Characteristic function and Esscher transform of a switching Levy model for the temperature dynamic

TL;DR

This paper introduces a regime-switching Levy process model for temperature dynamics, capturing jumps and regime changes, with an explicit characteristic function under an Esscher transform, enhancing weather modeling accuracy.

Contribution

It extends temperature models by incorporating Levy noise with regime switching and provides a closed-form characteristic function under an Esscher transform.

Findings

Model captures jumps and regime changes in temperature data

Provides an explicit characteristic function for the process

Enhances understanding of temperature dynamics with Levy processes

Abstract

In this paper we extend models for the dynamic of the temperatures by considering random switching between Levy noises instead of Brownian motions, with a mean-reverting movement towards a seasonal periodic function. The use of Levy noises allows for jumps, capturing, together with the regime changes, sudden and relatively persistent oscillations in the weather. An approximated close-form expression for the characteristic function of the temperature process under an Esscher transform is given.