Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10525811 | Statistics & Probability Letters | 2013 | 14 Pages |
Abstract
Let θ>0. We consider a one-dimensional fractional Ornstein-Uhlenbeck process defined as dXt=âθXtdt+dBt,tâ¥0, where B is a fractional Brownian motion of Hurst parameter Hâ(12,1). We are interested in the problem of estimating the unknown parameter θ. For that purpose, we dispose of a discretized trajectory, observed at n equidistant times ti=iÎn,i=0,â¦,n, and Tn=nÎn denotes the length of the 'observation window'. We assume that Înâ0 and Tnââ as nââ. As an estimator of θ we choose the least squares estimator (LSE) θÌn. The consistency of this estimator is established. Explicit bounds for the Kolmogorov distance, in the case when Hâ(12,34), in the central limit theorem for the LSE θÌn are obtained. These results hold without any kind of ergodicity on the process X.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Khalifa Es-Sebaiy,