Forecasting Time-dependent Conditional Densities: A Seminonparametric Neural Network Approach

In financial econometrics the modeling of asset return series is closely related to the estimation of the corresponding conditional densities. One reason why one is interested in the whole conditional density and not only in the conditional mean, is that the conditional variance can be interpreted as a measure of time-dependent volatility of the return series. In fact, the modeling and the prediction of volatility is one of the central topics in asset pricing. In this paper we propose to estimate conditional densities semi-nonparametrically in a neural network framework. Our recurrent mixture density networks realize the basic ideas of prominent GARCH approaches but they are capable of modeling any continuous conditional density also allowing for time-dependent higher-order moments. Our empirical analysis on daily DAX data shows that out-of-sample volatility predictions of the neural network model are superior to predictions of GARCH models in that they have a higher correlation with implied