Ergodic Estimators of double exponential Ornstein-Ulenbeck process

TL;DR

This paper develops ergodic estimators for the parameters of the double exponential Ornstein-Uhlenbeck process observed discretely, proving their statistical properties and demonstrating their effectiveness through simulations.

Contribution

It introduces new ergodic estimators for the process parameters, establishing their consistency and asymptotic normality for fixed sampling intervals.

Findings

Estimators are strongly consistent and asymptotically normal.

Existence and uniqueness of estimators are proven.

Simulation results confirm estimator effectiveness.

Abstract

The goal of this paper is to construct ergodic estimators for the parameters in the double exponential Ornstein-Uhlenbeck process, observed at discrete time instants with time step size h. The existence and uniqueness, the strong consistency, and the asymptotic normality of the estimators are obtained for arbitrarily fixed time step size h. A simulation method of the double exponential Ornstein-Uhlenbeck process is proposed and some numerical simulations are performed to demonstrate the effectiveness of the proposed estimators.