Fisher's Information for Discretely Sampled Levy Processes

TL;DR

This paper investigates how Fisher information behaves for Levy processes sampled at higher frequencies, enabling differentiation between continuous and jump components, as well as various jump types, with derived estimator convergence rates.

Contribution

It introduces methods to distinguish continuous and jump parts of Levy processes and different jump types, along with convergence rates of estimators for discretely sampled data.

Findings

Fisher information asymptotics for Levy processes

Ability to differentiate process components and jump types

Derived convergence rates for estimators

Abstract

This paper studies the asymptotic behavior of the Fisher information for a Levy process discretely sampled at an increasing frequency. We show that it is possible to distinguish not only the continuous part of the process from its jumps part, but also different types of jumps, and derive the rates of convergence of efficient estimators.