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arXiv · 1101.5790

Parameter estimation for alpha-fractional bridges

Khalifa Es-Sebaiy·Ivan Nourdin
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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.

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Khalifa Es-Sebaiy, Ivan Nourdin. 2011-01-30. Parameter estimation for alpha-fractional bridges. https://arxiv.org/abs/1101.5790

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