Comparing Conditional Variance Models: Theory and Empirical Evidence

The aim of this paper is to identify whether the GARCH or the SV based models provide the best goodness of fit to financial time-series data. To investigate the issue, three different formulations for each type (i.e., the standard model, the fat-tailed model, and the asymmetric model) are examined. The models are first compared on theoretical grounds, then estimated using the daily returns from four market indices, and finally subjected to some diagnostic tests. The results demonstrate that for the standard formulation, the SV model fits data better than the GARCH model, while the fat-tailed and the asymmetric models roughly equivalent in describing the key features of returns. The results provide a preliminary analysis for selecting the best model with which to forecast the volatility of financial returns.