Time Varying Quantile Lasso

SFB 649 Discussion Paper 2016-047

26 Pages Posted: 7 Nov 2016

See all articles by Lenka Zbonakova

Lenka Zbonakova

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Weining Wang

Humboldt University of Berlin

Date Written: November 3, 2016

Abstract

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 coeffcients 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.

Keywords: lasso, quantile regression, systemic risk, high dimensions, penalization parameter

JEL Classification: C21, G01, G20, G32

Suggested Citation

Zbonakova, Lenka and Härdle, Wolfgang K. and Wang, Weining, Time Varying Quantile Lasso (November 3, 2016). SFB 649 Discussion Paper 2016-047. Available at SSRN: https://ssrn.com/abstract=2865608 or http://dx.doi.org/10.2139/ssrn.2865608

Lenka Zbonakova

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE) ( email )

Spandauer Strasse 1
Berlin, D-10178
Germany

Wolfgang K. Härdle (Contact Author)

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Weining Wang

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

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