Minimum distance estimation for fractional Ornstein-Uhlenbeck type process

被引：5

作者：

Liu, Zaiming ^{[1
]}

Song, Na ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2014年

关键词：

long-range dependence; minimum distance estimation; consistency; asymptotic distribution; PARAMETER-ESTIMATION;

D O I：

10.1186/1687-1847-2014-137

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a one-dimensional linear stochastic differential equation defined as dX(t) = theta X-t dt + epsilon dB(t)(H), X-0 = x(0), with theta the unknown drift parameter, where {B-t(H), 0 <= t <= T} is a fractional Brownian motion with epsilon > 0. The consistency and the asymptotic distribution of the minimum Skorohod distance estimator theta*(epsilon) of theta based on the observation {X-t, 0 <= t <= T} is studied as T -> +infinity.

引用

页数：8

共 19 条

[1] Drift parameter estimation in fractional diffusions driven by perturbed random walks [J].

Bertin, Karine ;

Torres, Soledad ;

Tudor, Ciprian A. .

STATISTICS & PROBABILITY LETTERS, 2011, 81 (02) :243-249

[2]

Biagini F, 2008, PROBAB APPL SER, P1

[3]

Brouste A., 2010, STAT INFERENCE STOCH, V13, P1, DOI [10.1007/s11203-009-9035-x, DOI 10.1007/S11203-009-9035-X, DOI 10.1007/s11203-009-9035-x]

[4]

Brouste A., 2012, STAT INFERENCE STOCH, V15, P133, DOI [10.1007/s11203-012-9067-5, DOI 10.1007/S11203-012-9067-5]

[5] Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises [J].

Brouste, Alexandre .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (02) :551-558

[6] Minimum distance parameter estimation for Ornstein-Uhlenbeck processes driven by Levy process [J].

Diop, Aliou ;

Yode, Armel Fabrice .

STATISTICS & PROBABILITY LETTERS, 2010, 80 (02) :122-127

[7] Asymptotics of a minimum distance estimator of the parameter of the Ornstein-Uhlenbeck process [J].

Henaff, S .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (08) :911-914

[8]

Henry M, 2003, THEORY AND APPLICATIONS OF LONG-RANGE DEPENDENCE, P417

[9]

Hu YZ, 2011, ACTA MATH SCI, V31, P1851

[10] Parameter estimation for fractional Ornstein-Uhlenbeck processes [J].

Hu, Yaozhong ;

Nualart, David .

STATISTICS & PROBABILITY LETTERS, 2010, 80 (11-12) :1030-1038

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