Contributions to the asymptotic study of Hermite driven processes
Speaker: Tran Thi Thanh Diu (University of Jyvaskyla, Finland)

Time: 14h00, Thursday, July 2, 2020

Room 507, Building A6, Online via google meet meet.google.com/odg-dijq-dhs

Abstract: Let $(Z_t^{q, H})_{t geq 0}$ denote a Hermite process of order $qgeq 1$ and self-similarity parameter $H in (frac{1}{2},1)$. This process is $H$-selfsimilar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $qgeq 2$.

In the talk, we firstly focus on the asymptotic behaviour for quadratic functionals of Hermite-driven long memory moving average processes. In the non-Gaussian case $(q geq 2)$, it converges in the sense of finite-dimensional distribution to the Rosenblatt process, irrespective of self-similarity parameter. In the Gaussian case $(q=1)$, either central or non-central limit theorems may arise depending on the value of self-similarity parameter.

Secondly, we apply the above results to construct an estimator for the drift parameter of a Vasicek-type model driven by Hermite process $Z^{q,H}$. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations