The efficiency of the estimators of the parameters in GARCH processes

By István Berkes, Lajos Horv'ath. 2004

190 citations recorded by the source corpus.

We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the standard normal density-based quasi-likelihood estimator of Lee and Hansen and Lumsdaine.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e5795588f3bdff869949e10a044c545f127d46f4

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In Mathematical Physics

Citations in the corpus

ASYMPTOTIC NORMALITY OF THE QUASI MAXIMUM LIKELIHOOD ESTIMATOR FOR MULTIDIMENSIONAL CAUSAL PROCESSES (2007, methodology): “A proof of the efficiency of those estimators was obtained in Berkes and Horváth [1], in the case of one-dimensional GARCH(q, q′).”
Risk-parameter estimation in volatility models (2012, methodology): “Estimation of conditional volatility models under moment conditions different from (3) has been studied by Berkes and Horváth (2004), Zhu and Ling (2011), Francq and Zakoian (2012) using nonGaussian QML estimators.”
Optimal predictions of powers of conditionally heteroscedastic processes (2013, methodology): “In the case of standard GARCH models, Berkes and Horváth (2004) derived the asymptotic distribution of such estimators. Fan et al. (2010) and Francq et al. (2011) proposed two-stage procedures based on non-Gaussian QMLEs for estimating standard GARCH models under the standard identifiability conditi”
Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes (2004, background): “…models are those of Lee and Hansen (1994) and Lumsdaine (1996), both for the GARCH(1, 1) case, Straumann and Mikosch (2003) for a general heteroscedastic model including GARCH(1, 1), and Boussama (1998; 2000), Berkes and Horváth (2003a; 2003b) and Berkes et al. (2003) for general GARCH ( p, q).”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, methodology): “For the GARCHðr; sÞ model as given below in Section 2, Berkes et al. (2003) proved strong consistency and asymptotic normality of the QMLE. The same results were proved by Hall and Yao (2003) and Francq and Zakoı̈an (2004). But Hall and Yao (2003) assumed that Ee(2)to1 and discussed the case when EZ”
LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises (2015, methodology): “Furthermore, for the AR model with εt being G-GARCH(1, 1) noise in He and Terasvirta © 2015 American Statistical Association Journal of the American Statistical Association June 2015, Vol. 110, No. 510, Theory & Methods DOI: 10.1080/01621459.2014.977386 784 (1999), Zhang and Ling (in press) showed t”
SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS (2004, methodology): “…the parameters of a GARCH process developed by Lee and Hansen~1994!, Lumsdaine~1996!, and Berkes et al+ ~2003!+ ~For a more general method we refer to Berkes and Horváth, 2004+! To define this estimator for general GARCH~ p,q! processes, denote byu 5 ~x,s1, + + + ,sp, t1, + + + , tq! the generic…”
Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes (2009, methodology): “Franses and Paap (2000) have considered the PGARCH process as an innovation of a more general periodic ARMA-GARCH (PARMAPGARCH) model. In fact, empirical applications (see also Taylor, 2006) show that there is also evidence for a PARMA structure in time-series returns, which are better fitted by PAR”
Periodic Seasonal Reg-ARFIMA–GARCH Models for Daily Electricity Spot Prices (2007, methodology): “The statistical properties of GARCH processes are well established, see, for example, Bollerslev, Engle, and Nelson (1994). Further, Bollerslev and Ghysels (1996) introduced a periodic version of the GARCH model, which is slightly different from ours.”
QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF SEMI-STRONG GARCH MODELS (2009, unknown): “See also Berkes and Horváth (2003, 2004), Hall and Yao (2003), and Robinson and Zaffaroni (2006).”
Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero (2007, methodology): “Recent references dealing with the QML estimation of general GARCH(p, q) are the dissertation by Boussama [9], the monograph by Straumann [25] and the papers by Berkes and Horváth [4,3], Berkes, Horváth and Kokoszka [5], Hall and Yao [14] for GARCH models with heavy tailed errors, and Francq and Zak”
GARCH Models (2010, unknown): “Berkes, Horváth and Kokoszka (2003b) was the first paper to give a rigorous proof of the asymptotic properties of the QMLE in the GARCH(p, q) case under very weak assumptions; see also Berkes and Horváth (2003b, 2004), together with Boussama (1998, 2000).”
Recent Advances in ARCH Modelling (2007, background): “From (12) or (11) one can explicitly find the variance and covariance function of the GARCH(1,1) model in terms of the coefficients α0, α, β and the moments λ1, λ2: Var r(2) 0 = α(2)0κ (2)(1 − γ(2) + γαλ1) (1 − γ)2(1 − γ2 − α2κ2) ,”