Least Squares Estimation for α-Fractional Bridge with Discrete Observations

Abstract

We consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH, 0≤t1/2 and parameter α>0 is unknown. We are interested in the problem of estimating the unknown parameter α>0. Assume that the process is observed at discrete time ti=iΔn, i=0,…,n, and Tn=nΔn denotes the length of the “observation window.” We construct a least squares estimator α^n of α which is consistent; namely, α^n converges to α in probability as n→∞.