IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity

Listed author(s):
  • Sílvia Gonçalves
  • Lutz Kilian

The main contribution of this paper is twofold. First, we derive the consistency and asymptotic normality of the estimated autoregressive sieve parameters when the data are generated by a stationary linear process with martingale difference errors that are possibly subject to conditional heteroskedasticity of unknown form. To the best of our knowledge, the asymptotic distribution of the least-squares estimator has not been derived under these conditions. Second, we show that a suitably constructed bootstrap estimator will have the same limit distribution as the OLS estimator. Our results provide theoretical justification for the use of either the conventional asymptotic approximation or the bootstrap approximation of the distribution of smooth functions of autoregressive parameters. La contribution de ce papier est double. Premièrement, nous dérivons les propriétés asymptotiques (convergence et normalité asymptotique) des estimateurs de moindre carrés ordinaires des paramètres autoregressifs dans le cadre de modèles autoregressifs d'ordre infini dont les innovations sont des différences de martingale possiblement hétéroscédastiques. Deuxièmement, nous démontrons la validité asymptotique d'une méthode de bootstrap dans ce contexte. Nos résultats justifient théoriquement l'utilisation de la loi asymptotique ou l'utilisation de la distribution de bootstrap comme méthodes d'inférence pour les paramètres autoregressifs ou les fonctions de ceux-ci.

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.

File URL:
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-28.

in new window

Length: 35 pages
Date of creation: 01 May 2003
Handle: RePEc:cir:cirwor:2003s-28
Contact details of provider: Postal:
1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8

Phone: (514) 985-4000
Fax: (514) 985-4039
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2003s-28. 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: (Webmaster)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.