City Research Online

Time Varying Quantile Lasso

Zbonakova, L., Härdle, W.K. & Wang, W. (2016). Time Varying Quantile Lasso (16/07). London, UK: Department of Economics, City, University of London.


In the present paper we study the dynamics of penalization parameter λ 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 λ 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 λ and its dependency on model characteristics was brought into focus by Hardle 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 λ as a result of the optimization problem. This reveals three possible effects driving λ; 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 λ, which is conducted by a simulation study. After dealing with the theoretical impact of the three model characteristics on λ, empirical application is performed and the idea of implementing the parameter λ into a systemic risk measure is presented. The codes used to obtain the results included in this work are available on

Publication Type: Monograph (Discussion Paper)
Additional Information: Copyright 2016 the authors
Publisher Keywords: Lasso, quantile regression, systemic risk, high dimensions, penalization parameter
Subjects: Q Science > QA Mathematics
Departments: School of Policy & Global Affairs > Economics
School of Policy & Global Affairs > Economics > Discussion Paper Series
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