Modelling financial time series with switching state space models

The deeciencies of stationary models applied to nancial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for nancial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to Ghahramani and Hinton, 1998]. The performance of the SSSM is evaluated on several nancial data sets and it is shown to improve on a number of existing benchmark methods.