Francq, Christian and Horvath, Lajos and Zakoian, JeanMichel (2009): Merits and drawbacks of variance targeting in GARCH models.

PDF
MPRA_paper_15143.pdf Download (308kB)  Preview 
Abstract
Variance targeting estimation is a technique used to alleviate the numerical difficulties encountered in the quasimaximum likelihood (QML) estimation of GARCH models. It relies on a reparameterization of the model and a firststep estimation of the unconditional variance. The remaining parameters are estimated by QML in a second step. This paper establishes the asymptotic distribution of the estimators obtained by this method in univariate GARCH models. Comparisons with the standard QML are provided and the merits of the variance targeting method are discussed. In particular, it is shown that when the model is misspecified, the VTE can be superior to the QMLE for longterm prediction or ValueatRisk calculation. An empirical application based on stock market indices is proposed.
Item Type:  MPRA Paper 

Original Title:  Merits and drawbacks of variance targeting in GARCH models 
Language:  English 
Keywords:  Consistency and Asymptotic Normality; GARCH; Heteroskedastic Time Series; Quasi Maximum Likelihood Estimation; ValueatRisk; Variance Targeting Estimator. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  15143 
Depositing User:  Christian Francq 
Date Deposited:  09 May 2009 17:36 
Last Modified:  26 Sep 2019 18:12 
References:  Bauwens, L. and J. Rombouts (2007) Bayesian clustering of many GARCH models. {\it Econometric Reviews} 26, 365386. Berkes, I., Horv\'ath, L. and P. Kokoszka (2003) GARCH processes: structure and estimation. {\em Bernoulli} 9, 201227. Berkes, I. and W. Philipp (1979) Approximation theorems for independent and weakly dependent random vectors. \emph{The Annals of Probability} 7, 2954. Billingsley, P. (1961) The LindebergLevy theorem for martingales. {\em Proceedings of the American Mathematical Society} 12, 788792. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. {\em Journal of Econometrics} 31, 307327. Bradley, R.C. (2005) Basic properties of strong mixing conditions. A survey and some open questions. \emph{Probability Surveys} 2, 107144. Carrasco, M. and X. Chen (2002) Mixing and moment properties of various GARCH and sto\chastic volatility models. {\em Econometric Theory} 18, 1739. Christoffersen, P.F. (2008) ValueatRisk Models. {\it Handbook of Financial Time Series, T.G. Andersen, R.A. Davis, J.P. Kreiss, and T. Mikosch (eds.)}, Springer Verlag. Dehling, H. and W. Philipp (1982) Almost sure invariance principles for weakly dependent vectorvalued random variables. \emph{The Annals of Probability} 10, 689701. Dvoretzky, A. (1972) Asymptotic normality for sums of dependent random variables. \emph{Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability} (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, 513535. Engle, R.F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of the United Kingdom inflation. {\em Econometrica} 50, 9871007. Engle, R.F. (2002) Dynamic conditional correlation : a simple class of multivariate GARCH models. \emph{Journal of Business of Economic Statistics} 20, 339350. Engle, R.F. and K. Kroner (1995) Multivariate simultaneous generalized ARCH. \emph{Econometric Theory} 11, 122150. Engle, R.F. and J. Mezrich (1996) GARCH for Groups. \emph{Risk} 9, 3640. Francq, C. and JM. Zakoïan (2004) Maximum likelihood estimation of pure GARCH and ARMAGARCH processes. {\em Bernoulli} 10, 605637. Francq, C. and JM. Zakoïan (2006) Mixing properties of a general class of GARCH(1,1) models without moment assumptions on the observed process. {\it Econometric Theory} 22, 815834. Herrndorf, N (1984) A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables. \emph{ The Annals of Probability} 12, 141153. Horváth, L., Kokoszka, P. and R. Zitikis (2006) Sample and implied volatility in GARCH models. {\it Journal of Financial Econometrics} 4, 617635. Horváth, L. and F. Liese (2004) $L_p$ estimators in ARCH models. {\it Journal of Statistical Planning and Inference} 119, 277309. Ling, S. (2007) Selfweighted and local quasimaximum likelihood for ARMAGARCH/IGARCH models. {\it Journal of Econometrics} 140, 849873. Straumann, D. (2005) {\it Estimation in conditionally heteroscedastic time series models.} Lecture Notes in Statistics, Springer, Berlin. {van der Vaart, A.W.} (1998) {\it Asymptotic statistics.} Cambridge University Press, United Kingdom. Wald, A. (1949) Note on the consistency of the maximum likelihood estimate. {\em Annals of Mathematical Statistics} 20, 595601. White, H. (1982) Maximum likelihood estimation of misspecified models. {\it Econometrica} 50, 126. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/15143 