Inference for ergodic diffusions plus noise

Shogo H. Nakakita and Masayuki Uchida

Scandinavian Journal of Statistics, 2019, vol. 46, issue 2, 470-516

Abstract: We research an 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 analyze real data as the example such that the data contain observation noise with statistical significance.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:46:y:2019:i:2:p:470-516

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