Title: Modeling time scale in high-frequency data
Authors: Hiroki Masuda - Kyushu University (Japan) [presenting]
Shoichi Eguchi - Osaka University (Japan)
Abstract: The aim focuses on when and how time scale can be quantified based on high-frequency sample from a diffusion process. On the one hand, it is well-known that under the standard regularity conditions on the coefficients, the Gaussian quasi-likelihood efficiently works. On the other hand, however, one would get confused with the practical problem what value is to be assigned to the sampling stepsize, for there is no absolute correspondence between model-time and actual-time scales. In this respect, it should be noted that the sampling stepsize is a fine-tuning parameter affecting estimates. Although we could select it in a subjective manner to meet the theoretical requirements on the sampling frequency, it is obviously convenient to have a way to assign a specific value to the stepsize in a data-adaptive manner. We will propose a modified Gaussian quasi-likelihood function which is completely free from the stepsize fine-tuning, and also leads to the following desirable properties under an additional, seemingly non-standard identifiability condition. (1) The associated estimator is rate-efficient and asymptotically normally distributed. (2) The sampling stepsize can be estimated in some sense.