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February 1999 Whittle estimator for finite-variance non-Gaussian time series with long memory
Liudas Giraitis, Murad S. Taqqu
Ann. Statist. 27(1): 178-203 (February 1999). DOI: 10.1214/aos/1018031107


We consider time series $Y_t = G(X_t)$ where $X_t$ is Gaussian with long memory and $G$ is a polynomial. The series $Y_t$ may or may not have long memory. The spectral density $g_\theta(x)$ of $Y_t$ is parameterized by a vector $\theta$ and we want to estimate its true value $\theta_0$ . We use a least-squares Whittle-type estimator $\hat{\theta}_N$ for $\theta_0$, based on observations $Y_1,\dots,Y_N$. If $Y_t$ is Gaussian, then $\sqrt{N}(\hat{\theta}_N-\theta_0)$ converges to a Gaussian distribution. We show that for non-Gaussian time series $Y_t$ , this $\sqrt{N}$ consistency of the Whittle estimator does not always hold and that the limit is not necessarily Gaussian. This can happen even if $Y_t$ has short memory.


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Liudas Giraitis. Murad S. Taqqu. "Whittle estimator for finite-variance non-Gaussian time series with long memory." Ann. Statist. 27 (1) 178 - 203, February 1999.


Published: February 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0945.62085
MathSciNet: MR1701107
Digital Object Identifier: 10.1214/aos/1018031107

Primary: 62E20, 62F10
Secondary: 60G18

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 1 • February 1999
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