The generalized hyperbolic family and automatic model selection through the multiple-choice LASSO

TL;DR

This paper introduces a hierarchical multiple-choice LASSO method for automatic model selection within the generalized hyperbolic distribution family, enabling simultaneous inference and model choice, demonstrated through simulations.

Contribution

It presents a novel hierarchical multiple-choice LASSO approach for joint model selection and inference in the GH distribution family, including implementation in R.

Findings

Effective model selection among GH family models demonstrated in simulations

Hierarchical multiple-choice LASSO improves inference accuracy

Method implemented in accessible R functions

Abstract

We revisit the generalized hyperbolic (GH) distribution and its nested models. These include widely used parametric choices like the multivariate normal, skew-t, Laplace, and several others. We also introduce the multiple-choice LASSO, a novel penalized method for choosing among alternative constraints on the same parameter. A hierarchical multiple-choice LASSO penalized likelihood is optimized to perform simultaneous model selection and inference within the GH family. We illustrate our approach through a simulation study. The methodology proposed in this paper has been implemented in R functions which are available as supplementary material.