TY - JOUR
T1 - On drift parameter estimation for reflected fractional Ornstein–Uhlenbeck processes
AU - Lee, Chihoon
AU - Song, Jian
N1 - Publisher Copyright:
© 2016 Taylor & Francis.
PY - 2016/7/3
Y1 - 2016/7/3
N2 - We consider a reflected Ornstein–Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter (Formula presented.). Our goal is to estimate an unknown drift parameter (Formula presented.) on the basis of continuous observation of the state process. We establish Girsanov theorem for the process X, derive the standard maximum likelihood estimator of the drift parameter (Formula presented.) , and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential standard maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.
AB - We consider a reflected Ornstein–Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter (Formula presented.). Our goal is to estimate an unknown drift parameter (Formula presented.) on the basis of continuous observation of the state process. We establish Girsanov theorem for the process X, derive the standard maximum likelihood estimator of the drift parameter (Formula presented.) , and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential standard maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.
KW - Reflected fractional Ornstein–Uhlenbeck processes
KW - fractional Brownian motion
KW - fractional calculus
KW - maximum likelihood estimator
KW - parameter estimation
KW - sequential maximum likelihood estimator
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U2 - 10.1080/17442508.2016.1143472
DO - 10.1080/17442508.2016.1143472
M3 - Article
AN - SCOPUS:84958522964
SN - 1744-2508
VL - 88
SP - 751
EP - 778
JO - Stochastics
JF - Stochastics
IS - 5
ER -