Skip Navigation

Biometrika 2004 91(1):211-218; doi:10.1093/biomet/91.1.211
© 2004 by Biometrika Trust
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Choudhuri, N.
Right arrow Articles by Roy, A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Contiguity of the Whittle measure for a Gaussian time series

Nidhan Choudhuri1, Subhashis Ghosal2 and Anindya Roy3

1 Department of Statistics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.Anidhan{at}nidhan.cwru.edu 2 Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.ghosal{at}stat.ncsu.edu 3 Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, U.S.A. anindya{at}math.umbc.edu

For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators.In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of estimators and test statistics derived under the Whittle measure can be carried over to the actual distribution.

Key Words: Consistency; Contiguity; Discrete Fourier transform; Periodogram; Spectral density; Whittle likelihood

Received October 2002. Revised July 2003


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.