For this subclass of ambit fields, the kernel is an exponentially decaying function in time. There is no stochastic volatility and the ambit set satisfies certain conditions such as translation invariance and non-anticipation. Just as how the temporal Ornstein-Uhlenbeck process is used to model volatility clusters in time, this spatio-temporal process can model clusters in space-time. Different non-separable spatio-temporal covariances can also be achieved when we use different shapes for our ambit sets.
In a paper with Almut, we investigate theoretical properties and propose simulation as well as estimation methods. Particular focus is given to the so-called canonical case where space is one-dimensional and the ambit set has linear edges. Prediction formulae in the Gaussian setting and an application of the methods to radiation anomaly data are also discussed. The R code for the analysis is available on Bitbucket.
As an extension, we compared two ways of constructing confidence intervals for our parameter estimates in the Gaussian case. We found that those obtained via pairwise likelihood approximations had lower coverages and were more prone to the curse of dimensionality as opposed to those from a parametric bootstrap procedure. The report and R code are available online.