Advanced Search
MyIDEAS: Login

Asymptotic Inference For Nonstationary Fractionally Integrated Autoregressive Moving-Average Models


Author Info

  • Ling, Shiqing
  • Li, W.K.


This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ( 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ( 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

Download Info

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:
File Function: link to article abstract page
Download Restriction: no

Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 17 (2001)
Issue (Month): 04 (August)
Pages: 738-764

as in new window
Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17

Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page:

Related research



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


Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Søren Johansen & Morten Ørregaard Nielsen, 2007. "Likelihood Inference for a Nonstationary Fractional Autoregressive Model," Discussion Papers 07-27, University of Copenhagen. Department of Economics.
  2. Morten Oerregaard Nielsen, . "Efficient Inference in Multivariate Fractionally Integrated Time Series Models," Economics Working Papers 2002-6, School of Economics and Management, University of Aarhus.
  3. Jakob Roland Munch & Michael Svarer, . "Mortality and Socio-economic Differences in a Competing Risks Model," Economics Working Papers 2001-1, School of Economics and Management, University of Aarhus.


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


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17. 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: (Keith Waters).

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.