IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

A distribution-free transform of the residuals sample autocorrelations with application to model checking

  • Miguel A. Delgado


  • Carlos Velasco


We propose an asymptotically distribution-free transform of the sample autocorrelations of residuals in general parametric time series models, possibly non-linear in variables. The residuals autocorrelation function is the basic model checking tool in time series analysis, but it is useless when its distribution is incorrectly approximated because the effects of parameter estimation or of unnoticed higher order serial dependence have not been taken into account. The limiting distribution of residuals sample autocorrelations may be difficult to derive, particularly when the underlying innovations are not independent. However, the transformation we propose is easy to implement and the resulting transformed sample autocorrelations are asymptotically distributed as independent standard normals, providing an useful and intuitive device for model checking by taking over the role of the standard sample autocorrelations. We also discuss in detail alternatives to the classical Box-Pierce and Bartlett's Tp-process tests, showing that our transform entails no efficiency loss under Gaussianity. The finite sample performance of the procedures is examined in the context of a Monte Carlo experiment for the two goodness-of-fit tests discussed in the article. The proposed methodology is applied to modeling the autocovariance structure of the well known chemical process temperature reading data already used for the illustration of other statistical procedures.

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 Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we101707.

in new window

Date of creation: Apr 2010
Date of revision:
Handle: RePEc:cte:werepe:we101707
Contact details of provider: Postal: C./ Madrid, 126, 28903 Getafe (Madrid)
Phone: +34-91 6249594
Fax: +34-91 6249329
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. repec:cep:stiecm:/2005/482 is not listed on IDEAS
  2. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
  3. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  4. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  5. Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2002. "Testing For Zero Autocorrelation In The Presence Of Statistical Dependence," Econometric Theory, Cambridge University Press, vol. 18(03), pages 730-743, June.
Full references (including those not matched with items on IDEAS)

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:cte:werepe:we101707. 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: ()

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.