ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

被引：0

作者：

Hu Yaozhong ^{[1
]}

Long Hongwei ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] Florida Atlantic Univ, Dept Math Sci, Boca Raton, FL 33431 USA

来源：

ACTA MATHEMATICA SCIENTIA | 2009年 / 29卷 / 03期

基金：

美国国家科学基金会;

关键词：

asymptotic distribution of LSE; consistency of LSE; discrete observation; least squares method; Ornstein-Uhlenbeck processes; mean-reverting processes; singularity; alpha-stable processes; stable stochastic integrals; INFINITE-VARIANCE; INTEGRALS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the problem of parameter estimation for mean-reverting alpha-stable motion, dX(t) = (a(0) - theta X-0(t))dt + dZ(t), observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (a(0), theta(0)) = (0, 0). If a(0) = 0, then the mean-reverting alpha-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case theta(0) > 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case (theta(0) = 0) and for ergodic case (theta(0) > 0) axe completely different.

引用

页码：599 / 608

页数：10

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