• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.39-48
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• 2024

In this paper, we introduce an extended GARCH model designed to address asymmetric leverage effects. The variance in the standard GARCH model is composed of past conditional variances and past squared residuals. However, it is not possible to model asymmetric leverage effects with squared residuals alone, so in this paper, we propose a new extended GARCH model to explain the leverage effects using the Yeo-Johnson transformation which adjusts transformation parameter to make asymmetric data more normal or symmetric. We utilize the reverse properties of Yeo-Johnson transformation to model asymmetric volatility. We investigate the characteristics of the proposed model and parameter estimation. We also explore how to derive forecasts and forecast intervals in the proposed model. We compare it with standard GARCH and other extended GARCH models that model asymmetric leverage effects through empirical data analysis.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.159-168
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• 2014

The news impact curve(NIC) originally proposed by Engle and Ng (1993) is a graphical representation of volatility for financial time series. The NIC is a simple but a powerful tool for identifying variability of a given time series. It is noted that the NIC is suited to symmetric volatility. Recently a lot of attention has been paid to asymmetric volatility models and therefore asymmetric version of the NIC would be useful in the field of financial time series. In this article, we propose to incorporate LASSO in constructing asymmetric NICs based on asymmetric GARCH models. In particular, bilinear GARCH models are considered and illustrated via KOSDAQ data.

• Management & Information Systems Review
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• v.28 no.4
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• pp.93-108
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• 2009

This study examines the asymmetric volatility in the Korean bond market and stock market by using the KTB Prime Index and KOSPI. Because accurate estimation and forecasting of volatility is essential before investing assets, it is important to understand the asymmetric response of volatility in bond market. Therefore I investigate the existence of asymmetric volatility in Korean bond market unlike the previous studies which mainly focused on stock returns. The main results of the empirical analysis with GARCH and GJR-GARCH model are as follow. At first, it exists the asymmetric volatility on KOSPI returns like the previous studies. Also, I find that the GJR-GARCH is more suitable one than GARCH model for forecasting volatility. Second, it does not exist the asymmetric volatility on KTB Prime Index returns. This result is showed by that using the GARCH model for forecasting volatility in bond market is sufficient.

• 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 the Korean Data and Information Science Society
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• v.22 no.2
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• pp.353-360
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• 2011

We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1033-1043
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• 2011

In this paper, we use a nested family of models of Generalized Autoregressive Conditional Heteroscedasticity(GARCH) to verify asymmetric conditional heteroscedasticity in the KOSPI and Won-Dollar exchange rate. This study starts from an investigation of whether time series data have asymmetric features not explained by standard GARCH models. First, we use kernel density plot to show the non-normality and asymmetry in data as well as to capture asymmetric conditional heteroscedasticity. Later, we use three representative asymmetric heteroscedastic models, EGARCH(Exponential Garch), GJR-GARCH(Glosten, Jagannathan and Runkle), APARCH(Asymmetric Power Arch) that are improved from standard GARCH models to give a better explanation of asymmetry. Thereby we highlight the fact that volatility tends to respond asymmetrically according to positive and/or negative values of past changes referred to as the leverage effect. Furthermore, it is verified that how the direction of asymmetry is different depending on characteristics of time series data. For the KOSPI and Korean won-US dollar exchange rate, asymmetric heteroscedastic model analysis successfully reveal the leverage effect. We obtained predictive values of conditional volatility and its prediction standard errors by using moving block bootstrap.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1311-1317
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• 2010

A continuous time asymmetric power GARCH(1,1) model is suggested, based on a single background driving L$\'{e}$vy process. The stochastic differential equation for the given process is derived and the strict stationarity and kth order moment conditions are examined.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.611-622
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• 2021

With a wide recognition that financial time series typically exhibits asymmetry patterns in volatility so called leverage effects, various asymmetric GARCH(1, 1) processes have been introduced to investigate asymmetric volatilities. A lot of researches have also been directed to non-stationary volatilities to deal with frequent high ups and downs in financial time series. This article is concerned with both asymmetric and non-stationary GARCH-type models. As a subsequent paper of Choi et al. (2020), we review various asymmetric and non-stationary GARCH(1, 1) processes, and in turn propose how to compare competing models using a parametric bootstrap methodology. As an illustration, Dow Jones Industrial Average (DJIA) is analyzed.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.237-245
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• 2007

Nonlinear asymmetric time series models have the growing interest in econometrics and finance. Threshold model is one of the successful asymmetric model. We consider a smooth transition ARMA model which converges a.s. to a threshold ARMA model and show that the smooth transition ARMA model admits a stationary measure, provided a suitable condition on the coefficients of the autoregressive parts of the different regimes is satisfied. Stationarity of a smooth transition GARCH model is also obtained.