Copulas related to piecewise monotone functions of the interval and associated processes

Guilherme Pumi and Sílvia R. C. Lopes

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 2, 828-860

Abstract: In this work, we derive the copulas related to vectors obtained from the so-called chaotic stochastic processes. These are defined by the iteration of certain piecewise monotone functions of the interval [0, 1] to some initial random variable. We study some of its properties and present some examples. Since often these types of copulas do not have closed formulas, we provide a general approximation method which converges uniformly to the true copula. Our results cover a wide class of processes, including the so-called Manneville–Pomeau processes. The general theory is applied to the parametric estimation in certain chaotic processes. A Monte Carlo simulation study is also presented.

Date: 2017
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DOI: 10.1080/03610926.2015.1006781

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