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Autoregressive process modeling via the Lasso procedure

Author

Listed:
  • Nardi, Y.
  • Rinaldo, A.

Abstract

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular, we derive conditions under which the Lasso estimator for the autoregressive coefficients is model selection consistent, estimation consistent and prediction consistent. Simulation study results are reported.

Suggested Citation

  • Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:528-549
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030.
    4. 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.
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    Citations

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    Cited by:

    1. Ziel, Florian, 2016. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 773-793.
    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 1327, University of St. Gallen, School of Economics and Political Science.
    3. Florian Ziel, 2015. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes," Papers 1502.06557, arXiv.org, revised Dec 2015.
    4. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    5. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    6. MArcelo C. Medeiros & Eduardo F.Mendes, 2012. "Estimating High-Dimensional Time Series Models," Textos para discussão 602, Department of Economics PUC-Rio (Brazil).
    7. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "Adaptative LASSO estimation for ARDL models with GARCH innovations," Textos para discussão 637, Department of Economics PUC-Rio (Brazil).
    8. Lenka Zbonakova & Wolfgang Karl Härdle & Weining Wang, 2016. "Time Varying Quantile Lasso," SFB 649 Discussion Papers SFB649DP2016-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Francesco Audrino & Simon D. Knaus, 2016. "Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1485-1521, December.
    10. repec:bla:jorssb:v:79:y:2017:i:3:p:779-800 is not listed on IDEAS
    11. Smeekes, Stephan & Wijler, Etiënne, 2016. "Macroeconomic Forecasting Using Penalized Regression Methods," Research Memorandum 039, Maastricht University, Graduate School of Business and Economics (GSBE).
    12. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    13. Kascha, Christian & Trenkler, Carsten, 2015. "Forecasting VARs, model selection, and shrinkage," Working Papers 15-07, University of Mannheim, Department of Economics.
    14. repec:taf:emetrv:v:36:y:2017:i:6-9:p:622-637 is not listed on IDEAS
    15. Zbonakova, L. & Härdle, W.K. & Wang, W., 2016. "Time Varying Quantile Lasso," Working Papers 16/07, Department of Economics, City University London.

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