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Regression coefficient and autoregressive order shrinkage and selection via the lasso

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  • Hansheng Wang
  • Guodong Li
  • Chih-Ling Tsai

Abstract

The "least absolute shrinkage and selection operator" ('lasso') has been widely used in regression shrinkage and selection. We extend its application to the regression model with autoregressive errors. Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients and the other for autoregression coefficients). These tuning parameters can be easily calculated via a data-driven method, but the resulting lasso estimator may not be fully efficient. To overcome this limitation, we propose a second lasso estimator which uses different tuning parameters for each coefficient. We show that this modified lasso can produce the estimator as efficiently as the "oracle". Moreover, we propose an algorithm for tuning parameter estimates to obtain the modified lasso estimator. Simulation studies demonstrate that the modified estimator is superior to the traditional estimator. One empirical example is also presented to illustrate the usefulness of lasso estimators. The extension of the lasso to the autoregression with exogenous variables model is briefly discussed. Copyright 2007 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 69 (2007)
Issue (Month): 1 ()
Pages: 63-78

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Handle: RePEc:bla:jorssb:v:69:y:2007:i:1:p:63-78

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Cited by:
  1. 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.
  2. Søren Johansen & Marco Riani & Anthony C. Atkinson, 2012. "The Selection of ARIMA Models with or without Regressors," Discussion Papers 12-17, University of Copenhagen. Department of Economics.
  3. Leng, Chenlei & Li, Bo, 2010. "Least squares approximation with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 254-261, February.
  4. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.
  5. Camila Epprecht & Dominique Guegan & Álvaro Veiga, 2013. "Comparing variable selection techniques for linear regression: LASSO and Autometrics," Documents de travail du Centre d'Economie de la Sorbonne 13080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  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. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
  8. Zheng, Shurong, 2008. "Selection of components and degrees of smoothing via lasso in high dimensional nonparametric additive models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 164-175, September.
  9. Florian Ziel & Rick Steinert, 2014. "Efficient Modeling and Forecasting of the Electricity Spot Price," Papers 1402.7027, arXiv.org.
  10. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
  11. Anders Bredahl Kock & Laurent A.F. Callot, 2012. "Oracle Efficient Estimation and Forecasting with the Adaptive LASSO and the Adaptive Group LASSO in Vector Autoregressions," CREATES Research Papers 2012-38, School of Economics and Management, University of Aarhus.
  12. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, School of Economics and Management, University of Aarhus.
  13. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
  14. Zhang, Hao Helen & Lu, Wenbin & Wang, Hansheng, 2010. "On sparse estimation for semiparametric linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1594-1606, August.
  15. 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.
  16. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.

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