Data driven time scale in Gaussian quasi-likelihood inference

Shoichi Eguchi () and Hiroki Masuda ()
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Shoichi Eguchi: Osaka University
Hiroki Masuda: Kyushu University

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 3, 383-430

Abstract: 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.

Keywords: Bayesian information criterion; Ergodic diffusion process; Gaussian quasi-likelihood; Model-time scale (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11203-019-09197-x

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