Stylized facts of return series, robust estimates and three popular models of volatility

Financial return series of sufficiently high frequency display stylized facts such as volatility clustering, high kurtosis, low starting and slow-decaying autocorrelation function of squared returns and the so-called Taylor effect. In order to evaluate the capacity of volatility models to reproduce these facts, we apply both standard and robust measures of kurtosis and autocorrelation of squares to first-order Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Exponential GARCH (EGARCH) and Autoregressive Stochastic Volaticity (ARSV) models. Robust measures provide a fresh view of stylized facts, which is useful because many financial time series can be viewed as being contaminated with outliers.