GARCH based value-at-risk assessment when the observed process is iid

In this paper, we study the estimation of Value-at-Risk (VaR) using GARCH models when the observed process is actually iid. Such an overfitting situation entails that the almost sure consistency of the quasi-maximum likelihood estimator (QMLE) is not ensured. Therefore, a simulation experiment is performed to shed some light on the consequences of such a poor parameters estimation on the VaR assessment. Since the GARCH specification is not identified when the ARCH and persistence parameters are equal to zero, then a constant volatility is predicted. As a consequence, it turns out that the VaR evaluation is not affected by the estimation drawbacks.