Minimum $L_1$-norm estimation for fractional Ornstein-Uhlenbeck type process driven by a Hermite process

TL;DR

This paper studies the asymptotic behavior of the minimum L1-norm estimator for the drift parameter in a fractional Ornstein-Uhlenbeck process driven by a Hermite process, contributing to the understanding of parameter estimation in complex stochastic models.

Contribution

It introduces and analyzes the asymptotic properties of a new L1-norm estimator for the drift parameter in a Hermite-driven fractional Ornstein-Uhlenbeck process.

Findings

Establishes the asymptotic distribution of the estimator.

Provides conditions for consistency and asymptotic normality.

Extends estimation theory to processes driven by Hermite noise.

Abstract

We investigate the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process driven by a Hermite process.