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Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models

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  • Audrino, Francesco

    ()

  • Camponovo, Lorenzo

    ()

Abstract

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple (conservative) testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model.

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File URL: http://www1.vwa.unisg.ch/RePEc/usg/econwp/EWP-1327.pdf
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Bibliographic Info

Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1327.

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Length: 30 pages
Date of creation: Oct 2013
Date of revision:
Handle: RePEc:usg:econwp:2013:27

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Keywords: Adaptive lasso; Time series; Oracle properties; Finite sample inference; Taylor rule monetary policy model.;

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  1. Hans Dewachter & Marco Lyrio, 2003. "Macro Factors and the Term Structure of Interest Rates," International Economics Working Papers Series ces0304, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, International Economics.
  2. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
  3. 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.
  4. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, School of Economics and Management, University of Aarhus.
  5. 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.
  6. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February.
  7. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
  8. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
  9. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
  10. Glenn D. Rudebusch, 2010. "Macro-finance models of interest rates and the economy," Working Paper Series 2010-01, Federal Reserve Bank of San Francisco.
  11. Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Inequalities for High Dimensional Vector Autoregressions," CREATES Research Papers 2012-16, School of Economics and Management, University of Aarhus.
  12. Mönch, Emanuel, 2005. "Forecasting the yield curve in a data-rich environment: a no-arbitrage factor-augmented VAR approach," Working Paper Series 0544, European Central Bank.
  13. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.
  14. 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.
  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. Audrino, Francesco & Knaus, Simon, 2012. "Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics," Economics Working Paper Series 1224, University of St. Gallen, School of Economics and Political Science.
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