Title: Statistical inference for Vasicek-type model driven by Hermite processes.
Abstract: Let Z denote a Hermite process of order q >= 1 and self-similarity parameter $H \in (1/2, 1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q = 1$, it corresponds to the well-known fractional Brownian motion, whereas it is not Gaussian as soon as $q >= 2$. In the talk, we deal with a Vasicek-type model driven by $Z$, of the form $dX_t = a(b − X_t)dt + dZ_t$. This model includes the fractional Vasicek model and Hermite-driven Ornstein-Uhlenbeck process. Here, $a > 0$ and $b \in R$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations. This is a first step to estimate parameters of a stochastic equation driven by a Hermite process. Joint work with Prof. Ivan Nourdin from University of Luxembourg.
Reference:
I. Nourdin, D. Tran (2019): Statistical inference for Vasicek-type model driven by Hermite processes. Stoch. Proc. Appl., 129, no. 10, pp. 3774-3791.
I. Nourdin, D. Tran (2019): Statistical inference for Vasicek-type model driven by Hermite processes. Stoch. Proc. Appl., 129, no. 10, pp. 3774-3791.