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Subset selection for vector autoregressive processes using Lasso

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  • Hsu, Nan-Jung
  • Hung, Hung-Lin
  • Chang, Ya-Mei
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    Abstract

    A subset selection method is proposed for vector autoregressive (VAR) processes using the Lasso [Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58, 267-288] technique. Simply speaking, Lasso is a shrinkage method in a regression setup which selects the model and estimates the parameters simultaneously. Compared to the conventional information-based methods such as AIC and BIC, the Lasso approach avoids computationally intensive and exhaustive search. On the other hand, compared to the existing subset selection methods with parameter constraints such as the top-down and bottom-up strategies, the Lasso method is computationally efficient and its result is robust to the order of series included in the autoregressive model. We derive the asymptotic theorem for the Lasso estimator under VAR processes. Simulation results demonstrate that the Lasso method performs better than several conventional subset selection methods for small samples in terms of prediction mean squared errors and estimation errors under various settings. The methodology is applied to modeling U.S. macroeconomic data for illustration.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4RC6R3N-1/1/d314244937685c029b118d94ac5b4a3e
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 52 (2008)
    Issue (Month): 7 (March)
    Pages: 3645-3657

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    Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3645-3657

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    Web page: http://www.elsevier.com/locate/csda

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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. David Hendry & Hans-Martin Krolzig, 2000. "Computer Automation of General-to-Specific Model Selection Procedures," Economics Series Working Papers 3, University of Oxford, Department of Economics.
    3. Penm, J. H. W. & Terrell, R. D., 1984. "Multivariate subset autoregressive modelling with zero constraints for detecting 'overall causality'," Journal of Econometrics, Elsevier, vol. 24(3), pages 311-330, March.
    4. Chen, Changhua & Davis, Richard A. & Brockwell, Peter J., 1996. "Order Determination for Multivariate Autoregressive Processes Using Resampling Methods," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 175-190, May.
    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. Hans-Martin Krolzig, 2000. "Computer Automation of General-to-Specific Model Selection Procedures," Econometric Society World Congress 2000 Contributed Papers 0411, Econometric Society.
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    Cited by:
    1. Marcelo C. Medeiros & Eduardo F.Mendes, 2012. "Estimating High-Dimensional Time Series Models," Textos para discussão 602, Department of Economics PUC-Rio (Brazil).

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