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We develop two new classes of space-time Gaussian process models byspecifying covariance functions using what we call a half-spectralrepresentation. The half-spectral representation of a covariance function, $K$,is a special case of standard spectral representations. In addition to theintroduction of two new model classes, we also develop desirable theoreticalproperties of certain half-spectral forms. In particular, for a half-spectralmodel, $K$, we determine spatial and temporal mean-square differentiabilityproperties of a Gaussian process governed by $K$, and we determine whether ornot the spectral density of $K$ meets a regularity condition motivated by ascreening effect analysis. We fit models we develop in this paper to a windpower dataset, and we show our models fit these data better than otherseparable and non-separable space-time models.

Half-Spectral Space-Time Covariance Models