Next Article in Journal
A Fast, Accurate Method for Value-at-Risk and Expected Shortfall
Previous Article in Journal
Credible Granger-Causality Inference with Modest Sample Lengths: A Cross-Sample Validation Approach
Econometrics 2014, 2(2), 92-97; doi:10.3390/econometrics2020092

A One Line Derivation of EGARCH

1,2,3,4,*  and 5
Received: 16 June 2014 / Revised: 19 June 2014 / Accepted: 20 June 2014 / Published: 23 June 2014
View Full-Text   |   Download PDF [217 KB, uploaded 23 June 2014]
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 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.
Keywords: leverage; asymmetry; existence; random coefficient models; complex non-linear moving average process leverage; asymmetry; existence; random coefficient models; complex non-linear moving average process
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |

MDPI and ACS Style

McAleer, M.; Hafner, C.M. A One Line Derivation of EGARCH. Econometrics 2014, 2, 92-97.

AMA Style

McAleer M, Hafner CM. A One Line Derivation of EGARCH. Econometrics. 2014; 2(2):92-97.

Chicago/Turabian Style

McAleer, Michael; Hafner, Christian M. 2014. "A One Line Derivation of EGARCH." Econometrics 2, no. 2: 92-97.

Econometrics EISSN 2225-1146 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert