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...

In conditionally heteroskedastic models, the optimal prediction of powers, or logarithms, of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process. A standard procedure for estimating this prediction is to estimate...

This paper introduces the concept of risk parameter in conditional volatility models of the form $\epsilon_t=\sigma_t(\theta_0)\eta_t$ and develops statistical procedures to estimate this parameter. For a given risk measure $r$, the risk parameter is expressed as a function of the volatility...

A two-step approach for conditional Value at Risk (VaR) estimation is considered. In the first step, a generalized-quasi-maximum likelihood estimator (gQMLE) is employed to estimate the volatility parameter, and in the second step the empirical quantile of the residuals serves to estimate the...