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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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    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. Hans-Martin Krolzig, 2000. "Computer Automation of General-to-Specific Model Selection Procedures," Econometric Society World Congress 2000 Contributed Papers 0411, Econometric Society.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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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    Cited by:
    1. Ren, Yunwen & Zhang, Xinsheng, 2010. "Subset selection for vector autoregressive processes via adaptive Lasso," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1705-1712, December.
    2. Marcelo C. Medeiros & Eduardo F. Mendes, 2012. "Estimating High-Dimensional Time Series Models," CREATES Research Papers 2012-37, School of Economics and Management, University of Aarhus.
    3. Ren, Yunwen & Xiao, Zhiguo & Zhang, Xinsheng, 2013. "Two-step adaptive model selection for vector autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 349-364.
    4. Florian Ziel & Rick Steinert, 2014. "Efficient Modeling and Forecasting of the Electricity Spot Price," Papers 1402.7027, arXiv.org, revised Aug 2014.
    5. 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.
    6. Gefang, Deborah, 2014. "Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage," International Journal of Forecasting, Elsevier, vol. 30(1), pages 1-11.

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