Skip Navigation

Biometrika 1969 56(2):375-390; doi:10.1093/biomet/56.2.375
© 1969 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
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 BRILLINGER, D. R.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Asymptotic properties of spectral estimates of second order

DAVID R. BRILLINGER

London School of Economics and Political Science

Let X(t) (t = 0, ± 1,...) be a zero mean, r vector-valued, strictly stationary time series satisfying a particular assumption about the near-independence of widely separated values. Given the values X(t) (t = 0, 1,..., T– 1), we construct the statistics: I(T)/XX({gamma})(-{infty}{lambda}lt;{infty}),the matrix of second-order periodograms, FT/XX({lambda}),the matrix of sample spectral measures, fT/XX({lambda}), the matrix of sample spectral densities and c(T)/(u) (u = 0,± 1,...), the matrix of sample covariances. In the paper expressions are derived for the first- and second-order moments and the asymptotic distributions of IT/XX({lambda}), F(T)/XX({lambda}), f(T)/XX({lambda}) and c(T)/XX(u). Our purpose is to determine the form of these moments and to indicate the appearance of the Wishart distribution as an exact limiting distribution for f(T)/XX({lambda}). It has previously been suggested as an approximation.


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.