A Nonstationary Designer Space-Time Kernel

Michael McCourt, Gregory Fasshauer, David Kozak

Keywords: Gaussian random fields, kernel methods

TL;DR: A kernel is defined, using Mercer series, on the half-plane for the purpose of better modeling temporal phenomena with a fixed beginning but no fixed end.

Abstract:

In spatial statistics, kriging models are often designed using
a stationary covariance structure; this translation-invariance
produces models which have numerous favorable properties. This
assumption can be limiting, though, in circumstances where the
dynamics of the model have a fundamental asymmetry, such as in
modeling phenomena that evolve over time from a fixed initial
profile. We propose a new nonstationary kernel which is only
defined over the half-line to incorporate time more naturally
in the modeling process.