# Spatio-temporal circular models with non-separable covariance structure

## TL;DR

This paper develops a Bayesian spatio-temporal circular data model with non-separable covariance, enabling full inference, kriging, and forecasting, demonstrated on simulated and real wave direction data.

## Contribution

It introduces a novel Bayesian framework for spatio-temporal circular data with non-separable covariance, including covariates and time-dependent nugget effects.

## Key findings

- Bayesian models effectively capture spatio-temporal dependence in circular data.
- The framework allows for accurate kriging and forecasting.
- Comparison shows trade-offs between wrapped and projected Gaussian processes.

## Abstract

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 (MCMC) 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.