# Whittle estimator for finite-variance non-Gaussian time series with long memory

Giraitis, Liudas and Taqqu, M. S. (1999) Whittle estimator for finite-variance non-Gaussian time series with long memory. Annals of Statistics, 27 (1). pp. 178-203. ISSN 0090-5364

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## Abstract

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.

Item Type: Article http://imstat.org/aos/ © 1999 Institute of Mathematical Statistics Q Science > QA Mathematics Departments > Mathematics http://www.lse.ac.uk/library/collections/folder/LSERO.aspx 25 Feb 2010 14:44 http://eprints.lse.ac.uk/7163/