Modelling non-linear moving average processes using neural networks with error feedback: An application to implied volatility forecasting

We propose an extension to neural network time-series modelling methodology which is particularly appropriate for applications in the financial domain. We advocate the use of error feedback terms as a means of more parsimoniously modelling processes which are partly or wholly 'moving average' in nature (i.e, where new terms are related to past shocks or unpredictable events) rather than purely auto-regressive (where new values are related to both the predictable and the unpredictable components of previous values). We demonstrate that although in principle a (sufficiently high-order) auto-regressive process can approximate the MA process, in practice the diminishing information content of the high-order AR terms will at some point be offset by the increase in model variance caused by the additional model parameters, leading to a degradation in generalisation performance. We report empirical results obtained both by Monte-Carlo simulations and by applying the methodology to the non-trivial problem of forecasting implied volatility for option pricing. In both cases we show a substantial and consistent improvement in results. (C) 1999 Elsevier Science B.V. All rights reserved.