Oracle Inequalities for High Dimensional Vector Autoregressions
AbstractThis 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 InfoIf 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.
Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-16.
Date of creation: 04 2012
Date of revision:
Contact details of provider:
Web page: http://www.econ.au.dk/afn/
Vector autoregression; LASSO; Adaptive LASSO; Oracle inequality; Variable selection.;
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
- NEP-ECM-2012-05-15 (Econometrics)
- NEP-ETS-2012-05-15 (Econometric Time Series)
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.:
- 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.
- Kock, Anders Bredahl, 2013.
"Oracle Efficient Variable Selection In Random And Fixed Effects Panel Data Models,"
Cambridge University Press, vol. 29(01), pages 115-152, February.
- Anders Bredahl Kock, 2010. "Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models," CREATES Research Papers 2010-56, School of Economics and Management, University of Aarhus.
- 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.
- 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.
- Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
- Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2012.
"The impact of financial crises on the risk-return tradeoff and the leverage effect,"
1295, Queen's University, Department of Economics.
- 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.
- Kaufmann, Hendrik & Kruse, Robinson & Sibbertsen, Philipp, 2012.
"On tests for linearity against STAR models with deterministic trends,"
Diskussionspapiere der Wirtschaftswissenschaftlichen FakultÃ¤t der Leibniz UniversitÃ¤t Hannover
dp-492, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
- Kaufmann, Hendrik & Kruse, Robinson & Sibbertsen, Philipp, 2012. "On tests for linearity against STAR models with deterministic trends," Economics Letters, Elsevier, vol. 117(1), pages 268-271.
- 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.
- Francesco Audrino & Lorenzo Camponovo, 2013.
"Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models,"
- 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.
- MArcelo C. Medeiros & Eduardo F.Mendes, 2012.
"Estimating High-Dimensional Time Series Models,"
Textos para discussÃ£o
602, Department of Economics PUC-Rio (Brazil).
- 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.
- Matteo Barigozzi & Christian T. Brownlees, 2013.
"Nets: Network estimation for time series,"
Economics Working Papers
1391, Department of Economics and Business, Universitat Pompeu Fabra.
- 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.
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.