A Nonstationary Designer Space-Time Kernel

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.