• 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.21 no.3
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• pp.537-546
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• 2008

One of main goals of time series analysis is to estimate prediction of future values. In this paper, we investigate the bias problem when the transformation and back- transformation approach is applied in ARMA models and introduce a modified smearing estimation to reduce the bias. An empirical study on the returns of KOSDAQ index via Yeo-Johnson transformation was executed to compare the performance of existing methods and proposed methods and showed that proposed approaches provide a bias-reduced estimation of the prediction value.

• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.541-550
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• 2007

One of main aspects of time series analysis is to forecast future values of series based on values up to a given time. The prediction interval for future values is usually obtained under the normality assumption. When the assumption is seriously violated, a transformation of data may permit the valid use of the normal theory. We investigate the prediction problem for future values in the original scale when transformations are applied in ARMA models. In this paper, we introduce the methodology based on Yeo-Johnson transformation to solve the problem of skewed data whose modelling is relatively difficult in the analysis of time series. Simulation studies show that the coverage probabilities of proposed intervals are closer to the nominal level than those of usual intervals.

• Communications for Statistical Applications and Methods
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• v.16 no.6
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• pp.891-901
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• 2009

In this paper, we investigate the approach to estimate VaR under the transformed GARCH model. The time series are transformed to approximate to the underlying distribution of error terms and then the parameters and the one-sided prediction interval are estimated with the transformed data. The back-transformation is applied to compute the VaR in the original data scale. The analyses on the asset returns of KOSPI and KOSDAQ are presented to verify the accuracy of the coverage probabilities of the proposed VaR.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.971-979
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• 2009

In this paper, we introduce the method that reduces the bias when the transformation and back-transformation approach is applied in GARCH models. A parametric bootstrap is employed to compute the conditional expectation which is the prediction value to minimize mean square errors in the original scale. Through the analyese of returns of KOSPI and KOSDAQ, we verified that the proposed method provides a bias-reduced estimation for the prediction value.