• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.694-698
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• 2008

In hydrology, it is a difficult task to deal with multivariate time series such as modeling streamflows of an entire complex river system. Normal distribution based model such as MARMA (Multivariate Autorgressive Moving average) has been a major approach for modeling the multivariate time series. There are some limitations for the normal based models. One of them might be the unfavorable data-transformation forcing that the data follow the normal distribution. Furthermore, the high dimension multivariate model requires the very large parameter matrix. As an alternative, one might be decomposing the multivariate data into independent components and modeling it individually. In 1985, Lins used Principal Component Analysis (PCA). The five scores, the decomposed data from the original data, were taken and were formulated individually. The one of the five scores were modeled with AR-2 while the others are modeled with AR-1 model. From the time series analysis using the scores of the five components, he noted "principal component time series might provide a relatively simple and meaningful alternative to conventional large MARMA models". This study is inspired from the researcher's quote to develop a multivariate simulation model. The multivariate simulation model is suggested here using Principal Component Analysis (PCA) and Independent Component Analysis (ICA). Three modeling step is applied for simulation. (1) PCA is used to decompose the correlated multivariate data into the uncorrelated data while ICA decomposes the data into independent components. Here, the autocorrelation structure of the decomposed data is still dominant, which is inherited from the data of the original domain. (2) Each component is resampled by block bootstrapping or K-nearest neighbor. (3) The resampled components bring back to original domain. From using the suggested approach one might expect that a) the simulated data are different with the historical data, b) no data transformation is required (in case of ICA), c) a complex system can be decomposed into independent component and modeled individually. The model with PCA and ICA are compared with the various statistics such as the basic statistics (mean, standard deviation, skewness, autocorrelation), and reservoir-related statistics, kernel density estimate.

• 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.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.821-831
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• 2011

It has been relatively incomplete in the field of financial time series to adapt asymmetric features to multivar ate GARCH processes (McAleer et al., 2009). Retaining constant conditional correlation(CCC) structure, this article pursues to introduce asymmetric GARCH modelling in analysing multivariate volatilities in time series in a practical point of view. Multivariate Korean financial time series are analyzed in detail to compar our theory with conventional methodologies including GARCH and EGARCH.

• Journal of Korea Water Resources Association
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• v.30 no.6
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• pp.641-648
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• 1997

Mutual information is useful for analyzing nonlinear dependence in time series in much the same way as correlation is used to characterize linear dependence. We use multivariate kernel density estimators for the estimation of mutual information at different time lags for single and multiple time series. This approach is tested on a variety of hydrologic data sets, and suggested an appropriate delay time $ au$ at which the mutual information is almost zerothen multi-dimensional phase portraits could be constructed from measurements of a single scalar time series.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.7
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• pp.54-61
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• 2015

This paper presents short-term wind farm power forecasting method using multivariate analysis and time series. Based on factor analysis, the proposed method makes new independent variables which newly composed by raw independent variables such as wind speed, ramp rate, wind power. Newly created variables are used in the time series model for forecasting wind farm power. To demonstrate the improved accuracy, the proposed method is compared with persistence model commonly used as reference in wind power forecasting using data from Jeju Island. The results of case studies are presented to show the effectiveness of the proposed forecasting method.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1007-1017
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• 2009

Forecasting for air demand such as passengers and freight has been one of the main interests for air industries. This research has mainly focus on the comparison the performance between the univariate seasonal ARIMA models and the multivariate time series models. In this paper, we used real data to predict demand on international passenger and freight. And multivariate time series models are better than the univariate models based on the accuracy criteria.

• Journal of Korean Society for Quality Management
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• v.49 no.4
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• pp.539-550
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• 2021

Purpose: The purpose of this study is to propose a multivariate CUSUM control chart that can detect the out-of-control state fast while monitoring the cross- and auto- correlated multivariate time series data. Methods: We first build models to estimate the observation data and calculate the corresponding residuals. After then, a multivariate CUSUM chart is applied to monitor the residuals instead of the original raw observation data. Vector Autoregression and Artificial Neural Net are selected for the modelling, and Separated-MCUSUM chart is selected for the monitoring. The suggested methods are tested under a number of experimental settings and the performances are compared with those of other existing methods. Results: We find that Artificial Neural Net is more appropriate than Vector Autoregression for the modelling and show the combination of Separated-MCUSUM with Artificial Neural Net outperforms the other alternatives considered in this paper. Conclusion: The suggested chart has many advantages. It can monitor the complicated multivariate data with cross- and auto- correlation, and detects the out-of-control state fast. Unlike other CUSUM charts finding their control limits by trial and error simulation, the suggested chart saves lots of time and effort by approximating its control limit mathematically. We expect that the suggested chart performs not only effectively but also efficiently for monitoring the process with complicated correlations and frequently-changed parameters.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.73-80
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• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.

• International Journal of Contents
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• v.8 no.1
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• pp.23-29
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• 2012

Multiple expression levels of genes obtained using time series microarray experiments have been exploited effectively to enhance understanding of a wide range of biological phenomena. However, the unique nature of microarray data is usually in the form of large matrices of expression genes with high dimensions. Among the huge number of genes presented in microarrays, only a small number of genes are expected to be effective for performing a certain task. Hence, discounting the majority of unaffected genes is the crucial goal of gene selection to improve accuracy for disease diagnosis. In this paper, a non-Gaussian weight matrix obtained from an incremental model is proposed to extract useful features of multivariate time series microarrays. The proposed method can automatically identify a small number of significant features via discovering hidden variables from a huge number of features. An unsupervised hierarchical clustering representative is then taken to evaluate the effectiveness of the proposed methodology. The proposed method achieves promising results based on predictive accuracy of clustering compared to existing methods of analysis. Furthermore, the proposed method offers a robust approach with low memory and computation costs.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.825-835
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• 2008

Multivariate GARCH(MGARCH) has been useful in financial studies and econometrics for modeling volatilities and correlations between components of multivariate time series. An obvious drawback lies in that the number of parameters increases rapidly with the number of variables involved. This thesis tries to resolve the problem by using dimension reduction technique. We briefly review both factor models for dimension reduction and the MGARCH models including EWMA (Exponentially weighted moving-average model), DVEC(Diagonal VEC model), BEKK and CCC(Constant conditional correlation model). We create meaningful portfolios obtained after reducing dimension through statistical factor models and fundamental factor models and in turn these portfolios are applied to MGARCH. In addition, we compare portfolios by assessing MSE, MAD(Mean absolute deviation) and VaR(Value at Risk). Various financial time series are analyzed for illustration.