Advanced Search
MyIDEAS: Login

Oracle Inequalities for High Dimensional Vector Autoregressions

Contents:

Author Info

  • Anders Bredahl Kock

    ()
    (Aarhus University and CREATES)

  • Laurent A.F. Callot

    ()
    (Aarhus University and CREATES)

Abstract

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. Furthermore, it is shown that under suitable conditions the number of variables selected is of the right order of magnitude and that no relevant variables are excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sign pattern (and hence the correct sparsity pattern). Finally conditions under which the Adaptive LASSO reveals the correct sign pattern with probability tending to one are given. Again, the number of parameters may be much larger than the sample size. Some maximal inequalities for vector autoregressions which might be of independent interest are contained in the appendix.

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_16.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 2012-16.

as in new window
Length: 22
Date of creation: 04 2012
Date of revision:
Handle: RePEc:aah:create:2012-16

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

Related research

Keywords: Vector autoregression; LASSO; Adaptive LASSO; Oracle inequality; Variable selection.;

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. Kock, Anders Bredahl, 2013. "Oracle Efficient Variable Selection In Random And Fixed Effects Panel Data Models," Econometric Theory, Cambridge University Press, vol. 29(01), pages 115-152, February.
  2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
  3. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
  4. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  5. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911.
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. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series 1327, University of St. Gallen, School of Economics and Political Science.
  2. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2012. "The impact of financial crises on the risk-return tradeoff and the leverage effect," CREATES Research Papers 2012-19, School of Economics and Management, University of Aarhus.
  3. Hendrik Kaufmann & Robinson Kruse & Philipp Sibbertsen, 2012. "On tests for linearity against STAR models with deterministic trends," CREATES Research Papers 2012-20, School of Economics and Management, University of Aarhus.
  4. Marcelo C. Medeiros & Eduardo F. Mendes, 2012. "Estimating High-Dimensional Time Series Models," CREATES Research Papers 2012-37, School of Economics and Management, University of Aarhus.
  5. Matteo Barigozzi & Christian T. Brownlees, 2013. "Nets: Network estimation for time series," Economics Working Papers 1391, Department of Economics and Business, Universitat Pompeu Fabra.
  6. Mehmet Caner & Anders Bredahl Kock, 2013. "Oracle Inequalities for Convex Loss Functions with Non-Linear Targets," CREATES Research Papers 2013-51, School of Economics and Management, University of Aarhus.
  7. Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Efficient Estimation and Forecasting with the Adaptive LASSO and the Adaptive Group LASSO in Vector Autoregressions," CREATES Research Papers 2012-38, School of Economics and Management, University of Aarhus.

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:2012-16. 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.