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

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  • Guilherme Pumi
  • Sílvia R. C. Lopes

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.

Suggested Citation

  • Guilherme Pumi & Sílvia R. C. Lopes, 2017. "Copulas related to piecewise monotone functions of the interval and associated processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 828-860, January.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:2:p:828-860
    DOI: 10.1080/03610926.2015.1006781
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