Targeting estimation of CCC-Garch models with infinite fourth moments

As an alternative to quasi-maximum likelihood, targeting estimation is a much applied estimation method for univariate and multivariate GARCH models. In terms of variance targeting estimation recent research has pointed out that at least finite fourth-order moments of the data generating process is required if one wants to perform inference in GARCH models relying on asymptotic normality of the estimator, see Pedersen and Rahbek (2014) and Francq et al. (2011). Such moment conditions may not be satisfied in practice for financial returns highlighting a large drawback of variance targeting estimation. In this paper we consider the large-sample properties of the variance targeting estimator for the multivariate extended constant conditional correlation GARCH model when the distribution of the data generating process has infinite fourth moments. Using non-standard limit theory we derive new results for the estimator stating that its limiting distribution is multivariate stable. The rate of consistency of the estimator is slower than squareroot T (as obtained by the quasi-maximum likelihood estimator) and depends on the tails of the data generating process