A nonparametric model for stationary time series

We present a family of autoregressive models with nonparametric stationary and transition densities, which achieve substantial modelling flexibility while retaining desirable statistical properties for inference. Posterior simulation involves an intractable normalizing constant; we therefore present a latent extension of the model which enables exact inference through a trans-dimensional MCMC method. We argue the capacity of this family of models to capture time homogeneous transition mechanisms, making them a powerful tool for predictive inference even when the process generating the data does not have a stationary density. Numerical illustrations are presented.