  We consider modeling of angular or directional data viewed as a linear
variable wrapped onto a unit circle. In particular, we focus on the
spatio-temporal context, motivated by a collection of wave directions obtained
as computer model output developed dynamically over a collection of spatial
locations. We propose a novel wrapped skew Gaussian process which enriches the
class of wrapped Gaussian process. The wrapped skew Gaussian process enables
more flexible marginal distributions than the symmetric ones arising under the
wrapped Gaussian process and it allows straightforward interpretation of
parameters. We clarify that replication through time enables criticism of the
wrapped process in favor of the wrapped skew process. We formulate a
hierarchical model incorporating this process and show how to introduce
appropriate latent variables in order to enable efficient fitting to dynamic
spatial directional data. We also show how to implement kriging and forecasting
under this model. We provide a simulation example as a proof of concept as well
as a real data example. Both examples reveal consequential improvement in
predictive performance for the wrapped skew Gaussian specification compared
with the earlier wrapped Gaussian version.
