Research project Bayesian methods for general time-varying parameter models with global-local shrinkage process priors
Time series data are among the most common data types in all sciences. This research project develops new models and computationally efficient methods for time series models where the data generating process changes over time.
Statistical models for time series data typically assume stationarity - that the data generating process is unchanged over time. This simplifying assumption is often unreasonable in applications, where the system is naturally subject to change. Models with time-varying parameters are a natural alternative, but tend to have too simplistic models for the parameter evolution. A new strand of global-local shrinkage process priors have recently been developed, extending the widely used horseshoe-type of priors to time-varying parameter models for time series and other forms of dependent data.
Most of the existing methodological work with global-local shrinkage process priors is restricted to conditionally linear Gaussian models. The current project develops computationally efficient methods and software for Bayesian inference in non-linear and non-Gaussian time-varying parameter models with global-local shrinkage process priors. This extends the applicability of the models to, for example, counts and proportions data with multiple seasonal periods. The project also focuses on improved global-local shrinkage processes and methods for prior elicitation.