# The wrapped skew Gaussian process for analyzing spatio-temporal data

## TL;DR

This paper introduces a wrapped skew Gaussian process for modeling spatio-temporal directional data, offering greater flexibility and improved predictive performance over traditional wrapped Gaussian models.

## Contribution

The paper develops a novel wrapped skew Gaussian process that enhances modeling flexibility and interpretability for spatio-temporal directional data.

## Key findings

- Improved predictive accuracy with the wrapped skew Gaussian process.
- Effective hierarchical modeling and efficient inference methods.
- Successful application to real and simulated data demonstrating advantages.

## Abstract

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.