Parameter estimation for alpha-fractional bridges
Probability
2013-08-06 v3 Statistics Theory
Statistics Theory
Abstract
Let alpha,T>0. We study the asymptotic properties of a least squares estimator for the parameter alpha of a fractional bridge defined as dX_t=-alpha*X_t/(T-t)dt+dB_t, with t in [0,T) and where B is a fractional Brownian motion of Hurst index H>1/2. Depending on the value of alpha, we prove that we may have strong consistency or not as t tends to T. When we have consistency, we obtain the rate of this convergence as well. Also, we compare our results to the (known) case where B is replaced by a standard Brownian motion W.
Cite
@article{arxiv.1101.5790,
title = {Parameter estimation for alpha-fractional bridges},
author = {Khalifa Es-Sebaiy and Ivan Nourdin},
journal= {arXiv preprint arXiv:1101.5790},
year = {2013}
}
Comments
21 pages. To appear in the Festschrift in Honor of David Nualart, a volume to be published by Springer in the Proceedings in Mathematics Series