Volatility modulated moving averages

In this subclass of ambit fields, we consider only spatial fields. A volatility modulated moving average is formed by inserting a stochastic volatility process into the integral of a Gaussian moving average or process convolution. This enables us to model spatial heteroskedasticity. That is, differing covariance structures across space.

As in the previous project, we look at the theoretical properties of the moving average, and investigate simulation and estimation methods. A key example is in two dimensions and involves Gaussian kernels as well as a Lévy moving average for the stochastic volatility. This is fitted to sea surface temperature anomaly data. A paper co-written with Almut has been published in the Spatial Statistics journal and the R code for the analysis is available on Bitbucket.