Extrapolation of stable random fields

TL;DR

This paper introduces and justifies three novel extrapolation methods for alpha-stable random fields, providing theoretical guarantees and conditions for their existence, uniqueness, and path continuity.

Contribution

It presents a new extrapolation approach based on covariation maximization and offers rigorous proofs for the methods' validity and properties.

Findings

Existence and uniqueness of solutions are established for all methods.

Conditions for path continuity of the extrapolated fields are provided.

A new covariation-based extrapolation method is introduced.

Abstract

In this paper, we discuss three extrapolation methods for alpha-stable random fields with 1<alpha<=2. We justify them, giving proofs of the existence and uniqueness of the solutions for each method and providing sufficient conditions for path continuity. Two methods are based on minimizing the variability of the difference between the predictor and the theoretical value, whereas in the third approach we provide a new method that maximizes the covariation between these two quantities.