Non-linear versus non-gaussian volatility models

One of the most challenging topics in financial time series analysis is the modeling of conditional variances of asset returns. Although conditional variances are not directly observable there are numerous approaches in the literature to overcome this problem and to predict volatilities on the basis of historical asset returns. The most prominent approach is the class of GARCH models where conditional variances are governed by a linear autoregressive process of past squared returns and variances. Recent research in this field, however, has focused on modeling asymmetries of conditional variances by means of non-linear models. While there is evidence that such an approach improves the fit to empirical asset returns, most non-linear specifications assume conditional normal distributions and ignore the importance of alternative models. Concentrating on the distributional assumptions is, however, essential since asset returns are characterized by excess kurtosis and hence fat tails that cannot be explained by models with suffcient heteroskedasticity. In this paper we take up the issue of returns' distributions and contrast it with the specification of non-linear GARCH models. We use daily returns for the Dow Jones Industrial Average over a large period of time and evaluate the predictive power of different linear and non-linear volatility specifications under alternative distributional assumptions. Our empirical analysis suggests that while non-linearities do play a role in explaining the dynamics of conditional variances, the predictive power of the models does also depend on the distributional assumptions. (author's abstract)