Advanced Search
MyIDEAS: Login to save this paper or follow this series

On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions

Contents:

Author Info

  • Anders Bredahl Kock

    ()
    (Aarhus University and CREATES)

Abstract

We show that the Adaptive LASSO is oracle efficient in stationary and non-stationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if only these had been included in the model from the outset. In particular this implies that it is able to discriminate between stationary and non-stationary autoregressions and it thereby constitutes an addition to the set of unit root tests. However, it is also shown that the Adaptive LASSO has no power against shrinking alternatives of the form c/T where c is a constant and T the sample size if it is tuned to perform consistent model selection. We show that if the Adaptive LASSO is tuned to performed conservative model selection it has power even against shrinking alternatives of this form. Monte Carlo experiments reveal that the Adaptive LASSO performs particularly well in the presence of a unit root while being at par with its competitors in the stationary setting.

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: ftp://ftp.econ.au.dk/creates/rp/12/rp12_05.pdf
Download Restriction: no

Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-05.

as in new window
Length: 25
Date of creation: 02 Feb 2012
Date of revision:
Handle: RePEc:aah:create:2012-05

Contact details of provider:
Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Adaptive LASSO; Oracle efficiency; Consistent model selection; Conservative model selection; autoregression; shrinkage.;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 201-211, January.
  2. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(01), pages 21-59, February.
  3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
  4. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(9), pages 2065-2082, October.
  5. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1519-1554, November.
  6. Anders Bredahl Kock, 2010. "Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models," CREATES Research Papers, School of Economics and Management, University of Aarhus 2010-56, School of Economics and Management, University of Aarhus.
  7. Hansheng Wang & Guodong Li & Chih-Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 69(1), pages 63-78.
  8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 70(5), pages 849-911.
  9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
Full references (including those not matched with items on IDEAS)

Citations

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

Cited by:
  1. Matteo Barigozzi & Christian Brownlees, 2013. "Nets: Network Estimation for Time Series," Working Papers, Barcelona Graduate School of Economics 723, Barcelona Graduate School of Economics.
  2. Audrino, Francesco & Knaus, Simon, 2012. "Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1224, University of St. Gallen, School of Economics and Political Science.
  3. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1327, University of St. Gallen, School of Economics and Political Science.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:aah:create:2012-05. 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.