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Inference for ergodic diffusions plus noise

Author

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  • Shogo H. Nakakita
  • Masayuki Uchida

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.

Suggested Citation

  • Shogo H. Nakakita & Masayuki Uchida, 2019. "Inference for ergodic diffusions plus noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 470-516, June.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:2:p:470-516
    DOI: 10.1111/sjos.12360
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    Cited by:

    1. Tetsuya Kawai & Masayuki Uchida, 2023. "Adaptive inference for small diffusion processes based on sampled data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(6), pages 643-696, August.
    2. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.

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