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Time varying quantile Lasso

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  • Zbonakova, Lenka
  • Härdle, Wolfgang Karl
  • Wang, Weining

Abstract

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 (http://frm.wiwi.hu-berlin.de). 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 http://quantlet.de/d3/ia/.

Suggested Citation

  • Zbonakova, Lenka & Härdle, Wolfgang Karl & Wang, Weining, 2016. "Time varying quantile Lasso," SFB 649 Discussion Papers 2016-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-047
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    References listed on IDEAS

    as
    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.
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    More about this item

    Keywords

    Lasso; quantile regression; systemic risk; high dimensions; penalization parameter;
    All these keywords.

    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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