The Annals of Statistics

Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series

Robert Fox and Murad S. Taqqu

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Abstract

A strongly dependent Gaussian sequence has a spectral density $f(x, \theta)$ satisfying $f(x, \theta) \sim |x|^{-\alpha(\theta)} L_\theta(x)$ as $x \rightarrow 0$, where $0 < \alpha(\theta) < 1$ and $L_\theta(x)$ varies slowly at 0. Here $\theta$ is a vector of unknown parameters. An estimator for $\theta$ is proposed and shown to be consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA, two examples of strongly dependent sequences.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 517-532.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349936

Digital Object Identifier
doi:10.1214/aos/1176349936

Mathematical Reviews number (MathSciNet)
MR840512

Zentralblatt MATH identifier
0606.62096

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
Strong dependence long-range dependence maximum likelihood estimation fractional Gaussian noise fractional ARMA

Citation

Fox, Robert; Taqqu, Murad S. Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series. Ann. Statist. 14 (1986), no. 2, 517--532. doi:10.1214/aos/1176349936. https://projecteuclid.org/euclid.aos/1176349936


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