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

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217 KiB  
Article
A One Line Derivation of EGARCH
by Michael McAleer and Christian M. Hafner
Econometrics 2014, 2(2), 92-97; https://doi.org/10.3390/econometrics2020092 - 23 Jun 2014
Cited by 54 | Viewed by 10086
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 [...] Read more.
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
415 KiB  
Article
A Fast, Accurate Method for Value-at-Risk and Expected Shortfall
by Jochen Krause and Marc S. Paolella
Econometrics 2014, 2(2), 98-122; https://doi.org/10.3390/econometrics2020098 - 25 Jun 2014
Cited by 20 | Viewed by 7078
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 [...] Read more.
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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