"Inference for adaptive time series models: stochastic volatility and conditionally Gaussian state space form" Charles S Bos Tinbergen Institute and Vrije Universiteit Amsterdam, De Boelelann 1105, 1081 HV Amsterdam, The Netherlands and Neil Shephard Nuffield College, Oxford OX1 1NF, UK. Abstract: 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 algoritms 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 literature. We also develop an effective particle filter for this model which is useful to assess the fit of the model. Keywords: Markov chain Monte Carlo, particle filter, cubic spline, state space form, stochastic volatility.