• Journal of Electrical Engineering and Technology
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• 제11권6호
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• pp.1548-1555
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• 2016

This paper presents an application of time series analysis in hourly wind speed simulation and forecast in Jeju Island, Korea. Autoregressive - moving average (ARMA) model, which is well in description of random data characteristics, is used to analyze historical wind speed data (from year of 2010 to 2012). The ARMA model requires stationary variables of data is satisfied by power law transformation and standardization. In this study, the autocorrelation analysis, Bayesian information criterion and general least squares algorithm is implemented to identify and estimate parameters of wind speed model. The ARMA (2,1) models, fitted to the wind speed data, simulate reference year and forecast hourly wind speed in Jeju Island.

• 산업경영시스템학회지
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• 제34권4호
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• pp.57-65
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• 2011

Monitoring auto correlated processes is prevalent in recent manufacturing environments. As a proactive control for manufacturing processes is emphasized especially in the semiconductor industry, it is natural to monitor real-time status of equipment through sensor rather than resultant output status of the processes. Equipment's sensor data show various forms of correlation features. Among them, considerable amount of sensor data, statistically autocorrelated, is well represented by Box-Jenkins autoregressive moving average (ARMA) model. In this paper, we present a design method of statistical process control (SPC) used for monitoring processes represented by the ARMA model. The proposed method shows benefits in the power of detecting process changes, and considers robustness to ARMA modeling errors simultaneously. We prove benefits through Monte carlo simulation-based investigations.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.301-314
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• 2002

For autoregressive moving average (ARMA) models, robust unit root tests are developed using M-estimators. The tests are parametric in the sense ARMA parameters are estimated jointly with unit roots. A Monte-Carlo experiment reveals superiority of the parametric tests over the semipararmetric tests of Lucas (1995a) in terms of both empirical sizes and powers.

• 한국경영과학회지
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• 제34권4호
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• pp.91-112
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• 2009

The bullwhip effect means the phenomenon of increasing demand variation as moving UP to the upstream in the supply chain. Therefore, it is recognized that the bullwhip effect is problematic for effective supply chain operations. In this paper, we exactly quantifies the bullwhip effect for the case of stochastic lead time and seasonal demand in two-echelon supply chain where retailer employs a base-stock policy considering SARMA demand processes and stochastic lead time. We also investigate the behavior of the proposed measurement for the bullwhip effect with autoregressive and moving average coefficient, stochastic lead time, and seasonal factor.

• Journal of the Korean Statistical Society
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• 제36권2호
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• pp.183-200
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• 2007

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.

• 산업경영시스템학회지
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• 제35권3호
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• pp.52-61
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• 2012

The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.377-390
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• 2010

In the case of time-series analysis, it is often more convenient to rely on the frequency domain than the time domain. Spectral density is the core of the frequency-domain analysis that describes autocorrelation structures in a time-series process. Possible ways to estimate spectral density are to compute a periodogram or to average the periodogram over some frequencies with (un)equal weights. This can be an attractive tool to measure the similarity between time-series processes. We employ the metrics based on a smoothed periodogram proposed by Park and Kim (2008) for the classification of different classes of time-series processes. We consider several lag windows with unequal weights instead of a modified Daniel's window used in Park and Kim (2008). We evaluate the performance under various simulation scenarios. Simulation results reveal that the metrics used in this study split the time series into the preassigned clusters better than do the raw-periodogram based ones proposed by Caiado et al. 2006. Our metrics are applied to an economic time-series dataset.

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.405-415
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• 2000

한 구조물에 작용하는 풍압력 시계열이 자기회귀 이동평균(ARMA) 모델을 사용하여 모델화 된다. AR 과정에서 시계열의 현재 값은 유한한 수의 이전 값들의 선형적 결합과 한 백색잡음에 의해 나타난다. MA 과정에서 시계열의 현재값은 유한한 수의 이전 백색잡음들에 선형적이다. ARMA 과정은 AR과 MA 과정의 결합이다. 본 논문에서, AR, MA와 ARMA 모델이 풍압력 시계열에 적용되고, 데이터를 나타내기에 가장 적합한 ARMA 모델을 선정하는 과정이 소개된다. 모델의 변수들은 최대 가능도법을 사용하여 산정되고, 압력 시계열의 시간적 복잡성의 척도인 모델 차수를 최적화하기 위해 AICC 모델 선정 기준이 사용된다. 또한, 모델의 유효성을 조사하기 위해 LBP 검사가 사용된다. 본 연구로부터, AR 과정이 풍압력 시계열을 나타내기에 가장 적합하다는 결론이 얻어진다.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.559-564
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• 2016

The Durbin-Watson (DW) test in regression model and the Ljung-Box (LB) test in ARMA (autoregressive moving average) model are typical examples of correlated error tests. The DW test is used for detecting autocorrelation of errors using the residuals from a regression analysis. The LB test is used for specifying the correct ARMA model using the first some sample autocorrelations based on the residuals of a tted ARMA model. In this article, simulations with four data generating processes have been carried out to evaluate their performances as correlated error tests. Our simulations show that the DW test is severely dependent on the assumed AR(1) model but isn't sensitive enough to reject the misspecified model and that the LB test reports lackluster performance in general.

• 한국경영과학회지
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• 제17권2호
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• pp.91-106
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• 1992

It an inventory control system, the demand over time are often assumed to be independently identically distributed (i. i. d.). However, the demands may well be correlated over time in many situations. The estimation of reorder points is not simple for correlated demands with variable lead time. In this paper, a general class of autoregressive and moving average processes is considered for modeling the demands of an inventory item. The first four moments of the lead-time demand (L) are derived and used to approximate the distribution of L. The reorder points at given service level are then estimated by the three approximation methods : normal approximation, Charlier series and Pearson system. Numerical investigation shows that the Pearson system and the Charlier series performs extremely well for various situations whereas the normal approximation show consistent underestimation and sensitive to the distribution of lead time. The same conclusion can be reached when the parameters are estimated from the sample based on the simulation study.