# Copula-based piecewise regression

## TL;DR

This paper introduces a copula-based piecewise regression method that decomposes complex dependence structures into simpler, ordered copulas, enabling modeling of non-monotone regression functions.

## Contribution

It proposes a novel gluing copula approach to decompose copulas into totally ordered parts, allowing for non-monotone regression functions where traditional copulas fall short.

## Key findings

- Enables modeling of non-monotone regression functions
- Decomposes complex dependence structures into simpler components
- Extends the applicability of copula-based regression methods

## Abstract

Most common parametric families of copulas are totally ordered, and in many cases they are also positively or negatively regression dependent and therefore they lead to monotone regression functions, which makes them not suitable for dependence relationships that imply or suggest a non-monotone regression function. A gluing copula approach is proposed to decompose the underlying copula into totally ordered copulas that combined may lead to a non-monotone regression function.