• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.112-118
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• 1994

The generalized least squares estimator in the linear regression model is equivalent to difference estimator irrespective of the particular form of the regressor matrix when the disturbances are generated by a seasonally autoregressive provess and autocorrelation is closed to unity.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.3
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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.

• International Area Studies Review
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• v.13 no.3
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• pp.287-308
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• 2009

This article examines the distributional characteristics of the return of Chinese stock market indices. The majority of previous empirical researches have tended to focus upon the simple stock market index. However, this study focuses on the four indices which represent the characteristics of each stock market index. The empirical findings indicate that the returns of the four chinese indices are not normally distributed at conventional levels. The Ljimg-Box -statistics indicate the returns of the index of A shares are not serially autocorrelated. However, the returns of the index of B shares are serially autocorrelated. The empirical findings also indicate returns of the four chinese indices are not serially autocorrelated. The statistics of Regression Specification Error Test and ARCH indicate the returns of all four indices are not serially linear. The findings also indicate that E- GARCH model is the most fittest model for the returns of the four chinese indices and the forecast error can be reduced by using student t distribution rather normal distribution.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.373-381
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• 1998

In this paper a new control chart which accounts for correlation between process subgroups will be proposed. We consider the case where the process fluctuations are autocorrelated by a stationary AR(1) time series and where n($\geq1$) items are sampled from the process at each sampling time. A simulation study is presented and shows that for correlated subgroups, the proposed control chart makes a significant improvement over the traditionally employed X-bar chart which ignores subgroup correlations. Finally, we illustrate the proposed chart by comparing the standardized residuals and X-bar chart on a data set of motor shaft diameters.

• Journal of the Korean Statistical Society
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• v.4 no.1
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• pp.39-56
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• 1975

Ever since Gauss discussed the least-squares method in 1812 and Bertrand translated Gauss's work in French, the least-squares method has been used for various economic analysis. The justification of the least-squares method was given by Markov in 1912 in connection with the previous discussion by Gauss and Bertrand. The main argument concerned the problem of obtaining the best linear unbiased estimates. In some modern language, the argument can be explained as follow.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.36
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• pp.243-251
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• 1995

본 연구에서는 자동상관인 공정의 변화를 빠르게 탐지할 수 있는 Special-Cause CUSUM 관리도를 사용하여 다섯가지 시계열 모델에 대해 다음과 같은 연구를 수행한다. 첫째 ACF와 PACF로 파라미터에 따른 ARL의 변화를 쉽게 해석할 수 있는 방법과 둘째로 독립인 관측값에 적용하는 Hawkins(1992)의 ARL 간략계산법을 자동상관인 공정에서도 사용할 수 있는 기법을 제시하여 기존의 시뮬레이션을 이용한 ARL 계산법에 비해 빠르고도 정확한 값을 구한다. 끝으로 두가지 유형의 평균이동에 대한 ARL 변화를 각각 계산해 보아 그 효과를 비교분석 한다.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1539-1547
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• 2014

In this paper we apply the autoregressive process to the nonlinear quantile regression in order to infer nonlinear quantile regression models for the autocorrelated data. We propose a kernel method for the autoregressive data which estimates the nonlinear quantile regression function by kernel machines. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of quantile regression function in the presence of autocorrelation between data.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.313-318
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• 2006

Many control charting methods for both i.i.d and autocorrelated data can be viewed as charting the output of a linear filter applied to the process data. We propose a generalization of this concept, in which the filter parameters are optimally selected to minimize the out-of-control ARL while constraining the in-control ARL to some desired value. A number of interesting characteristics of the optimal fitters are discussed.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.2
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• pp.65-73
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• 2013

In the simulation output analysis, bootstrap method is an applicable resampling technique to insufficient data which are not significant statistically. The moving block bootstrap, the stationary bootstrap, and the threshold bootstrap are typical bootstrap methods to be used for autocorrelated time series data. They are nonparametric methods for stationary time series data, which correctly describe the original data. In the simulation output analysis, however, we may not use them because of the non-stationarity in the data set caused by the trend such as increasing or decreasing. In these cases, we can get rid of the trend by differencing the data, which guarantees the stationarity. We can get the bootstrapped data from the differenced stationary data. Taking a reverse transform to the bootstrapped data, finally, we get the pseudo-samples for the original data. In this paper, we introduce the applicability of bootstrap methods to the time series data having trend, and then verify it through the statistical analyses.

• Journal of Korean Society for Quality Management
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• v.35 no.2
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• pp.106-112
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• 2007

In statistical process control, it is assumed that the process data are independent. However, most of chemical processes such as semi-conduct processes do not satisfy the assumption because of presence of autocorrelation between process data. It causes abnormal out of control signal in the process control and misleading estimation in process capability. In this study, we adopted Shore's method to solve the problem and propose an optimal subgroup size to estimate the variance correctly for AR(1) processes. Especially, we focus on finding an actual subgroup size for small samples based on simulation study.