Inference for ergodic diffusions plus noise

TL;DR

This paper develops an adaptive maximum likelihood estimation method for ergodic diffusions with noisy observations, achieving asymptotic independence of estimators, reducing computational load, and including a noise detection test, validated on real data.

Contribution

It introduces a novel adaptive estimation approach for ergodic diffusions with noise, improving computational efficiency and providing a noise detection test.

Findings

Estimators for noise variance, diffusion, and drift are asymptotically independent.

The method reduces computational complexity compared to joint maximum likelihood estimation.

Real data analysis confirms the significance of observation noise.

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.