Adaptive estimation and noise detection for an ergodic diffusion with observation noises

TL;DR

This paper develops an adaptive maximum likelihood-type estimation method for ergodic diffusion processes with noisy observations, enabling noise detection, reducing computational load, and providing asymptotic independence of estimators.

Contribution

It introduces a novel adaptive estimation approach that separates noise and process parameters and includes a statistical test for noise presence.

Findings

Estimators are asymptotically independent.

Method reduces computational complexity.

Real data analysis confirms noise detection capability.

Abstract

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood-type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not, and analyse real data as the example such that data contains observation noise with statistical significance.