Minimum $L_1$-norm estimation for fractional Ornstein-Uhlenbeck process driven by a Gaussian 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 Gaussian process, expanding understanding of parameter estimation in such stochastic models.

Contribution

It introduces a new analysis of the minimum L1-norm estimator's asymptotic properties for fractional Ornstein-Uhlenbeck processes driven by general Gaussian processes.

Findings

Asymptotic properties of the estimator are characterized.

The estimator's consistency and distribution are established.

Results apply to a broad class of Gaussian-driven processes.

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 general Gaussian process.