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Econometrics, Volume 2, Issue 2 (June 2014), Pages 92-122

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Research

Open AccessArticle A One Line Derivation of EGARCH
Econometrics 2014, 2(2), 92-97; doi:10.3390/econometrics2020092
Received: 16 June 2014 / Revised: 19 June 2014 / Accepted: 20 June 2014 / Published: 23 June 2014
Cited by 10 | PDF Full-text (217 KB) | HTML Full-text | XML Full-text
Abstract
One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which
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One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator of the EGARCH parameters are not available under general conditions, but rather only for special cases under highly restrictive and unverifiable conditions. It is often argued heuristically that the reason for the lack of general statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives, and hence does not permit (quasi-) maximum likelihood estimation. It is shown in this paper for the non-leverage case that: (1) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (2) the reason for the lack of statistical properties of the estimators of EGARCH under general conditions is that the stationarity and invertibility conditions for the RCCNMA process are not known. Full article
Open AccessArticle A Fast, Accurate Method for Value-at-Risk and Expected Shortfall
Econometrics 2014, 2(2), 98-122; doi:10.3390/econometrics2020098
Received: 5 June 2014 / Revised: 21 June 2014 / Accepted: 22 June 2014 / Published: 25 June 2014
Cited by 8 | PDF Full-text (415 KB) | HTML Full-text | XML Full-text
Abstract
A fast method is developed for value-at-risk and expected shortfall prediction for univariate asset return time series exhibiting leptokurtosis, asymmetry and conditional heteroskedasticity. It is based on a GARCH-type process driven by noncentral t innovations. While the method involves the use of several
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A fast method is developed for value-at-risk and expected shortfall prediction for univariate asset return time series exhibiting leptokurtosis, asymmetry and conditional heteroskedasticity. It is based on a GARCH-type process driven by noncentral t innovations. While the method involves the use of several shortcuts for speed, it performs admirably in terms of accuracy and actually outperforms highly competitive models. Most remarkably, this is the case also for sample sizes as small as 250. Full article

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