Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters

02/17/2020

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by   Abdulaziz Alsenafi, et al.

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Let B^a,b:={B_t^a,b,t≥0} be a weighted fractional Brownian motion of parameters a>-1, |b|<1, |b|<a+1. We consider a least square-type method to estimate the drift parameter θ>0 of the weighted fractional Ornstein-Uhlenbeck process X:={X_t,t≥0} defined by X_0=0; dX_t=θ X_tdt+dB_t^a,b. In this work, we provide least squares-type estimators for θ based continuous-time and discrete-time observations of X. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all (a,b) such that a>-1, |b|<1, |b|<a+1. Here we extend the results of <cit.> (resp. <cit.>), where the strong consistency and the asymptotic distribution of the estimators are proved for -1/2<a<0, -a<b<a+1 (resp. -1<a<0, -a<b<a+1).