Half-Spectral Space-Time Covariance Models

TL;DR

This paper introduces two novel classes of space-time Gaussian process models using half-spectral covariance functions, providing theoretical insights and demonstrating improved data fitting over existing models.

Contribution

The paper develops two new space-time Gaussian process models based on half-spectral covariance functions and analyzes their theoretical properties.

Findings

Models fit wind power data better than existing space-time models.

Derived conditions for mean-square differentiability of processes.

Established regularity conditions for spectral densities.

Abstract

We develop two new classes of space-time Gaussian process models by specifying covariance functions using what we call a half-spectral representation. The half-spectral representation of a covariance function, $K$, is a special case of standard spectral representations. In addition to the introduction of two new model classes, we also develop desirable theoretical properties of certain half-spectral forms. In particular, for a half-spectral model, $K$, we determine spatial and temporal mean-square differentiability properties of a Gaussian process governed by $K$, and we determine whether or not the spectral density of $K$ meets a regularity condition motivated by a screening effect analysis. We fit models we develop in this paper to a wind power dataset, and we show our models fit these data better than other separable and non-separable space-time models.