  We propose a local version of spatio-temporal log-Gaussian Cox processes
using Local Indicators of Spatio-Temporal Association (LISTA) functions into
the minimum contrast procedure to obtain space as well as time-varying
parameters.
  We resort to the joint minimum contrast fitting method to estimate the set of
second-order parameters. This approach has the advantage of being suitable in
both separable and non-separable parametric specifications of the correlation
function of the underlying Gaussian Random Field.
  We present simulation studies to assess the performance of the proposed
fitting procedure, and show an application to seismic spatio-temporal point
pattern data.
