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## Merits and drawbacks of variance targeting in GARCH models

** ** Christian Francq, Lajos Horvath and Jean-Michel Zakoïan
** Keywords: ** Consistency and Asymptotic Normality, GARCH, Heteroskedastic Time Series,
Quasi Maximum Likelihood Estimation, Value-at-Risk, Variance Targeting Estimator

** Abstract: **Variance targeting estimation is a technique
used to alleviate the numerical difficulties encountered in the
quasi-maximum likelihood (QML) estimation of GARCH models. It relies
on a reparameterization of the model and a first-step 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 long-term prediction or Value-at-Risk calculation. An empirical
application based on stock market indices is proposed.

MPRA working paper

R code for the illustrations of the preprint : for the simulations of Table 3 , for the estimations of the 11 stock indices of Tables 4 and 5 , for Figure 1 and
for Figure 2 and Table 6

Slides of talks given at Montréal, March 5, 2009 and
Alger, May 11, 2009

Stock market indices used for the illustrations of the Alger talk : CAC 40,
SP500 (obtained from yahoo).

R code for the illustrations of the Alger talk : on the CAC40 and
on the SP500