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June, 1986 Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series
Robert Fox, Murad S. Taqqu
Ann. Statist. 14(2): 517-532 (June, 1986). DOI: 10.1214/aos/1176349936

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.

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Robert Fox. Murad S. Taqqu. "Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series." Ann. Statist. 14 (2) 517 - 532, June, 1986. https://doi.org/10.1214/aos/1176349936

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0606.62096
MathSciNet: MR840512
Digital Object Identifier: 10.1214/aos/1176349936

Subjects:
Primary: 62F12
Secondary: 60F99, 62M10

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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