Mixtures of autoregressive models for financial risk analysis

Abstract

The structure of the time-series of returns for the IBEX35 stock index is analyzed by means of a class of non-linear models that involve probabilistic mixtures of autoregressive processes. In particular, a specification and implementation of probabilistic mixtures of GARCH processes is presented. These mixture models assume that the time series is generated by one of a set of alternative autoregressive models whose probabilities are produced by a gating network. The ultimate goal is to provide an adequate framework for the estimation of conditional risk measures, which can account for non-linearities, heteroskedastic structure and extreme events in financial time series. Mixture models are sufficiently flexible to provide an adequate description of these features and can be used as an effective tool in financial risk analysis. © Springer-Verlag Berlin Heidelberg 2002.