Models with time-varying parameters are widely used, both in the natural and social sciences, but have until recently had too simplistic models for the parameter evolution. A new strand of global-local shrinkage process priors have recently been developed, but fast, efficient and robust algorithms for Bayesian inference are largely lacking. This project contribute on three fronts. First, we extend our recent work on time-varying multi-seasonal AR models with global-local parameter evolution to ARMA processes, using a parameterization that guarantees stability and invertibility at every time point. Second, we aim to develop efficient computational methods for Bayesian inference in time-varying parameter models with global-local shrinkage process priors, with a particular focus on non-linear models, such as the seasonal ARMA model; this is challenging since state-of-the-art particle MCMC methods tend to work poorly for this class of models. Third, we plan to substantially extend the applicability of the models by developing Bayesian inference metods for general non-linear/non-Gaussian models with global-local shrinkage process priors, e.g. for counts and proportions data.