In this paper we replace the Gaussian errors in the standard Gaussian, linear state space model with stochastic volatility processes. This is called a GSSF-SV model. We show that conventional MCMC algorithms for this type of model are ineffective, but that this problem can be removed by reparameterising the model. We illustrate our results on an example from financial economics and one from the nonparametric regression model. We also develop an effective particle filter for this model which is useful to assess the fit of the model.
Markov chain Monte Carlo particle filter cubic spline state space form stochastic volatility