Comparing conditional variance models: Theory and empirical evidence

The aim of this paper is to identify which model, between the two classes of conditionalvariance models, GARCH and SV, provide the best goodness of fit in order to describestylized facts of financial time series returns. Our strategy consists in choosing threedifferent formulations for each class, i.e., the standard model, the fat-tailed model, andthe asymmetric model. After comparing these models on a theoretical ground, we fit themto daily returns of market indices and carry out diagnostic tests to identify the model whichprovide the best goodness-of-fit and the best adequacy to some specific qualitative featuresof financial returns, such as heavy-tails, squared returns autocorrelations, and returnsvariances asymmetry. At last, we find that in most of the cases the SV models dominate theGARCH models. In particular, while the GARCH-t formulation fits outliers better thanstandard SV and SV-t, it shows a whole goodness of fit inferior to these latter; asymmetricmodels (EGARCH and SV asymmetric) are not as good as the previous ones in describingfat tails, but are very adequate in approximating squared returns ACFs; the asymmetricSV model is superior than EGARCH in capturing heavy tails and autocorrelations, butthe latter is preferable in describing the asymmetric eect when this is particularly strong.