Zhang (2007), was used by Hafner and Manner (2012) to obtain the likelihood function required for estimating the stochastic volatility model. Almeida and Czado (2012), Kim and Park (2018), and Kreuzer and Czado (2020), among others, have proposed MCMC algorithms for Bayesian inference on stochastic copula models. Although those simulation-based estimation methods are efficient, they have the disadvantage of taking a considerable amount of time for model estimation. For a small number of state variables, it is possible to calculate the likelihood function of a general discrete-time continuous state-space model using numerical integration. Kitagawa (1987) proposed a method of numerical integration by partitioning continuous state variables for the estimation of discrete-time non-normal state-space models. Similarly, Fridman and Harris (1998), Bartolucci and De Luca (2001, 2003), and others have proposed methods of approximating the likelihood function of stochastic volatility models using quadrature methods. The maximum likelihood estimation using the likelihood function obtained by numerical integration may take a considerable amount of time for numerical integration as the number of observed data and the dimension of the state variable increases due to the curse of dimensionality. Therefore, numerical integration-based maximum likelihood estimation is not commonly used for the estimation of stochastic volatility models. Langrock et al. (2012) used the HMM (hidden Markov model) approximation to obtain an approximate likelihood function of the stochastic volatility model by partitioning the state variable into multiple intervals and approximating the transition probability density function of the discrete-time continuous state variable with the transition probability of the discrete sta...

은닉 마르코프 모델을 이용한 버스 정보 시스템의 도착 시간 예측

박철영 ( Park Chul Young ),김홍근 ( Kim Hong Geun ),신창선 ( Shin Chang Sun ),조용윤 ( Cho Yong Yun ),박장우 ( Park Jang Woo ) 한국정보처리학회 2017 정보처리학회논문지. 컴퓨터 및 통신시스템 Vol.6 No.4

버스정보시스템은 버스도착시간 예측과 같은 버스와 관련한 여러 정보를 제공한다. BIS는 우리나라 거의 모든 도시에 구축되어 있고 대중교통의 편의성 개선에 능동적인 역할을 하고 있다. 현재 BIS 시스템에서 버스 도착 예정시간을 예측하기 위하여 사용되는 대표적인 방법으로는 이동평균필터, Kalman Filter, 회귀 모형 등이 있다. 버스 도착 시간 예측의 정확성은 BIS 시스템에서 고려하고 있는 교통 상황이나 예측 알고리즘에 따라 차이가 크다. 현재 BIS에서 사용하는 예측 기법은 구간 통과 시간과 거리만을 이용한다. 그러나 도착시간 예측은 교통흐름, 신호주기, 이상 상황, 데이터 결측 등에 큰 영향을 받는다. 버스 도착 시간 예측의 정확도를 높이기 위해서는 위의 문제를 고려하여 모델링해야 하는 어려움이 있다. 은닉 마르코프 모델은 이와 같은 다양한 상황을 효과적으로 모델링 할 수 있다. 따라서 버스 도착 시간 예측의 정확도를 높이기 위해 도착시간에 대한 HMM 예측 모델을 구축했다. 이 모델에서는 순천시의 2015년 한 해 동안 수집한 데이터가 이용되었으며, 순천시에는 2298개의 정류장과 217개의 노선이 있다. 모델은 주중과 주말의 패턴을 다르게 적용하며, 다른 구간과 시간에 대해 모델이 적용된다. 본 논문에서는 버스정보시스템에 은닉 마르코프 모델 적용방법과 검증을 통해 버스정보시스템에서 사용 중인 이동평균필터, Kalman Filter, 회귀 모형을 사용한 예측 방법 보다 정밀한 정확도를 얻는 방법을 제안한다. BIS(Bus Information System) provides the different information related to buses including predictions of arriving times at stations. BIS have been deployed almost all cities in our country and played active roles to improve the convenience of public transportation systems. Moving average filters, Kalman filter and regression models have been representative in forecasting the arriving times of buses in current BIS. The accuracy in prediction of arriving times depends largely on the forecasting algorithms and traffic conditions considered when forecasting in BIS. In present BIS, the simple prediction algorithms are used only considering the passage times and distances between stations. The forecasting of arrivals, however, have been influenced by the traffic conditions such as traffic signals, traffic accidents and pedestrians ets., and missing data. To improve the accuracy of bus arriving estimates, there are big troubles in building models including the above problems. Hidden Markov Models have been effective algorithms considering various restrictions above. So, we have built the HMM forecasting models for bus arriving times in the current BIS. When building models, the data collected from Sunchean City at 2015 have been utilized. There are about 2298 stations and 217 routes in Suncheon city. The models are developed differently week days and weekend. And then the models are conformed with the data from different districts and times. We find that our HMM models can provide more accurate forecasting than other existing methods like moving average filters, Kalmam filters, or regression models. In this paper, we propose Hidden Markov Model to obtain more precise and accurate model better than Moving Average Filter, Kalman Filter and regression model. With the help of Hidden Markov Model, two different sections were used to find the pattern and verified using Bootstrap process.

GCM Ensemble을 활용한 추계학적 강우자료 상세화 기법 개발

김태정,권현한,이동률,윤선권 한국수자원학회 2014 한국수자원학회논문집 Vol.47 No.9

정상성 마코프 연쇄 모형은 일강우모의 모형으로 광범위하게 이용되고 있다. 하지만 정상성 마코프 연쇄 모형의 기본가정은 통계학적 특성이 시간에 따라 변화하지 않는 것으로, 일강우모의 시에 평균 또는 분산의 경향적 변화를 효과적으로 반영할 수 없다. 이러한 문제점을 인지하여 본 연구에서는 연주기 및 계절변화에 대하여 우수한 모의 능력을 나타내는 GCM의 모의결과를 입력자료로 이용하여 일강우량을 모의하기 위한 통계학적 상세화(downscaling) 기법인 비정상성 은닉 마코프 모형을 개발하였다. 개발된 모형을 낙동강 유역에 존재하는 영주지점, 문경지점 및 구미지점의 관측강우량에 적용한 결과, 일단위 및 계절단위의 강우량의 통계적 특성을 기존 모형에 비하여 개선된 결과를 도출할 수 있었으며, 또한 개발된 모형은 극치강수량 복원에 있어서도 관측값과 보다 유사한 결과를 보여 주었다. 이러한 점에서 정확성이 확보된 GCM 계절예측자료가 입력자료로 NHMM 모형에 활용된다면 예측기반의 일강수 상세화 모형으로 활용될 수 있을 것으로 판단된다. 이와 더불어, 기후변화 시나리오 입력자료가 사용된다면 기후변화 상세화 모형으로서도 적용될 수 있을 것으로 사료된다. The stationary Markov chain model has been widely used as a daily rainfall simulation model. A main assumption of the stationary Markov model is that statistical characteristics do not change over time and do not have any trends. In other words, the stationary Markov chain model for daily rainfall simulation essentially can not incorporate any changes in mean or variance into the model. Here we develop a Non-stationary hidden Markov chain model (NHMM) based stochastic downscaling scheme for simulating the daily rainfall sequences, using general circulation models (GCMs) as inputs. It has been acknowledged that GCMs perform well with respect to annual and seasonal variation at large spatial scale and they stand as one of the primary sources for obtaining forecasts. The proposed model is applied to daily rainfall series at three stations in Nakdong watershed. The model showed a better performance in reproducing most of the statistics associated with daily and seasonal rainfall. In particular, the proposed model provided a significant improvement in reproducing the extremes. It was confirmed that the proposed model could be used as a downscaling model for the purpose of generating plausible daily rainfall scenarios if elaborate GCM forecasts can used as a predictor. Also, the proposed NHMM model can be applied to climate change studies if GCM based climate change scenarios are used as inputs.

Estimating Lifetime Duration of Diabetes by Age and Gender in the Korean Population Using a Markov Model

Cho, Seung Woo,Kim, Seon Ha,Kim, Young-Eun,Yoon, Seok-Jun,Jo, Min-Woo The Korean Academy of Medical Sciences 2019 JOURNAL OF KOREAN MEDICAL SCIENCE Vol.34 No.11

<P><B>Background</B></P><P>Duration of type 2 diabetes is clinically important. Duration of morbidity is an independent and critical predictor of developing its complications. This study aims to explore an applicability of a Markov model to estimate the duration of diabetes in the Korean population.</P><P><B>Methods</B></P><P>We constructed the Markov model with two Markov states, diabetes and death, for estimation of duration of diabetes. The cycle of the Markov model was 1 year. Each diabetes onset by 5 years was considered from 30 to 85 years old or above. The endpoint of the Markov was 100 years old. Type 2 diabetes was operationally defined using the 10th revision of International Statistical Classification of Diseases and prescriptions of anti-diabetic drugs from the National Health Insurance Services-National Sample cohort. In each incident and existing prevalence cases, survival probabilities were obtained. Durations of diabetes from the Markov model were compared with those from the DisMod II program. Reductions of life expectancy due to diabetes were defined as differences of life expectancies between diabetic patients and the general public. Sensitivity analyses were also conducted using a cure rate and 95% confidence interval of survival probability.</P><P><B>Results</B></P><P>The duration of diabetes gradually decreased with incident age in both genders. In the early 30s, the duration was the largest at 48.9 and 41.9 years in women and men, respectively. In the average incident age group of type 2 diabetes, the late 50s, the reduction of life expectancy due to diabetes was estimated to be about two years in both genders. As annual cure probabilities increased, the durations of diabetes were reduced.</P><P><B>Conclusion</B></P><P>This study estimated the duration of diabetes using a Markov model. The model seems to work well and diabetes could reduce life expectancy by about 2 years on average. This approach could be useful to estimate the duration of illness, calculate disability-adjusted life years, and conduct economic evaluation studies on interventions for diabetic patients.</P>