Garch models without positivity constraints: exponential or log garch?

Christian Francq, Olivier Wintenberger and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: This paper studies the probabilistic properties and the estimation of the asymmetric log-GARCH($p,q$) model. In this model, the log-volatility is written as a linear function of past values of the log-squared observations, with coefficients depending on the sign of the observations, and past log-volatility values. Conditions are obtained for the existence of solutions and finiteness of their log-moments. We also study the tail properties of the solution. Under mild assumptions, we show that the quasi-maximum likelihood estimation of the parameters is strongly consistent and asymptotically normal. Simulations illustrating the theoretical results and an application to real financial data are proposed.

Keywords: log-GARCH:; Quasi-Maximum; Likelihood:; Strict; stationarity:; Tail; index (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2012-09-16
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (15)

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Related works:
Journal Article: GARCH models without positivity constraints: Exponential or log GARCH? (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:41373

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