• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.459-468
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• 2002

A class of asymmetric beta-ARCH processes is proposed and connections to traditional ARCH models are explained. Geometric ergodicity of the model is discussed. Conditional least squares as well as maximum likelihood estimators of parameters and their limit results are also presented. A test for symmetry of the model is studied with limiting power of test statistic given.

• Journal of Information Technology Applications and Management
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• v.26 no.6
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• pp.47-63
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• 2019

The volatility of major crypto currencies was examined and they are diagnosed whether they have a systematic risk or not, by estimating market beta representing systematic risk using GARCH( Generalized Auto Regressive Conditional Heteroskedastieity) model. First, the empirical results showed that their prices are very volatile over time because of the existence of ARCH and GARCH effects. Second, in terms of efficiency, asymmetric GJR model was estimated to be the most appropriate model because the standard error of a market beta was less than that of the OLS model and GARCH model. Third, the estimated market beta of Bitcoin using GJR model was less than 1 at 0.8791, showing that there is no systematic risk. However, unlike OLS model, the market beta of Ethereum and Ripple was estimated at 1.0581 and 1.1222, showing that there is systematic risk. This result shows that bitcoin is less dangerous than Ripple and Ethereum, and ripple is the most dangerous of all three crypto currencies. Finally, the major cryptocurrency found that the negative impact caused greater variability than the positive impact, causing bad news to fluctuate more than good news, and therefore good news and bad news had a different effect on the variability.