Library Header Image
LSE Research Online LSE Library Services

Gaussian estimation of parametric spectral density with unknown pole

Giraitis, L, Hidalgo, J and Robinson, Peter M. (2001) Gaussian estimation of parametric spectral density with unknown pole. Annals of Statistics, 29 (4). pp. 987-1023. ISSN 0090-5364

Download (369kB) | Preview
Identification Number: 10.1214/aos/1013699989


We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency !. The case of known !, especially ! = 0, is standard in the long memory literature. When ! is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish n ¡ consistency of the estimate of !, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish P--n- consistency and asymptotic normality.

Item Type: Article
Official URL:
Additional Information: Published 2001 © Institute of Mathematical Statistics. LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL ( of the LSE Research Online website.
Divisions: Economics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 15 Feb 2008
Last Modified: 16 Nov 2022 00:09

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics