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Circular data arise in many areas of application. Recently, there has been
interest in looking at circular data collected separately over time and over space. Here,
we extend some of this work to the spatio-temporal setting, introducing space–time
dependence. We accommodate covariates, implement full kriging and forecasting,
and also allow for a nugget which can be time dependent. We work within a Bayesian
framework, introducing suitable latent variables to facilitate Markov chain Monte
Carlo model fitting. The Bayesian framework enables us to implement full inference,
obtaining predictive distributions for kriging and forecasting. We offer comparison
between the less flexible but more interpretable wrapped Gaussian process and the
more flexible but less interpretable projected Gaussian process. We do this illustratively
using both simulated data and data from computer model output for wave directions
in the Adriatic Sea off the coast of Italy.