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Oracle Inequalities for High Dimensional Vector Autoregressions

  • Anders Bredahl Kock


    (Aarhus University and CREATES)

  • Laurent A.F. Callot


    (Aarhus University and CREATES)

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.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-16.

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Length: 22
Date of creation: 04 2012
Date of revision:
Handle: RePEc:aah:create:2012-16
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  1. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
  2. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
  3. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
  4. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
  5. 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.
  6. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
  7. 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.
  8. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," SFB 649 Discussion Papers SFB649DP2011-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
  10. 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.
  11. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
  12. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
  13. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
  14. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for high-dimensional sparse econometric models," CeMMAP working papers CWP41/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  15. 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.
  16. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," Papers 1106.3915,
  17. 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, vol. 69(1), pages 63-78.
  18. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
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