Parameter Estimation from Occupation Times

TL;DR

This paper introduces a direct method to estimate parameters of the centered Ornstein-Uhlenbeck process using occupation times, validated through simulations, enabling efficient parameter recovery from observed data.

Contribution

The paper presents a novel equation for computing expected occupation times of the Ornstein-Uhlenbeck process, facilitating parameter estimation via least squares.

Findings

Accurate parameter recovery from simulated occupation times

Validation of the method through Monte-Carlo simulations

Efficient estimation technique for Ornstein-Uhlenbeck parameters

Abstract

We derive an equation to compute directly the expected occupation time of the centered Ornstein-Uhlenbeck process. This allows us to identify the parameters of the Ornstein-Uhlenbeck process for available occupation times via a standard least squares minimization. To test the method, we generate occupation times via Monte-Carlo simulations and recover the parameters with the above mentioned procedure.