Data driven time scale in Gaussian quasi-likelihood inference

2018/01/31 by Shoichi Eguchi, Eguchi, Shoichi, H. Masuda +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1801.10378

openalex publication_date 2018/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. The L^q-boundedness 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. Also provided is a real data example.

Citations

• The Commutation Matrix: Some Properties and Applications

Cited by

• Quasi-likelihood inference for SDE with mixed-effects observed at high frequency

Related

• Gaussian quasi-information criteria for ergodic Lévy driven SDE
• Estimation of ergodic square-root diffusion under high-frequency sampling
• Statistical inference for ergodic diffusion with Markovian switching
• Schwarz type model comparison for LAQ models
• Quasi-likelihood analysis of an ergodic diffusion plus noise