Data driven time scale in Gaussian quasi-likelihood inference

Shoichi Eguchi; Hiroki Masuda

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arXiv · 1801.10378

Data driven time scale in Gaussian quasi-likelihood inference

Shoichi Eguchi·Hiroki Masuda

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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.

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Shoichi Eguchi, Hiroki Masuda. 2018-01-31. Data driven time scale in Gaussian quasi-likelihood inference. https://arxiv.org/abs/1801.10378

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