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.
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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
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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
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)
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- 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.
- 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.
- 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.
- 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.
- 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.
- Matteo Barigozzi & Christian Brownlees, 2013.
"Nets: Network Estimation for Time Series,"
723, Barcelona Graduate School of Economics.
- 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.
- Kaufmann, Hendrik & Kruse, Robinson & Sibbertsen, Philipp, 2012.
"On tests for linearity against STAR models with deterministic trends,"
Elsevier, vol. 117(1), pages 268-271.
- 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.
- 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.
- MArcelo C. Medeiros & Eduardo F.Mendes, 2012.
"Estimating High-Dimensional Time Series Models,"
Textos para discussÃ£o
602, Department of Economics PUC-Rio (Brazil).
- 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.
- Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2012. "The impact of financial crises on the risk-return tradeoff and the leverage effect," Working Papers 1295, Queen's University, Department of Economics.
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