Variance Initialisation in GARCH Estimation

In setting up the (quasi) maximum likelihood (QML) estimation of the unknown parameters of a GARCH model the initial instances of the conditional variance process must be given values. Many software packages use the sample variance as default while others use exponentially weighted moving averages schemes. Many other alternatives are of course possible, but to the best of our knowledge nobody has studied the performance of QML estimators under the different alternatives. This is probably due to the fact that under rather weak conditions the choice of the initial values is asymptotically irrelevant. Nevertheless, in finite samples different initialisation criteria do matter in particular when highly persistent GARCH processes are considered. This work intends to fill this gap in the literature. The precision of QML estimates under different choices of initialisation and sample dimensions is analysed, and the closeness of the actual (Monte Carlo) finite-sample distributions to the asymptotic approximation is measured.