Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

SFB649DP2016 047

Time Varying Quantile Lasso

Lenka Zbonakova
Wolfgang Karl Härdle
Weining Wang

In the present paper we study the dynamics of penalization parameter lambda 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 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 lambda
as a result of the optimization problem. This reveals three possible effects driving lambda;
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 lambda, which is conducted by a simulation
study. After dealing with the theoretical impact of the three model characteristics on lambda,
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

Lasso, quantile regression, systemic risk, high dimensions, penalization parameter

JEL Classification:
C21, G01, G20, G32