Time series have traditionally been analyzed under the assumption of stationarity. Such assumptions are often unreasonable, particularly for processes observed over longer time periods, where the parameters are likely to vary. This project develops fully Bayesian approaches to non-linear and non-Gaussian time series models where the parameters are allowed to evolve. The evolution of the parameters is regularized using a global-local prior that has been popularized in the literature in recent years. The models are mostly estimated using computationally demanding MCMC- and/or particle algorithms. The computational resources at NAISS will be used to run experiments on simulated data over a range of different data-generating processes.