Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case

By R. Belfadli, Khalifa Es-Sebaiy, Y. Ouknine. 2011

83 citations recorded by the source corpus.

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d929a1c39b2f8de126aeae695c6f567115a572af

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Mohamed El Machkouri
2. Khalifa Es-Sebaiy
3. Y. Ouknine
4. Andreas Neuenkirch
5. Samy Tindel
6. Weilin Xiao
7. Frederi G. Viens
8. Jun Yu

In Finance

1. Khalifa Es-Sebaiy
2. Frederi G. Viens
3. Mohamed El Machkouri
4. Y. Ouknine
5. Andreas Neuenkirch
6. Samy Tindel
7. Weilin Xiao
8. Brahim El Onsy

Citations in the corpus

• A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise (2011, background): “In particular, for this process simple continuous time least-square estimators are obtained in [2, 14], for which also covergence rates and asymptotic error distributions are derived.”
• Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes (2015, methodology): “The case of non-ergodic fOU process of the first kind and of the second kind can be found in [4] and [7] respectively.”
• ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018, background): “Nualart, & H. Zhou (2018) Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter.”
• Optimal rates for parameter estimation of stationary Gaussian processes (2016, background): “The case of non-ergodic fOU process of the first kind and of the second kind can be found in [3], [11] and [12] respectively.”
• Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise (2015, background): “In the case ρ < 0, [5] established that ρT of ρ is strongly consistent and asymptotically Cauchy-distributed.”