Dynamic Quantile Lasso Regression

Quantile regression has been becoming a relevant and powerful technique to study the whole conditional distribution of a response variable without relying on strong assumptions about the underlying data generating process. Furthermore, quantile regression has been effectively used in many real applications, providing a representation of the relation between the response variable and the covariates, that overcomes traditional mean regression. In this paper, we consider a quantile regression model in which the regression coefficients are assumed to evolve over time, following a stationary stochastic process. Furthermore, since homoskedastic quantile regression models result in location shifts of the regression hyperplane, we extend the time–varying parameter model to allow for heteroskedastic innovations. A dynamic version of the adaptive–Lasso penalty is then introduced to force the dynamic evolution of non relevant parameters to shrink towards zero. A simulation study is carried out to illustrate the model performances