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Time Varying Quantile Lasso


  • Lenka Zbonakova
  • Wolfgang Karl Härdle
  • Weining Wang


In the present paper we study the dynamics of penalization parameter ? of the least absolute shrinkage and selection operator (Lasso) method proposed by Tibshirani (1996) and extended into quantile regression context by Li and Zhu (2008). The dynamic behaviour of the parameter ? can be observed when the model is assumed to vary over time and therefore the fitting is performed with the use of moving windows. The proposal of investigating time series of ? and its dependency on model characteristics was brought into focus by H¨ardle et al. (2016), which was a foundation of FinancialRiskMeter ( Following the ideas behind the two aforementioned projects, we use the derivation of the formula for the penalization parameter ? as a result of the optimization problem. This reveals three possible effects driving ?; variance of the error term, correlation structure of the covariates and number of nonzero coefficients of the model. Our aim is to disentangle these three effect and investigate their relationship with the tuning parameter ?, which is conducted by a simulation study. After dealing with the theoretical impact of the three model characteristics on ?, empirical application is performed and the idea of implementing the parameter ? into a systemic risk measure is presented. The codes used to obtain the results included in this work are available on

Suggested Citation

  • Lenka Zbonakova & Wolfgang Karl Härdle & Weining Wang, 2016. "Time Varying Quantile Lasso," SFB 649 Discussion Papers SFB649DP2016-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2016-047

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    References listed on IDEAS

    1. Härdle, Wolfgang Karl & Wang, Weining & Yu, Lining, 2016. "TENET: Tail-Event driven NETwork risk," Journal of Econometrics, Elsevier, vol. 192(2), pages 499-513.
    2. 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.
    3. Diebold, Francis X. & Yılmaz, Kamil, 2014. "On the network topology of variance decompositions: Measuring the connectedness of financial firms," Journal of Econometrics, Elsevier, vol. 182(1), pages 119-134.
    4. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, vol. 19(2), pages 685-738.
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    6. repec:ecb:ecbwps:20111426 is not listed on IDEAS
    7. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    8. Nardi, Y. & Rinaldo, A., 2011. "Autoregressive process modeling via the Lasso procedure," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 528-549, March.
    9. 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.
    10. Giglio, Stefano & Kelly, Bryan & Pruitt, Seth, 2016. "Systemic risk and the macroeconomy: An empirical evaluation," Journal of Financial Economics, Elsevier, vol. 119(3), pages 457-471.
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    12. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683.
    13. 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.
    14. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • G01 - Financial Economics - - General - - - Financial Crises
    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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