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Estimating High-Dimensional Time Series Models

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  • MArcelo C. Medeiros

    ()
    (Department of Economics PUC-Rio)

  • Eduardo F.Mendes

    ()
    (NORTHWESTERN UNIVERSITY)

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 quarterlyUS inflation one-step ahead, and in the second we are interested in the excess return of the S&P500 index. The method used outperforms the usual benchmarks in the literature.

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Bibliographic Info

Paper provided by Department of Economics PUC-Rio (Brazil) in its series Textos para discussão with number 602.

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Length: 33p
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:rio:texdis:602

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  1. Issler, João Victor & Lima, Luiz Renato Regis de Oliveira, 2007. "A Panel Data Approach to Economic Forecasting: The Bias-Corrected Average Forecast," Economics Working Papers (Ensaios Economicos da EPGE) 642, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  2. 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.
  3. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
  4. Eric Hillebrand & Tae-Hwy Lee & Marcelo C. Medeiros, 2012. "Let's Do It Again: Bagging Equity Premium Predictors," CREATES Research Papers 2012-41, School of Economics and Management, University of Aarhus.
  5. 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.
  6. 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.
  7. Amit Goyal & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," Yale School of Management Working Papers amz2412, Yale School of Management, revised 01 Jan 2006.
  8. 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.
  9. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," Working Paper Series in Economics and Finance 296, Stockholm School of Economics, revised 06 Apr 2000.
  10. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
  11. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
  12. 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, vol. 100(3), pages 514-537, June.
  13. repec:wop:humbsf:1999-26 is not listed on IDEAS
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Cited by:
  1. Francesco Audrino & Lorenzo Camponovo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Papers 1312.1473, arXiv.org.
  2. Matteo Barigozzi & Christian T. Brownlees, 2013. "Nets: Network estimation for time series," Economics Working Papers 1391, Department of Economics and Business, Universitat Pompeu Fabra.

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