The Annals of Statistics

Efficient Parameter Estimation for Self-Similar Processes

Rainer Dahlhaus

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Abstract

Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by Fox and Taqqu. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.

Article information

Source
Ann. Statist., Volume 17, Number 4 (1989), 1749-1766.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347393

Digital Object Identifier
doi:10.1214/aos/1176347393

Mathematical Reviews number (MathSciNet)
MR1026311

Zentralblatt MATH identifier
0703.62091

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 60F99: None of the above, but in this section 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Long range dependence fractional ARMA maximum likelihood estimation efficiency Toeplitz forms

Citation

Dahlhaus, Rainer. Efficient Parameter Estimation for Self-Similar Processes. Ann. Statist. 17 (1989), no. 4, 1749--1766. doi:10.1214/aos/1176347393. https://projecteuclid.org/euclid.aos/1176347393


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