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Data driven time scale in Gaussian quasi-likelihood inference

Author

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  • Shoichi Eguchi

    (Osaka University)

  • Hiroki Masuda

    (Kyushu University)

Abstract

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. High order uniform integrability of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings.

Suggested Citation

  • Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-019-09197-x
    DOI: 10.1007/s11203-019-09197-x
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    References listed on IDEAS

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    Cited by:

    1. Shoichi Eguchi & Yuma Uehara, 2021. "Schwartz‐type model selection for ergodic stochastic differential equation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 950-968, September.

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