• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.29-43
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• 2012

Financial data such as stock index returns and exchange rates have the properties of heavy tail and asymmetry compared to normal distribution. When we estimate VaR using the GARCH model (with the conditional return distribution of normal) it shows the tendency of the lower estimation and clustering in the losses over the estimated VaR. In this paper, we argue that this problem can be resolved through the adaptation of the unbounded Johnson distribution as that of the condition return. We also compare this model with the GARCH with the conditional return distribution of normal and student-t. Using the losses exceed the ex-ante VaR, estimates, we check the validity of the GARCH models through the failure proportion test and the clustering test. We nd that the GARCH model with conditional return distribution of unbounded Johnson provides an appropriate estimation of the VaR and does not occur the clustering of violations.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.219-234
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• 2010

In index investing according to KOSPI, we estimate Value at Risk(VaR) from the extreme losses of the daily returns which are obtained from KOSPI. To this end, we apply Block Maxima(BM) model which is one of the useful models in the extreme value theory. We also estimate the extremal index to consider the dependency in the occurrence of extreme losses. From the back-testing based on the failure rate method, we can see that the model is adaptable for the VaR estimation. We also compare this model with the GARCH model which is commonly used for the VaR estimation. Back-testing says that there is no meaningful difference between the two models if we assume that the conditional returns follow the t-distribution. However, the estimated VaR based on GARCH model is sensitive to the extreme losses occurred near the epoch of estimation, while that on BM model is not. Thus, estimating the VaR based on GARCH model is preferred for the short-term prediction. However, for the long-term prediction, BM model is better.

• Communications for Statistical Applications and Methods
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• v.30 no.2
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• pp.163-178
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• 2023

GARCH-X(1, 1) model specifies that conditional variance follows an AR(1) process and includes a past exogenous variable. This study proposes a new class from that model by allowing a more general (non-linear) variance function to follow an AR(1) process. The functions applied to the variance equation include exponential, Tukey's ladder, and Yeo-Johnson transformations. In the framework of normal and student-t distributions for return errors, the empirical analysis focuses on two stock indices data in developed countries (FTSE100 and SP500) over the daily period from January 2000 to December 2020. This study uses 10-minute realized volatility as the exogenous component. The parameters of considered models are estimated using the adaptive random walk metropolis method in the Monte Carlo Markov chain algorithm and implemented in the Matlab program. The 95% highest posterior density intervals show that the three transformations are significant for the GARCHX(1, 1) model. In general, based on the Akaike information criterion, the GARCH-X(1, 1) model that has return errors with student-t distribution and variance transformed by Tukey's ladder function provides the best data fit. In forecasting value-at-risk with the 95% confidence level, the Christoffersen's independence test suggest that non-linear models is the most suitable for modeling return data, especially model with the Tukey's ladder transformation.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.501-512
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• 2014

Stylized facts on asset return are fat-tail, asymmetry, volatility clustering and structure changes. This paper simultaneously captures these characteristics by introducing a multi-regime models: Finite mixture distribution and regime switching GARCH model. Analyzing the daily KOSPI return from $4^{th}$ January 2000 to $30^{th}$ June 2014, we find that a two-component mixture of t distribution is a good candidate to describe the shape of the KOSPI return from unconditional and conditional perspectives. Empirical results suggest that the equality assumption on the shape parameter of t distribution yields better discrimination of heterogeneity component in return data. We report the strong regime-dependent characteristics in volatility dynamics with high persistence and asymmetry by employing a regime switching GJR-GARCH model with t innovation model. Compared to two sub-samples, Pre-Crisis (January 2003 ~ December 2007) and Post-Crisis (January 2010 ~ June 2014), we find that the degree of persistence in the Pre-Crisis is higher than in the Post-Crisis along with a strong asymmetry in the low-volatility (high-volatility) regime during the Pre-Crisis (Post-Crisis).

• The Journal of Asian Finance, Economics and Business
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• v.7 no.12
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• pp.1-10
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• 2020

This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1041-1049
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• 2010

In Korean professional baseball, attendance is the largest source of revenue for development of professional baseball and the highest concern of professional baseball teams. So, if there is demand forecasting model, it will be helpful for pennant chasers to work out the strategies for drawing attendance. For this reason, this research intends to suggest the model which estimates Korean professional baseball's attendance and uses all usable variables which have an effect on attendance in limited circumstances. We supposed that dependent variable is attendance as well as several independent variables and error term are homoscedastic variance. And then, we compared the models which assume conditional heteroscedastic variance like GARCH and EGARCH with GARCH-t models which use the assumption that error term's distribution follows student-t distribution. In result of that, we could confirm that the models which were made by using GARCH(1,1)-t made estimates the most accurately among the several models considered.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.445-459
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• 2014

This paper investigates the dependence structure of Korean financial markets (stock, foreign exchange (FX) rates and bond) using copula-GARCH and dynamic conditional correlation (DCC) models. We examine GJR-GARCH with skewed elliptical distributions and four copulas (Gaussian, Student's t, Clayton and Gumbel) to model dependence among returns, and then employ DCC model to describe system-wide correlation dynamics. We analyze the daily returns of KOSPI, FX (WON/USD) and KRX bond index (Gross Price Index) from $2^{nd}$ May 2006 to $30^{th}$ June 2014 with 2,063 observations. Empirical result shows that there is significant asymmetry and fat-tail of individual return, and strong tail-dependence among returns, especially between KOSPI and FX returns, during the 2008 Global Financial Crisis period. Focused only on recent 30 months, we find that the correlation between stock and bond markets shows dramatic increase, and system-wide correlation wanders around zero, which possibly indicates market tranquility from a systemic perspective.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.61-69
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• 2011

In GARCH context, the conditional variance (or volatility) is of a quadratic function of the observation process. Examine standard ARCH/GARCH and their variant models in terms of quadratic formulations and it is interesting to note that most models in GARCH context have contained neither the first order term nor the interaction term. In this paper, we consider three models possessing the first order and/or interaction terms in the formulation of conditional variances, viz., quadratic GARCH, absolute value GARCH and bilinear GARCH processes. These models are investigated with a view to model comparisons and applications to financial time series in Korea

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1661-1671
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• 2016

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.