Stationarity and Persistence in the GARCH(1,1) Model

Daniel B. Nelson

Econometric Theory, 1990, vol. 6, issue 03, pages 318-334

Abstract: This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition of persistence. We also develop necessary and sufficient conditions for the finiteness of absolute moments of any (including fractional) order.

Date: 1990
View citations in EconPapers

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466600005296 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:6:y:1990:i:03:p:318-334_00

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Mike Eden ().