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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 Department of Economics and Business Economics, Aarhus University 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
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
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  4. Anders Bredahl Kock, 2010. "Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models," CREATES Research Papers 2010-56, Department of Economics and Business Economics, Aarhus University.
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  10. 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.
  11. Sydeny C. Ludvigson & Serena Ng, 2005. "Macro Factors in Bond Risk Premia," NBER Working Papers 11703, National Bureau of Economic Research, Inc.
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  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. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," SFB 649 Discussion Papers SFB649DP2011-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  15. 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.
  16. 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.
  17. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
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  19. Kock, Anders Bredahl, 2016. "Consistent And Conservative Model Selection With The Adaptive Lasso In Stationary And Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 32(01), pages 243-259, February.
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