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Asymptotic Inference For Nonstationary Garch

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  • Jensen, S ren Tolver
  • Rahbek, Anders

Abstract

Consistency and asymptotic normality are established for the highly applied quasi-maximum likelihood estimator in the GARCH(1,1) model. Contrary to existing literature we allow the parameters to be in the region where no stationary version of the process exists. This has the important implication that the likelihood-based estimator for the GARCH parameters is consistent and asymptotically normal in the entire parameter region including both stationary and explosive behavior. In particular, there is no knife edge result like the unit root case as hypothesized in Lumsdaine (1996, Econometrica 64, 575 596).Anders Rahbek is grateful for support from the Danish Social Sciences Research Council, the Centre for Analytical Finance (CAF), and the EU network DYNSTOCH. Both authors thank the two anonymous referees and the editor for highly valuable and detailed comments that have, we believe, led to a much improved version of the paper, both in terms of the econometric theory and of the presentation.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 20 (2004)
Issue (Month): 06 (December)
Pages: 1203-1226

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Handle: RePEc:cup:etheor:v:20:y:2004:i:06:p:1203-1226_20

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