Stochastic volatility versus autoregressive conditional heteroscedasticity

During the last few years there has been an increasing interest in modelling time-varying volatilities of high frequency financial time series. Several models have been proposed, being the most popular between econometricians the autoregressive conditional heteroscedasticity (ARCH) based models. However, in the financial literature stochastic volatility (SV) models have been widely used, mainly when dealing with option valuation models. Both kinds of models imply similar statistical properties on the returns series and both are able of explaining the stilized facts often observed in empirical time series of returns (high kurtosis, autocorrelations of the squares etc;). It is of interest to apply each of these alternative models to the same data set, with the aim of investigating the different implications each might have for the predictability of volatility. In particular, we consider three models, GARCH(l,l), EGARCH(l,l) and AR(l)-SV, and fit each of them to four daily exchange rates. Comparisons are made between the corresponding univariate models. The main conclusion is that there are important differences between the models in the one-step-ahead predictions of volatility. SV models fit better in the center of the distribution of returns while GARCH and EGARCH models are better in the tails of the distribution.