• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.495-506
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• 2015

Volatility is a variation measure in finance for returns of a financial instrument over time. GARCH models have been a popular tool to analyze volatility of financial time series data since Bollerslev (1986) and it is said that volatility is highly persistent when the sum of the estimated coefficients of the squared lagged returns and the lagged conditional variance terms in GARCH models is close to 1. Regarding persistence, numerous methods have been proposed to test if such persistency is due to volatility shifts in the market or natural fluctuation explained by stationary long-range dependence (LRD). Recently, Lee et al. (2015) proposed a residual-based cumulative sum (CUSUM) test statistic to test volatility shifts in GARCH models against LRD. We propose a bootstrap-based approach for the residual-based test and compare the sizes and powers of our bootstrap-based CUSUM test with the one in Lee et al. (2015) through simulation studies.

• Journal of Integrative Natural Science
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• v.13 no.4
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• pp.152-157
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• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

• Journal of Korea Society of Industrial Information Systems
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• v.15 no.3
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• pp.51-57
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• 2010

Steganography techniques can be used to hide data within digital images with little or no visible change in the perceived appearance of the image. I propose a steganalysis to detecting hidden message in sequential steganography. This paper presents adjusted technique for detecting abrupt jumps in the statistics of the stego signal during steganalysis. The repeated statistical test based on CUSUM-SPRT runs constantly until it reaches decision. In this paper, I deal with a new and improved statistic $g_t$ by computing $S^{t^*}_j$.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.4
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• pp.457-468
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• 2007

This paper proposes an adaptive moving average (A-MA) control chart with variable sampling intervals (VSI) for detecting shifts in the process mean. The basic idea of the VSI A-MA chart is to adjust sampling intervals as well as to accumulate previous samples selectively in order to increase the sensitivity. The VSI A-MA chart employs a threshold limit to determine whether or not to increase sampling rate as well as to accumulate previous samples. If a standardized control statistic falls outside the threshold limit, the next sample is taken with higher sampling rate and is accumulated to calculate the next control statistic. If the control statistic falls within the threshold limit, the next sample is taken with lower sampling rate and only the sample is used to get the control statistic. The VSI A-MA chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L-consecutive control statistics fall outside the threshold limit. The control length L is introduced to prevent small mean shifts from being undetected for a long period. A Markov chain model is employed to investigate the VSI A-MA sampling process. Formulae related to the steady state average time-to signal (ATS) for an in-control state and out-of-control state are derived in closed forms. A statistical design procedure for the VSI A-MA chart is proposed. Comparative studies show that the proposed VSI A-MA chart is uniformly superior to the adaptive Cumulative sum (CUSUM) chart and to the Exponentially Weighted Moving Average (EWMA) chart, and is comparable to the variable sampling size (VSS) VSI EWMA chart with respect to the ATS performance.

• Journal of the Korea Society of Computer and Information
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• v.25 no.12
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• pp.187-194
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• 2020

In today's process-oriented industries, such as semiconductor and petrochemical processes, autocorrelation exists between observed data. As a management method for the process where autocorrelation exists, a method of using the observations is to construct a batch so that the batch mean approaches to independence, or to apply the EWMA (Exponentially Weighted Moving Average) statistic of the observed value to the EWMA control chart. In this paper, we propose a method to determine the batch size of UBM (Unweighted Batch Mean), which is commonly used as a management method for observations, and a method to determine the optimal batch size based on ARL (Average Run Length) We propose a method to estimate the standard deviation of the process. We propose an improved control chart for processes in which autocorrelation exists.

• The Journal of Engineering Geology
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• v.19 no.3
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• pp.261-268
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• 2009

Tunnel measurements provide crucial information on the ground stability during the excavation, visualizing the ground behavioral characteristics with quantitative dada. Generally, the frequency of the measurements is greater during the early stage of the tunnelling process and reduced with time. However, there are no quantitative criteria established for either the activities, such as the time, location and frequency of the measurement or the management guidance, especially for the site of subtle and unexpected displacement during the excavation. It is, however, still challenging to assess behavioral characteristics of subtle and unexpected displacement after stabilization. In this study, we propose a new method to assess stability and to analysis the behavioral characteristics of subtle and unexpected displacement after stabilization using statistic control charts of displacements. We also present a test result on the applicability of control chart and CUSUM control chart to measured displacements.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.101-109
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• 1997

For the detection on variance changes in the nonstationary time series with a unit root two types of test statistics are proposed, of which one is based on the cumulative sum of squares and the other is based on the likelihood ratio test. The properties of the cusum type test statistic are derived and the performance of two tests in small samples are compared through Monte Carlo study. It is ovserved that the test based on the cumulative sum of squares can detect a samll change in the variance faster than the one based on the likelihood ratio.

• Journal of Integrative Natural Science
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• v.12 no.3
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• pp.78-84
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• 2019

In many cases, the quality of a product is determined by several correlated quality variables. Control charts have been used for a long time widely to control the production process and to quickly detect the assignable causes that may produce any deterioration in the quality of a product. Numerical switching performances of multivariate cumulative sum control chart for simultaneous monitoring all components in the dispersion matrix ${\Sigma}$ under multivariate normal process $N_p({\underline{\mu}},{\Sigma})$ are considered. Numerical performances were evaluated for various shifts of the values of variances and/or correlation coefficients in ${\Sigma}$. Our computational results show that if one wants to quick detect the small shifts in a process, CUSUM control chart with small reference value k is more efficient than large k in terms of average run length (ARL), average time to signal (ATS), average number of switches (ANSW).

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.369-388
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• 2023

In this paper, we develop the two-step procedure that detects and estimates the position of structural changes for multivariate nonstationary time series, either on mean parameters or second-order structures. We first investigate the presence of mean structural change by monitoring data through the aggregated cumulative sum (CUSUM) type statistic, a sequential procedure identifying the likely position of the change point on its trend. If no mean change point is detected, the proposed method proceeds to scan the second-order structural change by modeling the multivariate nonstationary time series with a multivariate locally stationary Wavelet process, allowing the time-localized auto-correlation and cross-dependence. Under this framework, the estimated dynamic spectral matrices derived from the local wavelet periodogram capture the time-evolving scale-specific auto- and cross-dependence features of data. We then monitor the change point from the lower-dimensional approximated space of the spectral matrices over time by applying the dynamic principal component analysis. Different from existing methods requiring prior information on the type of changes between mean and covariance structures as an input for the implementation, the proposed algorithm provides the output indicating the type of change and the estimated location of its occurrence. The performance of the proposed method is demonstrated in simulations and the analysis of two real finance datasets.