Copulas Related to Manneville-Pomeau Processes

TL;DR

This paper derives and analyzes copulas related to Manneville-Pomeau processes, addressing computational challenges and proposing an approximation method with practical applications for parameter estimation.

Contribution

It introduces new copulas for Manneville-Pomeau processes, provides properties, addresses computational issues, and develops a fast parameter estimation procedure.

Findings

The approximation to the copulas converges uniformly to the true copula.

A fast procedure for estimating the process parameter is proposed.

Numerical experiments validate the approximation methods.

Abstract

In this work we derive the copulas related to Manneville-Pomeau processes. We examine both bidimensional and multidimensional cases and derive some properties for the related copulas. Computational issues, approximations and random variate generation problems are addressed and simple numerical experiments to test the approximations developed are also performed. In particular, we propose an approximation to the copulas derived which we show to converge uniformly to the true copula. To illustrate the usefulness of the theory, we derive a fast procedure to estimate the underlying parameter in Manneville-Pomeau processes.