Skip Navigation

Biometrika 2004 91(1):195-209; doi:10.1093/biomet/91.1.195
© 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 Fan, J.
Right arrow Articles by Zhang, W.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Generalised likelihood ratio tests for spectral density

Jianqing Fan1 and Wenyang Zhang2

1 Department of Operation Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, U.S.Ajqfan{at}princeton.edu 2 Institute of Mathematics and Statistics, University of Kent, Canterbury, Kent CT2 7NF, U.K.w.zhang{at}kent.ac.uk

There are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models.In this paper, we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms. We propose a bias correction method for the generalised likelihood ratio test of Fan et al. (2001). In particular, our methods can be applied to test whether or not a residual series is white noise. Sampling properties of the proposed tests are established. A bootstrap approach is proposed for estimating the null distribution of the test statistics. Simulation studies investigate the accuracy of the proposed bootstrap estimate and compare the power of the various ways of constructing the generalised likelihood ratio tests as well as some classic methods like the Cramér–von Mises and Ljung–Box tests. Our results favour the newly proposed bias reduction method using the local likelihood estimator.

Key Words: ARMA model; Generalised likelihood ratio test; Local least squares; Local likelihood; Periodogram; Spectral density

Received January 2003. Revised May 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.