Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

By Christian Francq, Jean-Michel Zakoian. 2004

591 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/88cbc71b008847844bffaf27ed9d41640fd0a474

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Citations in the corpus

ASYMPTOTIC NORMALITY OF THE QUASI MAXIMUM LIKELIHOOD ESTIMATOR FOR MULTIDIMENSIONAL CAUSAL PROCESSES (2007, methodology): “For instance, if q = q′ = 1 and θ = (c0, c1, d1), we achieve the optimal condition of existence of a second-order stationary solution as e �(2) = {c1, d1 such that c1 > 0 and c1 + d1 15 ].”
ASYMPTOTIC THEORY FOR A FACTOR GARCH MODEL (2009, methodology): “the case of GARCH(p,q) was considered by Boussama (2000), Berkes et al. (2003) and Francq and Zakoian (2004) .”
Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes (2009, methodology): “J ; a:s: The proofs are very similar to those of Francq and Zakoı̈an (2004).”
GARCH models without positivity constraints: Exponential or log GARCH? (2012, methodology): “Assumptions A1, A2 and A4 are similar to those required for the consistency of the QMLE in standard GARCH models (see Berkes et al. 2003, Francq and Zakoian, 2004).”
Parameter Change Test for Poisson Autoregressive Models (2014, methodology): “Further, (A3), (A6), and (A7) are needed to obtain the asymptotic results of the CMLE: INGARCH models automatically satisfy these conditions as seen later (also Francq & Zakoïan, 2004).”
Merits and Drawbacks of Variance Targeting in GARCH Models (2011, background): “It is important to note that the asymptotic normality of the VTE requires the existence of E(ǫ4t ), whereas the strict stationarity is sufficient for the asymptotic normality of the QMLE (see Berkes, Horváth and Kokoszka (2003) and Francq and Zakoïan (2004)).”
Feasible invertibility conditions and maximum likelihood estimation for observation-driven models (2018, result): “Among others, [22] and [39] weaken the conditions for consistency and asymptotic normality and extend the results to a larger class of models.”
Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity (2008, background): “is necessary to obtain the asymptotic normality of the estimators, see Remark 2.7 of Francq and Zakoian (2004) .”
Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero (2007, methodology): “When θ0 ∈ ◦ Θ , FZ [12] (proof of Theorem 2.”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, methodology): “Similar to the proof of Lemma 4.2 in Ling and McAleer (2003a), we can show that S0 and O0 are positive definite (see also Francq and Zakoı̈an, 2004).”