Error bounds and asymptotic expansions for toeplitz product functionals of unbounded spectra
This paper establishes error orders for integral limit approximations to traces of powers (to the pth order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices are Fourier transforms of functions which we allow to be bounded, unbounded, or even to vanish on [ - π, π], thereby including important cases such as the spectral functions of fractional processes. Error rates are also given in the case in which the matrix product involves inverse matrices. The rates are sharp up to an arbitrarily small ϵ > 0. The results improve on the o(1) rates obtained in earlier work for analogous products. For the p = 1 case, an explicit second-order asymptotic expansion is found for a quadratic functional of the autocovariance sequences of stationary long-memory time series. The order of magnitude of the second term in this expansion is shown to depend on the long-memory parameters. It is demonstrated that the pole in the first-order approximation is removed by the second-order term, which provides a substantially improved approximation to the original functional. Copyright 2004 Blackwell Publishing Ltd.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 25 (2004)
Issue (Month): 5 (09)
|Contact details of provider:|| Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 |
|Order Information:||Web: http://www.blackwellpublishing.com/subs.asp?ref=0143-9782|
When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:25:y:2004:i:5:p:733-753. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.