GARCH models without positivity constraints: Exponential or Log GARCH?

Zakoïan, Jean-Michel; Wintenberger, Olivier; Francq, Christian

Zakoïan, Jean-Michel; Wintenberger, Olivier; Francq, Christian (2013), GARCH models without positivity constraints: Exponential or Log GARCH?, Journal of Econometrics, 177, 1, p. 34-46. http://dx.doi.org/10.1016/j.jeconom.2013.05.004

Type

Article accepté pour publication ou publié

Date

2013

Journal name

Journal of Econometrics

Volume

177

Number

Publisher

Elsevier

Pages

34-46

Abstract (EN)

This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH model, which are already known, with those of an asymmetric version of the log-GARCH. The quasi-maximum likelihood estimation of the log-GARCH parameters is shown to be strongly consistent and asymptotically normal. Similar estimation results are only available for particular EGARCH models, and under much stronger assumptions. The comparison is pursued via simulation experiments and estimation on real data.

Subjects / Keywords

Tail index; Strict stationarity; Quasi-Maximum Likelihood; log-GARCH; EGARCH

JEL

C13 - Estimation: General
C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes