IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v102y2011i3p528-549.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00218-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, February.
    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, November.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhatnagar, Sahir R. & Lu, Tianyuan & Lovato, Amanda & Olds, David L. & Kobor, Michael S. & Meaney, Michael J. & O'Donnell, Kieran & Yang, Archer Y. & Greenwood, Celia M.T., 2023. "A sparse additive model for high-dimensional interactions with an exposure variable," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    2. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    3. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    4. repec:hum:wpaper:sfb649dp2016-047 is not listed on IDEAS
    5. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    6. 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.
    7. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    8. 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.
    9. Panxu Yuan & Xiao Guo, 2022. "High-dimensional inference for linear model with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 21-52, January.
    10. Xie, Fang & Xu, Lihu & Yang, Youcai, 2017. "Lasso for sparse linear regression with exponentially β-mixing errors," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 64-70.
    11. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
    12. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    13. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    14. Philip Kostov & Thankom Arun & Samuel Annim, 2014. "Financial Services to the Unbanked: the case of the Mzansi intervention in South Africa," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 8(2), June.
    15. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    16. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    17. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    18. Xia Zheng & Yaohua Rong & Ling Liu & Weihu Cheng, 2021. "A More Accurate Estimation of Semiparametric Logistic Regression," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    19. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    20. Eduardo F. Mendes & Gabriel J. P. Pinto, 2023. "Generalized Information Criteria for Structured Sparse Models," Papers 2309.01764, arXiv.org.
    21. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:528-549. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.