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Estimating High-Dimensional Time Series Models

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  • Marcelo C. Medeiros

    ()
    (Pontifical Catholic University of Rio de Janeiro)

  • Eduardo F. Mendes

    ()
    (Pontifical Catholic University of Rio de Janeiro)

Abstract

We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume both the number of covariates in the model and candidate variables can increase with the number of observations and the number of candidate variables is, possibly, larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency), and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. A simulation study shows the method performs well in very general settings. Finally, we consider two applications: in the first one the goal is to forecast quarterly US inflation one-step ahead, and in the second we are interested in the excess return of the S&P 500 index. The method used outperforms the usual benchmarks in the literature.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-37.

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Length: 30
Date of creation: 04 Sep 2012
Date of revision:
Handle: RePEc:aah:create:2012-37

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Web page: http://www.econ.au.dk/afn/

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Keywords: sparse models; shrinkage; LASSO; adaLASSO; time series; forecasting.;

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References

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  1. Issler, João Victor & Lima, Luiz Renato, 2009. "A panel data approach to economic forecasting: The bias-corrected average forecast," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 153-164, October.
  2. Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Inequalities for High Dimensional Vector Autoregressions," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-16, School of Economics and Management, University of Aarhus.
  3. Erik Hillebrand & Tae-Hwy Lee & Marcelo Cunha Medeiros, 2012. "Let´s do it again: bagging equity premium predictors," Textos para discussão, Department of Economics PUC-Rio (Brazil) 604, Department of Economics PUC-Rio (Brazil).
  4. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(3), pages 528-549, March.
  5. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(7), pages 3645-3657, March.
  7. Amit Goval & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," NBER Working Papers 10483, National Bureau of Economic Research, Inc.
  8. repec:wop:humbsf:1999-26 is not listed on IDEAS
  9. Ferreira, Miguel A. & Santa-Clara, Pedro, 2011. "Forecasting stock market returns: The sum of the parts is more than the whole," Journal of Financial Economics, Elsevier, Elsevier, vol. 100(3), pages 514-537, June.
  10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
  11. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, Elsevier, vol. 146(2), pages 304-317, October.
  12. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
  13. 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, Royal Statistical Society, vol. 69(1), pages 63-78.
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Citations

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Cited by:
  1. Camila Epprecht & Dominique Guegan & Álvaro Veiga, 2013. "Comparing variable selection techniques for linear regression: LASSO and Autometrics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00917797, HAL.
  2. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series, University of St. Gallen, School of Economics and Political Science 1327, University of St. Gallen, School of Economics and Political Science.
  3. Matteo Barigozzi & Christian T. Brownlees, 2013. "Nets: Network estimation for time series," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1391, Department of Economics and Business, Universitat Pompeu Fabra.

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