• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• Journal of the military operations research society of Korea
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• v.11 no.1
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• pp.111-129
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• 1985

Markov chains with large transition probability matrices occur in many applications such as manpowr models. Under certain conditions the state space of a stationary discrete parameter finite Markov chain may be partitioned into subsets, each of which may be treated as a single state of a smaller chain that retains the Markov property. Such a chain is said to be 'lumpable' and the resulting lumped chain is a special case of more general functions of Markov chains. There are several reasons why one might wish to lump. First, there may be analytical benefits, including relative simplicity of the reduced model and development of a new model which inherits known or assumed strong properties of the original model (the Markov property). Second, there may be statistical benefits, such as increased robustness of the smaller chain as well as improved estimates of transition probabilities. Finally, the identification of lumps may provide new insights about the process under investigation.

• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.355-376
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• 2006

To identify whether the sequence of observations follows a chain dependent process and whether the chain dependent or repeated observations follow stationary process or not, alternative procedures are suggested in this paper. These test procedures are formulated on the basis of logistic regression model under the likelihood ratio test criterion and applied to the daily rainfall occurrence data of Bangladesh for selected stations. These test procedures indicate that the daily rainfall occurrences follow a chain dependent process, and the different types of transition probabilities and overall transition probabilities of Markov chain for the occurrences of rainfall follow a stationary process in the Mymensingh and Rajshahi areas, and non-stationary process in the Chittagong, Faridpur and Satkhira areas.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.29-42
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• 2018

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

• 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.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.477-491
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• 2021

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1043-1048
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• 2011

W. Choi([1]) identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. We denote by F the homozygosity and by S the average selection intensity. In this note, we define the Fleming-Viot process with generator of limiting diffusion and provide exact result for the relations of F and S.

• Proceedings of the KSRS Conference
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• 2007.03a
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• pp.55-60
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• 2007

The purpose of this study is to evaluate the temporal land cover change by gradual urbanization of Gyeongan-cheon watershed. This study used the five land use of Landsat TM satellite images(l987, 1991, 2001, 2004) which were classified by maximum likelihood method. The five land use maps examine its accuracy by error matrix and administrative district statistics. This study analyze land use patterns in the past using time.series Landsat satellite images, and predict 2004 year land use using a CA-Markov combined CA(Cellular Automata) and Markov process, and examine its appropriateness. Finally, predict 2030, 2060 year land use maps by CA-Markov model were constructed from the classified images.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.5
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• pp.891-897
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• 2009

This paper presents a novel load management technique that can lower the peak demand caused by package airconditioner loads in large apartment complex. An intelligent hierarchical load management system composed of a Central Intelligent Management System(CIMS) and multiple Local Intelligent Management Systems(LIMS) is proposed to implement the proposed technique. Once the required amount of the power reduction is set, CIMS issues tokens, which can be used by each LIMS as a right to turn on the airconditioner. CIMS creates and maintains a queue for fair and proper allocation of the tokens among the LIMS requesting tokens. By adjusting the number tokens and queue management policies, desired power reduction can be achieved smoothly. The Markov Birth and Death process and the Balance Equations utilizing the Diffusion Model are employed for evaluation of queue performances during transient periods until the static balances among the states are achieved. The proposed technique is tested using a summer load data of a large apartment complex and give promising results demonstrating the usability in load management while minimizing the customer inconveniences.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.6
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• pp.2452-2457
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• 2012

When a quality inspection process rejects a product unit, consecutive repeated inspections are sometimes conducted for the rejected unit to reduce a false reject possibility. This paper analyzes a special inspection process that allows up to two times of consecutive testing for each product to decrease type I inspection errors. This study uses a Markov chain to model the steps of the inspection process and a product unit's quality states during inspection. Historical inspection results from a company are used as the data for the Markov chain model. Using the Markov chain model and data, this study analyzes the effect of this special inspection rule on the proportion of the final quality levels and scrap rate. The results demonstrate that this inspection process of possible double testing could help reduce unnecessary rejects and consequently decrease material and production costs.