Bernoulli

  • Bernoulli
  • Volume 10, Number 4 (2004), 605-637.

Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

Christian Francq and Jean-Michel Zakoïan

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Abstract

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

Article information

Source
Bernoulli Volume 10, Number 4 (2004), 605-637.

Dates
First available in Project Euclid: 23 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.bj/1093265632

Digital Object Identifier
doi:10.3150/bj/1093265632

Mathematical Reviews number (MathSciNet)
MR2076065

Zentralblatt MATH identifier
1067.62094

Keywords
ARMA asymptotic normality consistency GARCH heteroscedastic time series, maximum likelihood estimation

Citation

Francq, Christian; Zakoïan, Jean-Michel. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes. Bernoulli 10 (2004), no. 4, 605--637. doi:10.3150/bj/1093265632. http://projecteuclid.org/euclid.bj/1093265632.


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