• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.563-568
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• 1995

It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.

• Proceedings of the Korean Statistical Society Conference
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• 2001.11a
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• pp.179-184
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• 2001

Schafer and Shenker(2000) mentioned the one of analytic imputation technique involving conditional means. We derive an approximate moments of a variance estimate with imputed conditional means.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.783-791
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• 2004

In this paper we review recent developments in nonlinear time series modeling on both conditional mean and conditional variance. Traditional linear model in conditional mean is referred to as ARMA(autoregressive moving average) process investigated by Box and Jenkins(1976). Nonlinear mean models such as threshold, exponential and random coefficient models are reviewed and their characteristics are explained. In terms of conditional variances, ARCH(autoregressive conditional heteroscedasticity) class is considered as typical linear models. As nonlinear variants of ARCH, diverse nonlinear models appearing in recent literature including threshold ARCH, beta-ARCH and Box-Cox ARCH models are remarked. Also, a class of unified nonlinear models are considered and parameter estimation for that class is briefly discussed.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.809-816
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• 2011

A tree-indexed autoregressive(AR) process is a time series defined on a tree which is generated by a branching process and/or a deterministic splitting mechanism. This short article is concerned with conditional heteroscedastic structure of the tree-indexed AR models. It has been usual in the literature to analyze conditional mean structure (rather than conditional variance) of tree-indexed AR models. This article pursues to identify quadratic conditional heteroscedasticity inherent in various tree-indexed AR models in a unified way, and thus providing some perspectives to the future works in this area. The identical conditional variance of sisters sharing the same mother will be referred to as the branching heteroscedasticity(BH, for short). A quasilikelihood but preliminary estimation of the quadratic BH is discussed and relevant limit distributions are derived.

• Journal of Korean Society for Quality Management
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• v.49 no.4
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• pp.467-482
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• 2021

Purpose: The main theme of this study is to determine the optimal control limit of conditional variance investigation by mathematical approach. According to the determination approach of control limit presented in this study, it is possible with only one parameter to calculate the control limit necessary for budgeting control system or standard costing system, in which the limit could not be set in advance, that's why it has the advantage of high practical application. Methods: This study followed the analytical methodology in terms of the decision model of information economics, Bayesian probability theory and Taguchi's quality loss function concept. Results: The function suggested by this study is as follows; ${\delta}{\leq}\frac{3}{2}(k+1)+\frac{2}{\frac{3}{2}(k+1)+\sqrt{\{\frac{3}{2}(k+1)\}^2}+4$ Conclusion: The results of this study will be able to contribute not only in practice of variance investigation requiring in the standard costing and budgeting system, but also in all fields dealing with variance investigation differences, for example, intangible services quality control that are difficult to specify tolerances (control limit) unlike tangible product, and internal information system audits where materiality standards cannot be specified unlike external accounting audits.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.287-297
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• 2009

In terms of generalized autoregressive conditional heteroscedastic(GARCH) model, estimation of prediction interval based on likelihood is quite sensitive to distribution of error. Moveover, it is not an easy job to construct prediction interval for conditional variance. Recent studies show that the bootstrap method can be one of the alternatives for solving the problems. In this paper, we introduced the bootstrap approach proposed by Pascual et al. (2006). We employed it to Korean stock price data set.

• Journal of Korea Port Economic Association
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• v.31 no.1
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• pp.1-14
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• 2015

The standard GARCH model imposing symmetry on the conditional variance, tends to fail in capturing some important features of the data. This paper, hence, introduces the models capturing asymmetric effect. They are the EGARCH model and the GJR model. We provide the systematic comparison of volatility models focusing on the asymmetric effect of news on volatility. Specifically, three diagnostic tests are provided: the sign bias test, the negative size bias test, and the positive size bias test. This paper shows that there is significant evidence of GARCH-type process in the data, as shown by the test for the Ljung-Box Q statistic on the squared residual data. The estimated unconditional density function for squared residual is clearly skewed to the left and markedly leptokurtic when compared with the standard normal distribution. The observation of volatility clustering is also clearly reinforced by the plot of the squared value of residuals of export volume and values. The unconditional variance of both export volumes and export value indicates that large shocks of either sign tend to be followed by large shocks, and small shocks of either sign tend to follow small shocks. The estimated export volume news impact curve for the GARCH also suggests that $h_t$ is overestimated for large negative and positive shocks. The conditional variance equation of the GARCH model for export volumes contains two parameters ${\alpha}$ and ${\beta}$ that are insignificant, indicating that the GARCH model is a poor characterization of the conditional variance of export volumes. The conditional variance equation of the EGARCH model for export value, however, shows a positive sign of parameter ${\delta}$, which is contrary to our expectation, while the GJR model exhibits that parameters ${\alpha}$ and ${\beta}$ are insignificant, and ${\delta}$ is marginally significant. That indicates that the asymmetric volatility models are poor characterization of the conditional variance of export value. It is concluded that the asymmetric EGARCH and GJR model are appropriate in explaining the volatility of export volume, while the symmetric standard GARCH model is good for capturing the volatility.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.925-937
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• 2008

In this study, we considered the clustering analysis for stock return traded in the stock market. Most of financial time-series data, for instance, stock price and exchange rate have conditional heterogeneous variability depending on time, and, hence, are not properly applied to the autoregressive moving-average(ARMA) model with assumption of constant variance. Moreover, the variability is font and center for stock investors as well as academic researchers. So, this paper focuses on the generalized autoregressive conditional heteroscedastic(GARCH) model which is known as a solution for capturing the conditional variance(or volatility). We define the metrics for similarity of unconditional volatility and for homogeneity of model structure, and, then, evaluate the performances of the metrics. In real application, we do clustering analysis in terms of volatility and structure with stock return of the 11 Korean companies measured for the latest three years.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.721-729
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• 2000

In this paper, we propose a new conditional randomized response model that has improved the Carr et al.'s model in view of he variance and the protection of privacy of respondents. We show that he suggested model is more effective and protective than the Loynes' model and Carr et al.' model.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.63-73
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• 2002

The one of analytic imputation technique involving conditional means was mentioned by Schafer and Schenker(2000). And their derivations are based on asymptotic expansions of point estimator and their associated variance estimator, and the result of imputation can be thought of as first-order approximations to the estimators. Specially in this paper, we are presenting the method of estimating a Binomial proportion with Bayesian approach of imputed conditional means. That is, instead of using maximum likelihood(ML) estimator to estimate a Binomial proportion, in general, we use the Bayesian estimators and will show the result of estimated Imputed conditional means.