• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.87-92
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• 2002

A stochastic process {$A_n$, n = 1, 2, ...} is an arithmetic process (AP) if there exists some real number, d, so that {$A_n$ + (n-1)d, n =1, 2, ...} is a renewal process (RP). AP is a stochastically monotonic process and can be used for modeling a point process, i.e. point events occurring in a haphazard way in time (or space), especially with a trend. For example, the vents may be failures arising from a deteriorating machine; and such a series of failures id distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for an AP, similar to those for a geometric process (GP) proposed by Lam (1992). Two statistics are suggested for testing whether a given process is an AP. If this is so, we can estimate the parameters d, ${\mu}_{A1}$ and ${\sigma}^{2}_{A1}$ of the AP based on the techniques of simple linear regression, where ${\mu}_{A1}$ and ${\sigma}^2_{A1}$ are the mean and variance of the first random variable $A_1$ respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

• Management Science and Financial Engineering
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• 제14권2호
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• pp.105-118
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• 2008

There are many debates on the topic of the relationship between oil prices and economic growth. Through the repeated processes of conformations and contractions on the subject, two main issues are developed; one is how to define and drive oil shocks from oil prices, and the other is how to specify an econometric model to reflect the asymmetric relations between oil prices and output growth. The study, thus, introduces the unobserved component model to pick up the oil shocks and a first-order Markov switching model to reflect the asymmetric features. We finally employ unique oil shock variables from the stochastic trend components of oil prices and adapt four lags of the mean growth Markov Switching model. The results indicate that oil shocks exert more impact to recessionary state than expansionary state and the supply-side oil shocks are more persistent and significant than the demand-side shocks.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.277-286
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• 1998

This paper investigates the problem of determining optimal replacement policies for equipment subject to failures with cyclic rates. In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonhomogeneous process with/without a cyclic component in the failure rate function. The analytical results for various situations are presented along with numerical examples using simulated data.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2009년도 학술발표회 초록집
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• pp.1282-1286
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• 2009

최근에 빈번하게 발생하는 집중호우로는 강우자료의 경향성에 영향을 주고 있다. 하지만, 우리나라의 강우관측기록이 충분하지 못하여 통계학적 경향성 분석은 유의한 결과를 보여주고 있지 않아, 확률강우량 산정시 강우자료가 정상성을 지니고 있다고 가정하여 빈도분석을 실시하고 있다. 본 연구에서는 경향성이 나타나지 않는 강우관측소 49개지점중 4개의 지점을 선정하여 향후 경향성 여부를 분석하였다. 이들 관측자료가 가지는 경향성을 유지하면서 추계학적 시계열 모의발생기법을 이용하여 강우자료를 발생시킨 후 경향성 검정을 실시하였다. 이를 위하여 Regression model, ARMA model을 이용하여 강우자료를 발생시켰으며, 발생된 강우자료는 Mann-Kendall test, Hotelling-Pabst test, Wald-Wolfowitz test를 사용하였다. 그 결과 거의 모든 지점에서 가까운 미래에 경향성을 갖게 될 것임을 알 수 있었다.

• East Asian Economic Review
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• 제21권2호
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• pp.123-146
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• 2017

This paper examines the persistence of relative consumer price indices for 15 regions in Korea including 6 metropolitan cities and 9 provinces over the period of 1990-2016. In particular, we ask if relative regional price indices contain a common stochastic trend and find that they are not. We then investigate how quickly these relative prices converge to their long run value and find that a half-life of a deviation from the long run value is in the range of 13 to 22 months for the aggregate consumer price indices and in the range of 7 to 13 months for the tradable goods price indices, which is much quicker than the estimates of previous studies. These estimates suggest that existing monetary models with the realistic duration of price rigidities can generate the persistence in relative price indices.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.265-272
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• 2002

An Integer-valued autoregressive integrated (INARI) model is introduced to eliminate stochastic trend and seasonality from time series of count data. This INARI extends the previous integer-valued ARMA model. We show that it is stationary and ergodic to establish asymptotic normality for conditional least squares estimator. Optimal estimating equations are used to reflect categorical and serial correlations arising from panel count data and variations arising from three random processes for obtaining observation into estimation. Under regularity conditions for martingale sequence, we show asymptotic normality for estimators from the estimating equations. Using cancer mortality data provided by the U.S. National Center for Health Statistics (NCHS), we apply our results to estimate the probability of cells classified by 4 causes of death and 6 age groups and to forecast death count of each cell. We also investigate impact of three random processes on estimation.

• Management Science and Financial Engineering
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• 제5권2호
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• pp.43-53
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• 1999

In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonho-mogeneous process with/without a cyclic component in the failure rate function. The analytical re-sults for various situations are presented along with numerical examples using simulated data.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.407-416
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• 1997

Suppose that { $X_{i}$ } is a stationary AR(1) process and { $Y_{j}$ } is an ARX process with { $X_{i}$ } as exogeneous variables. Let $Y_{j}$ $^{*}$ be the stochastic process which is the sum of $Y_{j}$ and a nonstochastic trend. In this paper we consider the problem of estimating the conditional probability that $Y_{{n+1}}$$^{*}$ is bigger than $X_{{n+1}}$, given $X_{1}$, $Y_{1}$$^{*}$,..., $X_{n}$ , $Y_{n}$ $^{*}$. As an estimator for the tolerance probability, an Mann-Whitney statistic based on least squares residuars is suggested. It is shown that the deviations between the estimator and true probability are stochatically bounded with $n^{{-1}$2}/ order. The result may be applied to the stress-strength reliability theory when the stress and strength variables violate the classical iid assumption.umption.n.

• 한국안전학회지
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• 제7권2호
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• pp.5-13
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• 1992

If zero-accident movement is to be successful, the objective goal period should be surely obtainable, and much more in our country where frequency rate of injury are remarkably fluc-tuating. However In our country, as far as we know, no method to establish a reasonable zero-accident goal period is guaranteed. In thls paper, a new establishing-method of reasonable goal period for individual industry with considering recent accident trend is presented. A mathematical model for industrial accidents generation was analyzed, and a stochastic process model for the accident generation inteual was formulated. This model could tell the accident generation rate in future by understanding the accident tendency through the time-series analysis and search for the distribution of numbers of accidents and accident interval. On the basis of this, the forecasting method of goal achievement probability by the size and the establishment method of reasonable goal period were developed.

• 물과 미래
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• 제22권3호
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• pp.331-339
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• 1989

추계학적 모형 중의 하나인 Multiplicative ARIMA 모형을 사용하여 주기성과 경향성을 가지는 월유량계열을 예측하였으며 그 모형의 적합성은 낙동강 유역의 진동 수위 관측 지점에서의 23년간의 월 유량자료를 사용하여 검정하였다. 최종적으로 산정된 ARIMA (2,0,0)$\times$$(0,1,1)_{12}$ 모형의 변수는 21년간의 자료를 사용하여 산정하였으며 나머지 2년간의 월 유량자료는 예측치와 관측치를 비교하는데 사용하였다. 본 모형에 의한 에측치와 관측치의 비교결과 Multiplicative ARIMA 모형은 진동지점의 월유량 계열의 예측에 적합함이 판명되었다.