• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1047-1057
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• 2009

The nonparametric bivariate two-sample test of Bennett (1967) is extended to the multivariate k sample test. This test has been easily modified for a monotone trend among k samples. Often in applications it is important to consider a set of multivariate response variables simultaneously, rather than individually, and also important to consider testing k samples altogether. Different approaches of estimating the null covariance matrices of the test statistics resulted in the same limiting form. The multivariate k sample test is applied to the non-normal data of a randomized trial conducted for a period of four weeks in mental hospitals. The purpose of the trial is to compare the efficacy of three different interventions for a relief of the frequently occurring problems of constipation, caused as a side effect of antipsychotic drugs during hospitalization. The bowel movement status of patient for a week is summarized into a single severity score, and severity scores of four weeks comprise a four-dimensional multivariate variable. It is desirable with this trial data to consider a multivariate testing among k samples.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.397-412
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• 2020

In this paper, a notion of data depth is used to propose nonparametric multivariate two sample tests for difference between scale parameters. Data depth can be used to measure the centrality or outlying-ness of the multivariate data point relative to data cloud. A difference in the scale parameters indicates the difference in the depth values of a multivariate data point. By observing this fact on a depth vs depth plot (DD-plot), we propose nonparametric multivariate two sample tests for scale parameters of multivariate distributions. The p-values of these proposed tests are obtained by using Fisher's permutation approach. The power performance of these proposed tests has been reported for few symmetric and skewed multivariate distributions with the existing tests. Illustration with real-life data is also provided.

• 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.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.747-757
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• 2017

We investigate multivariate volatilities based on high frequency time series. The PCA (principal component analysis) method is employed to achieve a dimension reduction in multivariate volatility. Multivariate realized volatilities (RV) with various frequencies are calculated from high frequency data and "optimum" frequency is suggested using PCA. Specifically, RVs with various frequencies are compared with existing daily volatilities such as Cholesky, EWMA and BEKK after dimension reduction via PCA. An analysis of high frequency stock prices of KOSPI, Samsung Electronics and Hyundai motor company is illustrated.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.995-1005
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• 2009

Conditional correlation between financial time series plays an important role in risk management, asset allocation and portfolio selection and therefore diverse efforts for modeling conditional correlations in multivariate-GARCH processes have been made in last two decades. In particular, CCC (cf. Bollerslev, 1990) and DCC(dynamic conditional correlation, cf. Engle, 2002) models have been commonly used since they are relatively parsimonious in the number of parameters involved. This article is concerned with DCC modeling for multivariate GARCH processes in comparison with CCC specification. Various multivariate financial time series are analysed to illustrate possible advantages of DCC over CCC modeling.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.72-79
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• 1989

In this article the problem of characterizing multivariate distributions, possessing certain conditional distributions that have the same form as the parent model, are considered. It is shown that the forms of such conditional distributions characterize some well known distributions like the multivariate exponential, multivariate Burr, multivariate Lomax etc.

• The Korean Journal of Applied Statistics
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• v.27 no.7
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• pp.1139-1149
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• 2014

Multivariate volatility is summarized through canonical correlation analysis (CCA). Along with the standard CCA, non-negative and sparse canonical correlation analysis (NSCCA) is introduced to make sure that volatility coefficients are non-negative and the number of coefficients in the volatility CCA is as small as possible. Various multivariate financial time series are analyzed to illustrate the main contribution of the paper.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.915-925
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• 2007

Multivariate GARCH has been useful to model dynamic relationships between volatilities arising from each component series of multivariate time series. Methodologies including EWMA(Exponentially weighted moving-average model), DVEC(Diagonal VEC model), BEKK and CCC(Constant conditional correlation model) models are comparatively reviewed for bivariate time series. In addition, these models are applied to evaluate VaR(Value at Risk) and to construct joint prediction region. To illustrate, bivariate stock prices data consisting of Samsung Electronics and LG Electronics are analysed.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.79-89
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• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.