Title: Locally stable regression with unknown activity index
Authors: Hiroki Masuda - Kyushu University (Japan) [presenting]
Abstract: Typically, transition of large-scale dependent data, such as those sampled at ultra high-frequency, are highly non-Gaussian. One of natural ways of modeling such data would be to use continuous-time stochastic processes driven by a non-Gaussian pure-jump noise. The related existing literature is, however, still far from being well-developed. We present tailor-made quasi-likelihood inference results that can efficiently handle such locally and highly non-Gaussian statistical models with the activity index of the driving noise process being unknown. The model setup includes not only Markovian stochastic differential equations but also a class of semimartingale regression models. Of primary interest are cases where estimation target includes not only the rapidly varying scale structure but also the slowly varying trend one.