Statistical inference for nonergodic weighted fractional Vasicek models
Open Access
- 26 March 2021
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 8 (3), 291-307
- https://doi.org/10.15559/21-vmsta176
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Statistical inference for nonergodic weighted fractional Vasicek models, Authors: Khalifa Es-Sebaiy, Mishari Al-Foraih, Fares Alazemi , A problem of drift parameter estimation is studied for a nonergodic weighted fractional Vasicek model defined as $d{X_{t}}=\theta (\mu +{X_{t}})dt+d{B_{t}^{a,b}}$, $t\ge 0$, with unknown parameters $\theta >0$, $\mu \in \mathbb{R}$ and $\alpha :=\theta \mu $, whereas ${B^{a,b}}:=\{{B_{t}^{a,b}},t\ge 0\}$ is a weighted fractional Brownian motion with parameters $a>-1$, $|b|<1$, $|b|<a+1$. Least square-type estimators $({\widetilde{\theta }_{T}},{\widetilde{\mu }_{T}})$ and $({\widetilde{\theta }_{T}},{\widetilde{\alpha }_{T}})$ are provided, respectively, for $(\theta ,\mu )$ and $(\theta ,\alpha )$ based on a continuous-time observation of $\{{X_{t}},\hspace{2.5pt}t\in [0,T]\}$ as $T\to \infty $. The strong consistency and the joint asymptotic distribution of $({\widetilde{\theta }_{T}},{\widetilde{\mu }_{T}})$ and $({\widetilde{\theta }_{T}},{\widetilde{\alpha }_{T}})$ are studied. Moreover, it is obtained that the limit distribution of ${\widetilde{\theta }_{T}}$ is a Cauchy-type distribution, and ${\widetilde{\mu }_{T}}$ and ${\widetilde{\alpha }_{T}}$ are asymptotically normal.
Keywords
This publication has 22 references indexed in Scilit:
- Least Squares Type Estimation for Discretely Observed Non-Ergodic Gaussian Ornstein-Uhlenbeck ProcessesActa Mathematica Scientia, 2019
- Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic meanJournal of the Korean Statistical Society, 2017
- Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noiseStochastics, 2016
- Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processesJournal of the Korean Statistical Society, 2016
- Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic meanStatistical Inference for Stochastic Processes, 2016
- Parameter Estimation for α-Fractional BridgesPublished by Springer Science and Business Media LLC ,2013
- Stochastic volatility and option pricing with long-memory in discrete and continuous timeQuantitative Finance, 2012
- Estimation and pricing under long-memory stochastic volatilityAnnals of Finance, 2010
- Some Extensions of Fractional Brownian Motion and Sub-Fractional Brownian Motion Related to Particle SystemsElectronic Communications in Probability, 2007
- Parameter estimation for some non-recurrent solutions of SDEStatistics & Decisions, 2003