Acta mathematica scientia, Series B >
ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS
Received date: 2008-11-19
Online published: 2009-05-20
Supported by
Hu is supported by the National Science Foundation under Grant No. DMS0504783; Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science
We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = (α0 − θ0Xt)dt + dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (α0, θ0) = (0, 0). If α0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 > 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case (θ0 = 0) and for ergodic case (θ0 > 0) are completely different.
HU Yao-Zhong , LONG Gong-Wei . ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 599 -608 . DOI: 10.1016/S0252-9602(09)60056-4
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