Forecasting time-dependent conditional densities: A semi-non-parametric neural network approach

In financial econometrics the modelling 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 modelling and the prediction of volatility is one of the central topics in asset pricing. In this paper we propose to estimate conditional densities semi-non-parametrically in a neural network framework. Our recurrent mixture density networks realize the basic ideas of prominent GARCH approaches but they are capable of modelling any continuous conditional density also allowing for time-dependent higher-order moments. Our empirical analysis of daily FTSE 100 data demonstrates the importance of distributional assumptions in volatility prediction and shows that the out-of-sample forecasting performance of neural networks slightly dominates those of GARCH models.