A Nonstationary Designer Space-Time Kernel

TL;DR

This paper introduces a nonstationary space-time kernel designed for spatial statistics, allowing more natural modeling of asymmetric temporal phenomena by focusing on the half-line, overcoming limitations of traditional stationary covariance models.

Contribution

The paper proposes a novel nonstationary kernel that is defined over the half-line, enabling better modeling of asymmetric temporal dynamics in spatial statistics.

Findings

The new kernel effectively models nonstationary, asymmetric temporal phenomena.

It improves upon stationary models by capturing time-evolving dynamics.

The kernel is applicable to phenomena with a fixed initial profile.

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.