Data driven time scale in Gaussian quasi-likelihood inference

Shoichi Eguchi, Hiroki Masuda

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)383-430
Number of pages48
JournalStatistical Inference for Stochastic Processes
Volume22
Issue number3
DOIs
Publication statusPublished - Oct 15 2019

Fingerprint

Likelihood Inference
Quasi-likelihood
Data-driven
Model Selection
Time Scales
Uniform Integrability
Parametric Estimation
Estimator
Numerical Experiment
Higher Order
Statistics
Unknown
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Data driven time scale in Gaussian quasi-likelihood inference. / Eguchi, Shoichi; Masuda, Hiroki.

In: Statistical Inference for Stochastic Processes, Vol. 22, No. 3, 15.10.2019, p. 383-430.

Research output: Contribution to journalArticle

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