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Nonnegative-lasso and application in index tracking

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  • Wu, Lan
  • Yang, Yuehan
  • Liu, Hanzhong

Abstract

This paper proposes the nonnegative-lasso method for variable selection in high dimensional sparse linear regression models with the nonnegative constraints on the coefficients. This method is an extension of Lasso and is shown to have variable selection consistency and estimation consistency under certain condition similar to Irrepresentable Condition in Lasso. To get the solution of the nonnegative-lasso, many algorithms such as Lars, coordinate decent can be used, among which multiplicative updates approach is preferred since it is faster and simpler. The constrained index tracking problem in stock market without short sales is studied in the latter part. The tracking results indicate that nonnegative-lasso can get small tracking error and is successful in assets selection.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:116-126
    DOI: 10.1016/j.csda.2013.08.012
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    Cited by:

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    3. Yang, Yuehan & Xia, Siwei & Yang, Hu, 2023. "Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    4. Anis, Hassan T. & Kwon, Roy H., 2022. "Cardinality-constrained risk parity portfolios," European Journal of Operational Research, Elsevier, vol. 302(1), pages 392-402.
    5. David Puelz & Carlos M. Carvalho & P. Richard Hahn, 2015. "Optimal ETF Selection for Passive Investing," Papers 1510.03385, arXiv.org, revised Nov 2015.
    6. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989, arXiv.org, revised Feb 2020.
    7. Kang, Kai & Maroulas, Vasileios & Schizas, Ioannis & Bao, Feng, 2018. "Improved distributed particle filters for tracking in a wireless sensor network," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 90-108.
    8. Sant’Anna, Leonardo Riegel & Caldeira, João Frois & Filomena, Tiago Pascoal, 2020. "Lasso-based index tracking and statistical arbitrage long-short strategies," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    9. Julio Cezar Soares Silva & Adiel Teixeira de Almeida Filho, 2023. "A systematic literature review on solution approaches for the index tracking problem in the last decade," Papers 2306.01660, arXiv.org, revised Jun 2023.
    10. Chen, Qi-an & Hu, Qingyu & Yang, Hu & Qi, Kai, 2022. "A kind of new time-weighted nonnegative lasso index-tracking model and its application," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    11. Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2019. "Nonparametric estimation of the random coefficients model: An elastic net approach," DICE Discussion Papers 326, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    12. Chungen Shen & Xiao Liu, 2021. "Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations," Journal of Global Optimization, Springer, vol. 81(4), pages 1019-1055, December.
    13. Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2022. "Nonparametric estimation of the random coefficients model: An elastic net approach," Journal of Econometrics, Elsevier, vol. 229(2), pages 299-321.
    14. Sant’Anna, Leonardo Riegel & Righi, Marcelo Brutti & Müller, Fernanda Maria & Guedes, Pablo Cristini, 2022. "Risk measure index tracking model," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 361-383.
    15. Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2019. "Nonparametric estimation of the random coefficients model: An elastic net approach," Ruhr Economic Papers 824, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    16. Ling Peng & Yan Zhu & Wenxuan Zhong, 2023. "Lasso regression in sparse linear model with $$\varphi $$ φ -mixing errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 1-26, January.
    17. Siwei Xia & Yuehan Yang & Hu Yang, 2022. "Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 255-277, March.
    18. Ma, Shaohui & Fildes, Robert, 2017. "A retail store SKU promotions optimization model for category multi-period profit maximization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 680-692.
    19. Ning Li & Hu Yang, 2021. "Nonnegative estimation and variable selection under minimax concave penalty for sparse high-dimensional linear regression models," Statistical Papers, Springer, vol. 62(2), pages 661-680, April.
    20. Xia, Siwei & Yang, Yuehan & Yang, Hu, 2023. "High-dimensional sparse portfolio selection with nonnegative constraint," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    21. Yu Zheng & Bowei Chen & Timothy M. Hospedales & Yongxin Yang, 2019. "Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach," Papers 1911.05052, arXiv.org, revised Nov 2019.

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