Merits and drawbacks of variance targeting in GARCH models

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